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# A Mixed Models Approach to the Age-Period-Cohort Analysis of Repeated Cross-Section Surveys, with an Application to Data on Trends in Verbal Test Scores

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## Abstract

We develop a mixed (fixed and random effects) models approach to the age-period-cohort (APC) analysis of micro data sets in the form of a series of the repeated cross-section sample surveys that are increasingly available to sociologists. This approach recognizes the multilevel structure of the individual-level responses. As a substantive illustration, we apply our proposed methodology to data on verbal test scores from 15 cross-sections of the General Social Survey, 1974–2000. These data have been the subject of recent debates in the sociological literature. We show how our approach can be used to shed new light on these debates by identifying and estimating age, period, and cohort components of change.

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... Even when researchers focus on the identification of APC effects, for example in longitudinal studies outside the field of HRM (Alwin, 1991;Glenn, 1994;Wilson & Gove, 1999;Yang & Land, 2006), they present us with ways forward that would allow categorical (cohort-specific) impacts to emerge from studies but also leave researchers free to uncover changes that manifest in other ways. These studies are described by Frenk et al. (2013) to illustrate development of Hierarchical Age-Period-Cohort (HAPC) models in the investigation of changes in verbal ability 864 -PARRY AND URWIN among American adults over time. ...
... Each study is essentially an analysis of the trend in verbal ability, with the key challenge being the separate identification of what is driving these trends-cohort, age or period effects. For example, Yang and Land (2006) find that when considering trends in verbal ability over time-cohort effects dominate, there are only modest period effects and highlight that, 'The cohort effects were bimodal, with an increase in verbal knowledge from the early 1900s to the 1940s and then declining until increasing again in the 1980s'. This last finding exemplifies the nuance of our provocation, in that there seems to be a step change in the verbal ability of cohorts, with those born in the 1950s, 1960s and 1970s experiencing declining verbal knowledge compared to the cohorts before or after-these findings hint at a dynamic that may be generational in nature but does not adopt a prior assumption that such dynamics only manifest as 'categorical' change. ...
... To clarify further, one can see how the findings from approaches using, for instance, HAPC models might potentially give rise to more deductive strands of research-returning to Yang and Land (2006), we can see the potential for other studies to test specific hypotheses relating to any distinct generational differences that emerged during the 1950s, 1960s and 1970s that might be related to verbal ability. We argue that this approach represents a pragmatic solution to the problems of generational research, allowing a process of iterative formulation and testing of emerging theories, in order to uncover the dynamics of generational change and difference. ...
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This provocation challenges the use of generational categories as a valid and useful basis for the development of human resource management (HRM) research and practice. We present two provocations. First, that a focus solely on year of birth as a driver of attitudes, values and behaviours is wholly inadequate. Second, we go beyond existing empirical challenges to argue that any approach to the study of generations that focuses solely on generational categories should be abandoned. We consider the theoretical basis for generations, together with specific examples from empirical studies to show how the current reliance on largely unsubstantiated categories leaves even longitudinal studies unable to make an effective contribution to this field. We draw on cross‐disciplinary insights to consider the implications for academic research and for HRM practice, showing how the current approach limits the usefulness of findings and suggesting a potential way forward.
... For instance, quadratic age effect (Fannon & Nielsen, 2019). The HAPC model of Yang and Land (2006) is an A model, where i is restricted to be quadratic, but the period and cohort effects have zero mean random effects. ...
... The matrix X will have full column rank as long as I,J,K ≥ 2. We will require that the combined design matrix (Z,X) also has full column rank. Yang and Land (2006) and Yang (2008) have proposed related models for repeated cross sections. Their models are essentially of the same structure as here, but with two differences. ...
... The p-value for testing A against Ad is negligible at 0.000. Since the A model is rejected we rule out the HAPC model of Yang and Land (2006), which has a quadratic age effect and zero mean PC random effects. The double differences can be interpreted as accelerations or differences-in-differences. ...
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We develop an age‐period‐cohort model for repeated cross‐section data with individual covariates, which identifies the non‐linear effects of age, period and cohort. This is done for both continuous and binary dependent variables. The age, period and cohort effects in the model are represented by a parametrization with freely varying parameters that separates the identified non‐linear effects and the unidentifiable linear effects. We develop a test of the parametrization against a more general ‘time‐saturated’ model. The method is applied to analyse the obesity epidemic in England using survey data. The main non‐linear effects we find in English obesity data are age‐related among women and cohort‐related among men.
... Finally, I weigh in on the more general methodological debate about APC analysis. In recent years, this debate has primarily focused on whether socalled hierarchical APC estimation with cross-classified random effects modeling (HAPC-CCREM) (Yang and Land 2006, 2008 "solves" the identification problem (Reither et al. 2015a(Reither et al. , 2015bYang and Land 2006) or not (Bell and Jones 2014, 2018Luo and Hodges 2020;O'Brien 2017). The analyses of this paper lend support to O'Brien's (2017) argument that HAPC-CCREM models intrinsically shrink linear effects in one of the two variables that are specified as random due to the fitting function of mixed effects models. ...
... Finally, I weigh in on the more general methodological debate about APC analysis. In recent years, this debate has primarily focused on whether socalled hierarchical APC estimation with cross-classified random effects modeling (HAPC-CCREM) (Yang and Land 2006, 2008 "solves" the identification problem (Reither et al. 2015a(Reither et al. , 2015bYang and Land 2006) or not (Bell and Jones 2014, 2018Luo and Hodges 2020;O'Brien 2017). The analyses of this paper lend support to O'Brien's (2017) argument that HAPC-CCREM models intrinsically shrink linear effects in one of the two variables that are specified as random due to the fitting function of mixed effects models. ...
... 3 This breaks the linear dependency in the statistical model (since keeping two variables constant no longer keeps the third constant) and implies the assumption that the cohorts grouped together have exactly the same effect on the dependent variable. As pointed out by Yang and Land (2006, 2008, this kind of model can either be specified with age as a fixed effect and period and cohort as cross-classified random effects (HAPC-CCREM) or with fixed effects for all three variables (HAPC-CCFEM). Generally, HAPC-CCREM performs better than HAPC-CCFEM with regard to model fit Land 2008, 2013) and is the more widely used specification as illustrated by the fact that it is used by all the aforementioned studies. ...
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Prior analyses of age, period, and cohort effects in American attitudes to homosexuality have resulted in conflicting findings. I show that this is due to insufficient attention to the statistical identification problem facing such analyses. By means of more than four decades worth of survey data and two attitudinal measures taping social tolerance of homosexuality, I demonstrate that the conflicting results of prior research can be explained by differences in the implicit and unsubstantiated assumptions made to ensure model identification. To make up for the lack of attention to these assumptions in prior work, I discuss which age, period, and cohort effects we might expect to see based on prior knowledge about the case at hand, socialization theory, and research on how aging affects outgroup attitudes. On that basis, I also discuss which conclusions about age, period, and cohort effects we can actually draw in the case at hand. On a more general level, this article joins a growing literature that cautions against age-period-cohort analysis that does not give sufficient attention to theoretical expectations and side information when making the identifying assumptions on which the analysis must unavoidably rest.
... I retrace the level of repression and mobilization experienced by certain cohorts of citizens during their formative years and test the effect of exposure to these contexts on protest participation. I do this while accounting for the simultaneous clustering of observations in cohorts and periods using logistic randomeffects models (Neundorf et al., 2020;Yang & Land, 2006. The analysis combines micro and macro data from different sources to control for potential confounders at the country, country-wave, and individual level. ...
... The statistical approach used in this chapter is inspired from Neundorf et al. (2020) who adapted Yang and Land's (2006; hierarchical age-period-cohort modeling technique to fit crossnational data. Based on this approach, observations are assumed to be simultaneously nested in country-cohorts and country-periods (i.e. ...
Thesis
Viele Studien zeigen, dass die Beteiligung an politischen Protesten in mittel- und osteuropäischen Ländern geringer ausfällt als in Westeuropa. Das Ausmaß und die Ursachen dieser Ost-West-Partizipationslücke werden jedoch immer noch debattiert. Diese Dissertation untersucht die Ursachen dieses europäischen Protestgefälles. Inspiriert von den Theorien politischer Sozialisation wird untersucht, inwiefern ein frühes Erleben von (1) Repression und (2) Mobilisierung während der Transition zur Demokratie das Protestverhalten verschiedener Generationen in Mittel- und Osteuropa geprägt hat. Hierfür werden mehrebenen Alters-Perioden-Kohorten-Modelle mit wiederholten länderübergreifenden Umfragedaten genutzt. Studie 1 zeigt, dass ein frühes Erleben von Repression einen nachhaltigen Effekt auf die Teilnahme an Demonstrationen hat, nicht aber auf Petitionen und Boykotte. Darüber hinaus beeinflusst die Art der erlebten Repression die Richtung des Effekts: Personen, deren Bürgerrechte während ihrer Jugend eingeschränkt wurden, scheinen in ihrem späteren Leben häufiger an Demonstrationen teilzunehmen. Das Gegenteil ist der Fall für Personen, die Verletzungen persönlicher Integrität erlebt haben. Studie 2 zeigt, dass das Erleben der Mobilisierung während der Transition zur Demokratie diese Ost-West-Protestlücke nicht moderiert. Studie 3, eine Analyse des Protestverhaltens von Ostdeutschen, bestätigt, dass die Erfahrung der bottom-up Transition die mit gewaltsamer Repression verbundene Demobilisierung nicht kompensiert. Durch diese neu gewonnen Erkenntnisse zum Verhältnis von Regimewechsel und Zivilgesellschaft, verbindet und bereichert diese Dissertation die Forschungsfelder zu politischem Verhalten, sozialen Bewegungen und Demokratisierung.
... Age-period-cohort (APC) analysis is a valuable approach to decompose the time-related aspects of alcohol consumption. It allows separation of the effects of life course variations (age), secular historical events (period) and generational changes (cohort), and assessment of their independent contribution to aggregated trend data [25,26]. ...
... With age = period-cohort, the time-related variables are perfectly collinear [30]. To solve the 'identification problem', at least one of the three variables needs to be reparametrised or transformed so that the relationship with the others is nonlinear [26]. Thus, for the APC analysis, the monthly survey data were collapsed into periods of 6 months (January to June and July to December), resulting in two observations per year. ...
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Introduction: In recent years, beverage composition of total alcohol consumption has changed substantially in Sweden. As beverage choice is strongly associated with drinking practices, our paper aims to analyse trends in beverage composition of alcohol consumption by age, period and cohort. Methods: Age-period-cohort (APC) analysis was conducted using monthly data from the Swedish Alcohol Monitoring Survey (2003-2018). The sample consisted of n = 260 633 respondents aged 16-80 years. APC analysis was conducted on drinkers only (n = 193 954; 96 211 males, 97 743 females). Beverage composition was defined as the beverage-specific proportion of total intake in litre ethanol. Fractional multinomial logit regression was applied to estimate the independent effects of age, period and cohort on trends in beverage composition. Results: Regression models revealed statistically significant effects of age on all beverages except for medium-strength beer and spirits in males. Controlling for age and cohort, decreasing trends were found over time for medium-strength beer and spirits. The proportion of regular beer increased statistically significantly in males and the proportion of wine in females, whereas the trends for the opposite sex remained stable in each case. Predictions for cohorts showed statistically significant decreasing trends for medium-strength beer in males, lower proportions for regular beer and higher proportions for spirits in the youngest cohorts. Discussion and conclusions: The increasing proportion of wine drinking, which is associated with less risky drinking practices, may decrease alcohol-related morbidity and mortality. Increasing proportions of spirits in the youngest cohorts raises concerns of a possible revival in spirits consumption among the youngest.
... See similar timing convention in Berg et al. (2018) for instance. 16 The approach used for the construction of the panel departs from the Age-Period-Cohort analysis in that it aggregates the macro-level variable of interest from the proper and targeted cohorts (age groups) (see Yang &Land, 2006 andHamilton, 2013 for instance). The selection rules for age intervals, however, still need to be addressed with caution. ...
... See similar timing convention in Berg et al. (2018) for instance. 16 The approach used for the construction of the panel departs from the Age-Period-Cohort analysis in that it aggregates the macro-level variable of interest from the proper and targeted cohorts (age groups) (see Yang &Land, 2006 andHamilton, 2013 for instance). The selection rules for age intervals, however, still need to be addressed with caution. ...
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The relationship between intergenerational mobility and inequality is widely explored but yet to reach conclusive results. The convention is to provide descriptive analysis with data of several developed countries, termed as the Great Gatsby Curve (GGC). This paper constructs a panel data containing a wide range of modern societies to replicate and extend the GGC with alternative measures. Through investigations, this study confirms that inequality skews the intergenerational upward mobility. Ceteris paribus, every one percent increase in inequality measured by top 10% income share will decrease the upward mobility by about 5 percent on average. On the other hand, every one percent increase in the bottom 50% income share contributes to 12 percent increase in the upward mobility. In comparison, it implies that it is not only the degree but also the structure of the inequality, that matters for the intergenerational mobility. The increase in the income share held by the bottom earners prompts the overall upward mobility with much greater and more meaningful magnitude. Besides, economic development benefits to the overall upward mobility.
... While due to the identification problem induced by the exact linear dependency between APC (period = age + cohort), it is not possible to directly estimate the linear effect of any one of the APC variables holding the other two constant (Fosse and Winship 2019). Nowadays, numerous strategies to separate APC effects were developed, such as constrained generalized linear model (CGLM) (Fienberg and Mason 1979), APC model with intrinsic estimator algorithm (Yang et al. 2004), APC characteristic model (APCCM) (O'Brien 2015), hierarchical APC growth curve model (HAPC-GCM) (Lynch 2003) and hierarchical APC cross-classified random effects model (HAPC-CCREM) (Yang and Land 2006). The HAPC-CCREM was developed by Yang et al. in 2006, in which period and cohort effects are treated as level 2 variables to solve the identification problem (Yang and Land 2009). ...
... Nowadays, numerous strategies to separate APC effects were developed, such as constrained generalized linear model (CGLM) (Fienberg and Mason 1979), APC model with intrinsic estimator algorithm (Yang et al. 2004), APC characteristic model (APCCM) (O'Brien 2015), hierarchical APC growth curve model (HAPC-GCM) (Lynch 2003) and hierarchical APC cross-classified random effects model (HAPC-CCREM) (Yang and Land 2006). The HAPC-CCREM was developed by Yang et al. in 2006, in which period and cohort effects are treated as level 2 variables to solve the identification problem (Yang and Land 2009). The HAPC-CCREM had been a useful tool to identify age, period, and cohort trends in health (Jiang and Wang 2018;Lin et al. 2014) and happiness (Yang 2008). ...
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... In empirical studies, the accurate linear dependence among age, period and cohort (cohort = period-age) is an inevitable problem, and several statistical methods have been developed to solve this problem. Based on a multilevel design, researchers believe the ageperiod-cohort (APC) problem can be well addressed in repeated cross-sectional data analysis (O'Brien et al., 2008;Yang & Land, 2006. They propose the hierarchical ageperiod-cohort-cross-classified random effects model (HAPC-CCREM) that treats the age effect as a fixed effect at the individual level and the period and cohort effects as two parallel random effects at the macro level (Yang & Land, 2006). ...
... Based on a multilevel design, researchers believe the ageperiod-cohort (APC) problem can be well addressed in repeated cross-sectional data analysis (O'Brien et al., 2008;Yang & Land, 2006. They propose the hierarchical ageperiod-cohort-cross-classified random effects model (HAPC-CCREM) that treats the age effect as a fixed effect at the individual level and the period and cohort effects as two parallel random effects at the macro level (Yang & Land, 2006). That is to say, HAPC-CCREM separates age, period, and cohort into two different levels to solve the APC conundrum. ...
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People’s social participation is deeply rooted in social change and development. Based on the World Values Survey data from 1990 to 2018, this study analyzed the temporal trend of social participation across successive cohorts in China using the hierarchical age-period-cohort-cross-classified random effects model. The results show that social participation continued to fall among Chinese born before 1972 and then successively rose in the following cohorts. However, this cohort effect was mainly attributed to the participation in Olsonian associations, and it could be partly explained by people’s education attainment. The cohort effects of participation in three Olsonian associations, including trade unions, political associations and professional organizations, were similar to that of general social participation. The significant increase in social participation in cohorts born after the 1970s is mainly attributed to China’s socioeconomic and educational development, and a favorable environment for social development is a critical factor for civic social participation.
... The logic of this approach is that, by fitting a crossclassified random-effects model to repeated cross-sectional data, it is possible to estimate the effect of each cohort (averaged across periods and controlling for age) and the effect of each period (averaged across cohorts and controlling for age) (Schwadel & Ellison, 2017;Yang & Land, 2013). Initially developed by Yang and Land (2006), the HAPC models involve two steps. First, model specification tests are conducted that compare model fit statistics of partial models against the full fixed-effects APC model to determine whether age, period, and cohort effects are meaningful. ...
Thesis
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Recently, the concept of “generation” has received considerable commentary in academic and popular circles. Millennials—ages 24 to 39 on Election Day 2020—have gained particular attention due to the generation’s size (more than 75 million), spending power (about 1.3 trillion per year), and growing political influence. Accordingly, a host of studies from disciplines such as business, education, political science, and psychology have investigated the nature and possible distinctiveness of Millennials’ beliefs and behaviors. Only limited research, however, has been undertaken exploring the possible effects of generational membership on crime and criminal justice issues. This dissertation seeks to help close this void in the literature. This omission in the research is consequential considering the impact that Millennials’ public opinion might have on the future of the U.S. criminal justice system. Notably, American corrections is in the midst of a historic policy turning point from offender exclusion to offender inclusion. For four decades, the United States was enmeshed in a punitive era during which offenders were removed and/or ostracized from society through exclusionary policies (e.g., mass incarceration, punitive laws, expansion of debilitating collateral sanctions). Beginning around 2010, however, a paradigmatic shift occurred marked by a halt in the growth of prison populations and the spread of inclusionary policies (e.g., prisoner reentry programs, criminal record expungement). In this context, one way to prognosticate if the current changes are likely to continue into the future is to examine Millennials’ views on corrections. If this large generation is supportive of offender inclusion, then its members are likely to be political force favoring progressive policies and reforms as they proceed across their life course. Based on a 2017 opt-in internet panel survey conducted by YouGov (N = 1,000), this dissertation assesses the nature of Millennials’ correctional policy opinions and compares these to the views of other generations. The levels of support for 13 correctional policies are reported, and generational differences are estimated through multivariate analyses. Three correctional themes are explored: (1) public support for punitiveness (the death penalty, court harshness, and punishment as the goal of prisons); (2) offender rehabilitation, reentry, and reintegration (restoration of civil rights, fair-chance hiring, reducing collateral sanctions, expungement of criminal records, general attitudes toward expungement, having the FBI review criminal records); and (3) offender redemption (formal redemption rituals, redeemability). As a result, this study presents the most comprehensive assessment of what Millennials think about American corrections. The main findings of this dissertation are twofold. First, as a generation in and of themselves, Millennials are only modestly punitive but clearly supportive of progressive policies. Millennials favor a rehabilitative correctional orientation, believe in offender redeemability, and prefer policies that reduce exclusion and increase inclusion. Second, generational differences in public support for correctional policies are limited. Regardless of generation, the respondents tend to embrace inclusionary policies. Thus, in the future, Millennials will likely seek to transform the current correctional turning point into a lengthy era of progressive reform—a project that will be similarly endorsed by Americans of all generations. ... This analytical conceptualization indicates that the effects of cohorts can be calculated indirectly as a variation in time effects encountered by various age groups. We calculated the longitudinal panel data model with the mixed-effects framework of hierarchical age-period-cohort (HAPC) (Yang and Land 2008;Yang and Lee 2010;Yang and Land 2006;Mubarik et al. 2020). The explicit evaluation of variations in BC mortality and DALY among population level over age (age impact) as well as the over time (period effects) was conducted using a number of mixed-effect models (models 1, 2, and 3) with fixed and random population level effects and random slopes. ... Article Full-text available Background Statistical evidence on breast cancer (BC) burden related to health and lifestyle risk factors are valuable for health policy-making. This study aimed to compare the trends in BC mortality and disability adjusted life years (DALYs) attributable to various health and life style risk factors among different world’s regions according to sociodemographic index (SDI).Methods We extracted the age-standardized and age-specific rate of mortality and DALYs of women BC during 1990–2017 using the comparative risk assessment framework of the 2017 global burden of disease (GBD) study. We performed hierarchical age-period-cohort analysis to estimate age- and time-related trends, and effect of interactions between different risk factors on BC risk.ResultsDuring 1990–2017, the age-standardized rate of mortality and DALYs of women BC was increasing in less developed and under developing regions. The risk factor alcohol use [RR 51.3(95%CI 17.6–149.7)] and smoking [5.9(2.0–17.3)] were significantly highly contributor to increased mortality risk in high SDI region. Whereas in the low-SDI region, the greater mortality risk was observed in alcohol use [6.9(2.4–17)] and high FPG [2.7(1.5–3.1)]-related deaths. The adjusting for individual age, period, and risk factor effects, the significant interaction effect between metabolic risk factors and older ages were observed in all SDI regions and globally as well. However, an increasing cohort effect of alcohol, high fasting plasma glucose (FPG) and smoking-related death, and DALYs was observed during 1960 to 1985 cohorts among low-SDI regions.Conclusions The age-standardized rates of mortality and DALYs due to BC has been increasing in low-SDI region. Alcohol consumption, high body mass index (BMI), high FPG, and smoking are potential BC risk factors particularly in older ages that leading to adverse disease outcomes. Therefore, rapid aging and prevalence of these prospective risk factors may strengthen the increasing mortality and DALYs of BC in low-SDI region. Hence, preventive measure along with strict action against concerned BC risk factors should be taken to reduce the disease burden specifically among lower-SDI regions.Graphical abstract ... The identification problem in APC analysis has been discussed extensively in the social science literature, and scholars have proposed a number of solutions for the problem (Fosse and Winship 2019). Yang and Land (2006) developed the hierarchical age-period-cohort (HAPC) models and this model has been widely used in public opinion research. However, as suggested by empirical studies, the methods impose constraints that sets the linear cohort effect to zero or close to zero and assumes trendless fluctuation in cohort effects (Bell and Jones 2018;Luo and Hodges 2020). ... Article Full-text available The current study examines the gendered reaction to victimization threats from 1973 to 2016 using the General Social Survey and the hierarchical age-period-cohort-characteristics model. Results suggest the gender gap is narrowing across time with a gradual decline among women who report feeling afraid to walk alone at night. The period-level change in violent crime rates and the cohort differences in gender ideology have significant impact on the gender-specific reaction to the threats of victimization. The macro-level variables explain some variance in the gender gap across time. ... This study pools data collected by the European Social Survey between 2002 and 2017. I use cross-classified, random-effect models to disentangle age, period, and cohort (APC) effects on protest participation among East and West Germans (Yang and Land 2006). Random slopes at the cohort and period levels allow for an estimation of convergence between the two groups. ... Article Full-text available How is the protest behavior of citizens in new democracies influenced by their experience of the past? Certain theories of political socialization hold that cohorts reaching political maturity under dictatorship are subject to apathy. Yet, it remains unclear whether mobilization during the transition can counterbalance this effect. This article examines the protest behavior of citizens socialized in Eastern Germany, a region marked by two legacies: a legacy of autocracy and, following the 1989-90 revolution, a legacy of transitional mobilization. Using age-period-cohort models with data from the European Social Survey, the analysis assesses the evolution of gaps in protest across generations and time between East and West Germans. The results demonstrate that participation in demonstrations, petitions, and boycotts is lower for East Germans socialized under communism in comparison with West Germans from the same cohorts. This participation deficit remains stable over time and even increases for certain protest activities. ... 24 The goal was to understand the impact of state-level household firearm ownership on age−period−cohort effect estimates. Hence, hierarchical cross-classified random effect models, which allow for the inclusion of covariates, 25,26 were implemented. All models included individual-level variables for race and sex and were restricted to the 2001−2016 period and all states, excluding Alaska on the basis of covariate information availability. ... Article Introduction In the U.S., state-level household firearm ownership is strongly associated with firearm suicide mortality rates. Whether the recent increases in firearm suicide are explained by state-level household firearm ownership rates and trends remains unknown. Methods Mortality data from the U.S. National Vital Statistics System and an estimate of state-level household firearm ownership rate were used to conduct hierarchical age–period–cohort (random-effects) modeling of firearm suicide mortality between 2001 and 2016. Models were adjusted for individual-level race and sex and for state-level poverty rate, unemployment rate, median household income in U.S. dollars, population density, and elevation. Results Between 2001 and 2016, the crude national firearm suicide mortality rate increased from 6.8 to 8.0 per 100,000, and household firearm ownership rate remained relatively stable, at around 40%. Both variables were markedly heterogeneous and correlated at the state level. Age–period–cohort models revealed period effects (affecting people across ages) and cohort effects (affecting specific birth cohorts) underlying the recent increases in firearm suicide. Individuals born after 2000 had higher firearm suicide rates than most cohorts born before. A 2001–2006 decreasing period effect was followed, after 2009, by an increasing period effect that peaked in 2015. State-level household firearm ownership rates and trends did not explain cohort effects and only minimally explained period effects. Conclusions State-level firearm ownership rates largely explain the state-level differences in firearm suicide but only marginally explain recent increases in firearm suicide. Although firearms in the home increase firearm suicide risk, the recent national rise in firearm suicide might be the result of broader, more distal causes of suicide risk. ... For example, application of ridge regression led to the intrinsic estimator (IE), which assumes that α, π, and γ are collectively as close to zero as possible (Kupper et al. 1983;Yang et al. 2008). Use of mixed models led to hierarchical APC, which assumes the age effect is fixed with a quadratic trend, then estimates period and cohort slopes to minimize unexplained variance (Yang and Land 2006). The smoothing cohort model uses a spline smooth to estimate cohort effects and iteratively adjusts fixed age and period effects to fit (Fu 2008). ... Article Full-text available Objective Identify the effect of differences in criminal activity among birth cohorts on crime rates over time. Determine the extent to which cohort effects are responsible for nationwide crime reductions of the last thirty years. Methods Use a panel of state age-arrest data and frequently used economic, social, and criminal justice system covariates to estimate a proxy or characteristic function for current period effects. Combine these results with national age-arrest data to estimate nationwide age, current period, and birth cohort effects on crime rates for 1980–2016. Results Criminal activity steadily declined between the 1916 and 1945 birth cohorts. It increased among Baby Boomers and Generation X, then dropped rapidly among Millennials, born after 1985. The pattern was similar for all index crimes. Period effects were mostly responsible for the late 1980s crack boom and the 1990s crime drop, but age and cohort effects were primarily responsible for crime rate reductions after 2000. In general, birth cohort and current period effects are about equally important in determining crime rates. Conclusions Policies aimed at reducing delinquency among young children may be more effective in the long run than current policies aimed at incapacitation, deterrence, and opportunity reduction. ... In this article, we distinguish theoretically between past and present conditions and their respective relationships to attitudes. In the past, similarly motivated scholars have relied on age, period, cohort (APC) models, and their contemporary variant, hierarchical age, period, cohort models (HAPC) (Yang and Land, 2006;Wilkes and Corigall-Brown, 2011;Gorodzeisky and Semyonov, 2018). While the efficacy of these models is intensely debated (e.g. ... Article Full-text available Scholarship, including seminal research on prejudice, identifies adolescence as a critical period for the development of attitudes. Yet most sociological research on prejudice, especially in the form of anti-immigrant sentiment, focuses on the relationship between contemporaneous social conditions and attitudes towards out-groups while neglecting the demographic context during one’s impressionable years. Therefore, we design research to investigate the relationship among temporally distal and temporally proximal sub-national contexts and native-born attitudes towards immigration and immigrants. To do this, we merge geocoded data from the General Social Survey (1994–2016) with a unique US state-level dataset (1900–2015). Results from multilevel models reveal that immigrant presence during adolescence is a more consistent predictor of attitudes towards immigration and immigrants in adulthood. Thus, while the majority of sociological research on anti-immigrant sentiment asks if societal conditions matter, our results suggest that a more important question is when the context matters. ... 28 Estimating the experienced generation effect may require some caution. A person's political attitudes and behavior at any point reflect the person's age (life cycle effect), the timing of the survey (period effect), and generation (cohort effect), as assumed in the framework of an age-period-cohort (APC) model (Glenn 1976;Yang and Land 2006;Smets and Neundorf 2014;Huang 2019). Therefore, to identify the generational or cohort effect, that is, the effect of an event on a particular generation differing from the effect on other generations, it is necessary to disentangle it from the confounding age and period effects. ... Article This article examines how violence against citizens affects their political attitudes and behavior in the long run, and how those effects vary over time. We construct and analyze a novel dataset on the victims of Taiwan's February 28 Incident, in 1947, with survey data spanning 1990 to 2017. Our empirical analysis shows that cohorts having directly or indirectly experienced the Incident are less likely to support the Kuomintang Party (KMT), the former authoritarian ruling party responsible for the Incident. They tend to disagree with the key conventional policy stand of the KMT (unification with mainland China), are more likely to self-identify as Taiwanese, and are less likely to vote for KMT presidential candidates. Taiwan's residents who were born in towns with larger number of casualties during the Incident are more likely to reject unification. Finally, the effects are found to vary over the period following democratization. ... All the analyses were conducted separately according to 6 sex-race-ethnicity groups: non-Hispanic White (White) men, White women, non-Hispanic Black (Black) men, Black women, Hispanic men, and Hispanic women. For each group, we estimated generalized linear mixed-effects models to obtain the estimates of birth cohort after controlling for age, period, and basic sociodemographic characteristics (26). Specifically, these models estimated the fixed effects of age, education, marriage, and random effects of cohort and period (Web Appendix 2 provides a detailed explanation of model specification). ... Article Morbidity and mortality have been increasing among middle-aged and young-old Americans since the turn of the century. We investigate whether these unfavorable trends extend to younger cohorts and their underlying physiological, psychological, and behavioral mechanisms. Applying generalized linear mixed effects models to 62,833 adults from the National Health and Nutrition Examination Surveys (1988-2016) and 625,221 adults from the National Health Interview Surveys (1997-2018), we find that for all gender and racial groups, physiological dysregulation has increased continuously from Baby Boomers through late-Gen X and Gen Y. The magnitude of the increase is higher for White men than other groups, while Black men have a steepest increase in low urinary albumin (a marker of chronic inflammation). In addition, Whites undergo distinctive increases in anxiety, depression, and heavy drinking, and have a higher level than Blacks and Hispanics of smoking and drug use in recent cohorts. Smoking is not responsible for the increasing physiological dysregulation across cohorts. The obesity epidemic contributes to the increase in metabolic syndrome, but not in low urinary albumin. The worsening physiological and mental health profiles among younger generations imply a challenging morbidity and mortality prospect for the United States, one that may be particularly inauspicious for Whites. ... Mobility was lagged by the number of days until maximum positive correlation as identified by cross-correlation analysis; this lag was unique for each state. We included random intercepts for each state (u 0j ) to account for resampling, and random slopes based on the number of days since a state entered the study (u 1k ) to account for different within-state relationships between mobility and case numbers and the temporal non-independence of these variables (Goldberg et al., 2016;Yang & Land, 2006). An autoregressive model was not implemented due to the overdispersed nature of the outcome variable necessitating the use of a negative binomial model, which accounts for variance in the data by use of an overdispersion parameter rather than Gaussian distributed residuals. ... Article Full-text available Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a viral pathogen that quickly became a global pandemic in the winter of 2020-2021. In response, governments issued social distancing orders to minimize transmission by reducing community contacts. We tested the efficacy of this social distancing at the state level during the first 2 months of the pandemic in the United States. We utilized data on daily SARS-CoV-2 case numbers and human community mobility (anonymized, aggregated cell phone location data stratified into six categories used as an index of social distancing), the date of government-issued social distancing orders, demographics, urbanization and public transportation. We implemented cross-correlation to identify lag times between declines in mobility and SARS-CoV-2 cases. Incorporating state-specific lag times, we tested for associations between case counts and mobility metrics using Bayesian multilevel models. Decreased mobility around grocery stores/pharmacies, retail/recreation locations, transit stations and workplaces was correlated with decreases in SARS-CoV-2 cases with significant lag times of ≥21 days. Social distancing orders were associated with fewer cumulative SARS-CoV-2 cases when they were put in place earlier. Community mobility had already started declining prior to most social distancing orders, especially the more restrictive orders implemented later in the pandemic. Social distancing is an important tool that has been implemented throughout the pandemic to decrease SARS-CoV-2 transmission, although with significant social and economic impacts. Our results suggest that declines in cases were observed several weeks subsequent to implementation of social distancing measures, and that implementing social distancing earlier could potentially minimize the duration of time these policies need to be in effect. Our findings can inform ongoing management of this pandemic and other emerging infectious disease outbreaks by identifying areas where reductions in mobility are associated with reduced disease transmission, and the expected time frame between behavioural changes and measurable population outcomes. ... Third, we test the possibility that part of the temporal trend is attributable to generational replacement and change in the composition of different cohorts. To do so, we re-estimated 'opposition to immigration' between 1996 and 2018 in nine and seven time-points for GSS and ANES, respectively, using the following two regression models: a bi-level hierarchal model and a hierarchical age-period-cohort (HAPC) model (Yang & Land, 2006). In the bi-level hierarchal model, individuals (first-level observations) are nested in nine and seven time-points (second-level units) in GSS and ANES, respectively. ... Article The ‘competitive threat’ theoretical model leads to the expectation that flows of documented and undocumented immigrants, economic downturns, and spread of conservative-nationalist ideologies would increase opposition to immigration. Recent studies on attitudes toward immigrants in American society do not show any increase in anti-immigrant sentiment. In the present study, we use data from the General Social Surveys (GSS) and American National Election Survey (ANES) to study change in opposition to immigration between 1996 and 2018. The findings obtained from the two data sources are strikingly similar and lead to the following conclusions. First, opposition to immigration had steadily and monotonously declined throughout the period. Second, the decline is evident even after considering variations and changes in the composition of the population, shifts in political ideologies, regional variations and cohort replacement. Third, the trend of decline in opposition to immigration takes a linear form. Fourth, opposition to immigration is stronger among Republicans and Independent voters than among Democrats. Fifth, the overtime decline in opposition to immigration was evident mostly among supporters of the Democratic Party increasing the division along party lines. The findings suggest that immigration is becoming a major political issue that is steadily polarizing American society. ... By borrowing ideas form the age-period-cohort (APC) approach proposed by Yang and Land (2006), we employed a multilevel modelling approach to analyse cohort differences in migrants' settlement intentions and their determinants. In the conventional statistical APC analysis, both the period and cohort are taken as the level-2 unit. ... Article Full-text available Research on Chinese internal migrants has gradually shifted from a focus on the rapid expansion of this population to its relationship with the restructuring of spatial distribution in cities. The settlement intentions of migrants are key to how China's urbanisation and urban system will evolve. Yet, although there is a considerable body of research on this subject, the determinants of migrants' settlement intentions remain debatable. In this paper, in light of the dramatic economic and social transition undergone by China in the past 70 years, we demonstrate the importance of considering the cohort perspective in relation to Chinese migrants' settlement intentions. Specifically, we examine the effects of differences between migrants' origins and their destinations on settlement intentions in relation to year of birth. Our results show that destination‐to‐origin differences in terms of population size, administrative level, economic condition and public services are positively associated with migrants' settlement intentions, whereas geographic distance and cultural distance between origin and destination are negatively related to the intention to settle in destination cities. Further, these effects vary significantly across birth cohorts. Our findings demonstrate the importance of going beyond the standard dichotomy between old generation and new generation that is often used in the analysis of migration trends. To achieve more inclusive urbanisation in the future, targeted policies that take into account inter‐city and inter‐cohort variations are critical to addressing obstacles to the settlement of migrants in destination cities. ... (For discussion of these issues, see seminal work by Fienberg andMason 1985 andHobcraft et al. 1985.) However, methodological advancements in recent years have provided some workarounds that, although they cannot solve the age-period-cohort identification problem, do provide new ways to conceptualize and to estimate cohort effects net of one's age and period (Harding 2009;Luo and Hodges 2020a;Reither et al. 2015;Yang and Land 2006). The italicization of estimate is to emphasize that there is no one consensus method that can unequivocally quantify the additive, independent effects of ages (net of period and cohort membership), periods (net of age and cohort membership), and cohorts (net of age and period). ... ... The second analysis tests the possibility that period effects are present, so that all age groups are affected equally by one or more events which influence their lives. Finally, generational effects are represented by the period in which the individual was born, which may reflect different formative childhood experiences that are retained for the rest of the person's life (Yang and Land 2006). ... Article Over the last decade, the debate about Australia’s relationship with Indigenous people has entered a new phase with the prospect of a referendum to amend the Constitution. In this paper we use a wide range of survey data going back to the 1970s to examine public opinion towards Indigenous issues and likely voting in any future referendum to recognise Indigenous Australians. Our results show a long-term liberalisation in public opinion which can be traced mainly to period effects within the electorate. This liberalisation in opinion is the major explanation for the large majority who would currently support a change in the Constitution to recognise Indigenous peoples. Our results have significant policy implications for how governments approach the inherent difficulties surrounding Indigenous recognition. ... In other words, if we found an age effect, we needed to be sure it was not a cohort or period effect in disguise. However, when modelling age, period, and cohort variables in the same model, there is always an identification problem (Yang & Land, 2006), as there is an exact linear relationship between the variables: "age = period-cohort" (Bell & Jones, 2014). To deal with this problem, we adopted a Hierarchical age-period-cohort (HAPC) modelling strategy proposed by Land (2006, 2008). ... Article Full-text available Previous studies on political trust found ageing leads to support for authority, while education encourages a critical view of governments. We speculated the two effects would moderate each other and complicate the story. By applying Hierarchical age-period-cohort (HAPC) modelling to the Asian Barometer Survey (2001–2016) data, we found significant interaction effects of age and education in shaping political trust. During the transition from youth to middle age, ageing reinforces people’s original disposition formed in the early years. From middle to old age, ageing mainly plays a conservatizing role. Ageing also conditions the educational gap in political trust: people with little education’s political trust increases as they age; well-educated individuals’ political trust decline until middle age and conservatize later. In sum, ageing has a variant effect during the life course; we found evidence of ageing’s radicalizing and conservatizing effects on political trust in the context of Asia. ... One of the advantages of using archival data is the ability to use more sophisticated methodological approaches to answer important research questions, especially when using a lifespan approach to study age and work. For example, having repeated cross-sectional archival data allows researchers to use hierarchical Age-Period-Cohort (APC) models ( Yang & Land, 2006 ) when investigating age-and work-related research questions. Repeated cross-sectional surveys ask the same or similar questions of di erent samples of respondents over multiple timeframes (e.g., annually or biennially). ... ... In sum, the best techniques rely on methods that are based on minimal assumptions and estimable functions (Robertson et al. 1999). One such approach is the cross-classified random-effects model, which addresses the APC identification problem presented in repeated cross-sectional survey data via a hierarchical modeling strategy where one dimension of time is treated as fixed and the other two are included in the random effects portion of the model (Yang and Land 2006). ... Chapter Full-text available ... A repeated cross-sectional survey design was adopted (Yang & Land, 2006). The data were conceptualized as a two-level hierarchically nested data structure with individual measurements nested within each of the 15 samples. ... Article Full-text available Changes in socioeconomic conditions can affect how people understand themselves. The present analyses tested hypotheses on individuals’ self-construal and insecure attachment variation and co-variation during a period of severe and prolonged economic downturn in Greece, a typically more collectivist culture. Adult attachment and self-construal were surveyed in 15 independent samples of young adults collected consecutively between 2004 and 2016. Significantly lower independence, but not higher interdependence, was observed in recent crisis-stricken years of higher unemployment compared to earlier (pre-crisis) years. Participants also reported higher insecure attachment, particularly higher anxious attachment in recent years. However, it were temporal changes in avoidance that were associated with a greater decline in independent self-construal during the time period studied. Avoidance also preceded temporal variability in independent self-construal during this period. The results highlight links between socioeconomic conditions and individual-level variation in cultural understandings of the self and insecure attachment, and point to socio-cognitive processes that may explain interrelationships between two constructs that partly lie at different levels of understanding the self. ... Cohort effects can also be conceptualized as a unique rate of an outcome for individuals depending on birth year. 7 Before reviewing the current literature on cohort effects in alcohol use, it is important to understand that cohort effects are powerfully predictive of many health outcomes, and critical to consider when evaluating trends. There are numerous historical examples of particular birth cohorts with increased rates of disease outcomes and mortality in the United States, including all-cause mortality, 8,9 tuberculosis, 10 peptic ulcer, 11 lung cancer, 12 and other diseases. ... Article This article is part of a Festschrift commemorating the 50th anniversary of the National Institute on Alcohol Abuse and Alcoholism (NIAAA). Established in 1970, first as part of the National Institute of Mental Health and later as an independent institute of the National Institutes of Health, NIAAA today is the world's largest funding agency for alcohol research. In addition to its own intramural research program, NIAAA supports the entire spectrum of innovative basic, translational, and clinical research to advance the diagnosis, prevention, and treatment of alcohol use disorder and alcohol-related problems. To celebrate the anniversary, NIAAA hosted a 2-day symposium, "Alcohol Across the Lifespan: 50 Years of Evidence-Based Diagnosis, Prevention, and Treatment Research," devoted to key topics within the field of alcohol research. This article is based on Dr. Keyes' presentation at the event. NIAAA Director George F. Koob, Ph.D., serves as editor of the Festschrift. ... Previous research on marijuana attitudes using the GSS has utilized the Age, Period, and Cohort (APC) model developed by Yang Yang and colleagues (Schwadel and Ellison, 2017;Yang and Land, 2006;Yang 2008). This model is used to differentiate the effects of age, period, and cohort by overcoming the linear dependency that exists between these disparate conceptualizations of time (i.e., one can calculate age if you know the survey year and birth year of a respondent). ... Article Full-text available This research aims to enhance our understanding of the relationship between racial prejudice and White Americans’ views on cannabis legalization. The recent legalization of recreational cannabis in a handful of states, along with many other states legalizing medical cannabis in recent years, has catapulted the flowering plant back into the spotlight and nightly news cycles. Given the historically racist propaganda used to criminalize the plant, it follows that Whites’ support for legalization may be associated with racial prejudice. Using data from the General Social Survey data from 1972–2018, we find that different forms of racial prejudice have a negative effect on Whites’ support for cannabis legalization generally. Additionally, as the negative effect of overt, old-fashioned racism diminishes over time and across birth cohorts it is supplanted by the more subtle laissez-faire racism. In conclusion, we discuss the implication of the relationship between racial prejudice and views on marijuana for the increasingly complicated racial dynamics surrounding cannabis legalization. Article China has undergone extensive changes since its transition from the socialist era to the reform era in 1978. It is said there was a revival of traditional gender ideologies in the reform era. Nonetheless, individuals’ socioeconomic status improved greatly, and according to cohort replacement theory and interest- and exposure-based theories, this should imply progress in gender attitudes. Drawing on nationwide repeated cross-sectional data from the 2010–2015 Chinese General Social Survey ( N = 44,900), this study explores changes in gender attitudes in relation to cohort in China. Sex-stratified hierarchical age–period–cohort cross-classified random-effects models are used to (a) explore cohort differences in attitude for four gender norm dimensions (ability and work dimensions in the public sphere and division of labor and marriage dimensions in the private sphere), and across three cohort groups, that is, the “war baby” (born 1926–1948), the “pre-reform baby” (born 1949–1977), and the “reform baby” (born 1978–1995) groups, and (b) examine how cohort differences in relation to each attitude have been modified by socioeconomic status and demographic characteristics, and how men’s and women’s gender attitudes are influenced in different ways by these factors. The results reveal the uneven pace of development toward egalitarian gender ideologies in China, with respondents being more supportive of egalitarianism in the public sphere than in the private sphere. Although the movement toward greater gender egalitarianism in the public sphere started from the pre-reform baby cohort, the movement in the private sphere began to emerge only in the reform baby cohort. Additionally, the sex gap in gender attitudes widened and peaked in the reform baby cohort. Women’s attitudes were influenced to a greater extent by socioeconomic and demographic factors than men’s. Article Estimable functions play an important role in learning about certain aspects of the impact of ages, periods, and cohorts in age‐period‐cohort multiple classification (APCMC) models. The advantage of these estimates is that they are unbiased estimates of, for example, the deviations of age, period, and cohort effects from their linear trends, or changes in the linear trends of cohort effects within cohorts, or the residuals of fixed effect APCMC models. If the fixed effect APCMC model contains the relevant variables (is well specified), these estimable functions are unbiased estimates of functions of the parameters that generated the dependent variable data, even though the parameters that generated that data are not identified. I provide a simplified approach to establishing which functions are estimable in fixed effect APCMC models that provides an intuitive understanding of estimable functions by showing clearly and simply why they are estimable. This approach involves the partitioning of the age, period, and cohort effects into linear components and deviations from the linear components; the use of the “line of solutions”; and of the “extended null vector.” Chapter This chapter examines patterns of change and continuity in the territorial and national identities of members of parliament (MPs). In contrast to other countries, Spain’s history and type of quasi-federal state offer a unique heterogeneous setting to explore the degree of compatibility between Spanish regional identities over time. The findings show substantial continuity in the importance of dual identities among MPs—that is, that they feel both Spanish and regional identity. However, MPs’ pro-Spain identities are on the rise, while pro-regional identities are declining. This pattern is observed less strongly among citizens. Due to the breakdown of Spain’s two-party system, this chapter focuses on how parliaments’ new partisan and social composition affect MPs’ territorial and national identities. Findings show that the two mainstream parties, the Partido Popular (PP) and Partido Socialista Obrero Español (PSOE), exhibited the highest degrees of dual identities in 2010 and 2018. However, the PP and Ciudadanos have the strongest pro-Spain identities. By contrast, nationalist parties, followed by Unidas Podemos, fell closer to pro-regional identities. Regarding the social bases of territorial identities and nationalism, regression analyses reveal the importance of ideology and gender. In particular, leftist MPs identify more strongly with regions than right-wing MPs. Additionally, gender differences were found regarding territorial and national identities. Female MPs are more likely to embrace dual identities but are more supportive of Spanish nationalism than male MPs. This evidence suggests a source of potential intra-party conflict in dealing with territorial issues, such as state reforms. Article In most advanced democracies, the decline in electoral turnout has been disproportionately concentrated amongst young people. This study investigates whether young Australians are turning away from the principles and processes of democracy. If so, it further enquires which of the three highly collinear time effects – age, period and cohort (APC) – best explains youth disengagement. Existing works, which focus mostly on generational effects, fail to control for the confounding age and period effects. Using survey data from 2001 to 2019 in the Australian Election Study (AES) and applying multilevel models, this study disentangles the three-time effects. The findings suggest that young Australians are no different from older people and older cohorts in their commitment to principles and both traditional and contemporary (online) processes of democracy. Instead, period effects – that is, short-term political, economic and social context – best explain democratic attitudes and behaviours in Australia. Article Mental health outcomes have shown dramatic changes over the past half-century, yet these trends are still underexplored. I utilize an age-period-cohort analysis of the National Health Interview Survey from 1997 to 2017 (N = 627,058) to disentangle trends in mental health outcomes in the United States over time. Specifically, I leverage the contrast between reported psychological distress and rates of mental health treatment to isolate which has changed, how, and for whom. There is little evidence that psychological distress is worsening over time. Yet, treatment seeking has increased over the past 20 years. The increase in treatment seeking is best modeled as a period effect, providing initial evidence that the historical context has influenced responses to mental health over time for Americans of all ages and birth cohorts. I conclude with potential mechanisms and implications for future mental health research. Article Morbidity and mortality are on the rise among Baby Boomers and younger cohorts. This study investigates whether this unfavorable health trend across birth cohorts 1925–1999 is related to rising income inequality Americans face during childhood. We use two nationally representative datasets: National Health and Nutrition Examination Surveys (NHANES) 1988–2018 and Panel Studies of Income Dynamics (PSID) 1968–2013, and two health outcomes: biomarkers of physiological dysregulation, and a chronic disease index. Childhood income inequality is measured by the average of the Gini index at the national level each birth cohort is exposed to between birth and age 18, where the Gini index from 1925 to 2016 is computed based on Internal Revenue Service income data. By merging childhood income inequality to individual level data from NHANES or PSID based on birth cohort, we find childhood income inequality is positively associated with the risk of physiological dysregulation in adulthood for all gender and racial groups in the NHANES data. It is also significantly related to the risk of chronic disease in the PSID data. This association is robust to controls for individual level childhood health and family background, adulthood socioeconomic and marital status, and contemporary macro socioeconomic factors. More importantly, childhood income inequality exposure explains a substantial amount of variation in these two health outcomes across cohorts, a pattern not observed for other early life exposures that display negative temporal trends similar to those for childhood income inequality. This study provides important evidence that income inequality experienced during childhood may have a long-lasting negative consequence for adult health, which partially explains the adverse health trends experienced by Baby Boomers and younger cohorts in the United States. Article Studies show that both democratization and war mobilization boost levels of participation enduringly among members of the generational cohort that come of age around the time. But little is known about the relative effects of war mobilization and democratization on long-term participation rates among impressionable generations that experience both. We address this question by examining generational cohort effects by gender, drawing on newly available data on the case of Japan. Age-period-cohort analyses of the Survey on Japanese Value Orientations (1973–2013) show that the increase in lifelong participation rates of the “war generation” over prewar generations was much greater for men than for women, thus suggesting that the high rates of participation among members of this cohort are driven more by mobilization than by democratization. This finding yields significant implications for the analysis of democratic consolidation in different parts of the world. Article This article presents an alignment model of cultural formation, arguing that belief systems become increasingly constrained from earlier periods of life-course to adulthood. I show that the pairwise correlations between cultural beliefs increase and the structure of personal culture becomes relatively more aligned before entering adulthood. Moreover, the rate of personal change slows down with each year of age, suggesting that the alignment process is most prevalent in specific socialization periods. Using four waves of data from the National Study of Youth and Religion, I test these propositions through an analysis of religious belief networks. I find that the results are robust to sampling variability, population heterogeneity, and item selection. Article Full-text available 近年來，臺灣社會輿論關注所得差距擴大、特別是世代之間所得差異的原因與後果。本文採用臺灣社會變遷基本調查，以內部估計模型（Intrinsic estimator, IE）分離人口學關注的年齡、時期與世代三個時間因素（age, period, cohort, APC）對臺灣民眾所得差異的影響，發現除了年齡、時期、教育、階級、性別等因素之外，有顯著的世代差異。戰後到1972年以前出生的嬰兒潮世代，享有經濟成長時期所帶來的所得優勢，而1978年後出生的年輕世 代則普遍的所得較低。勞動市場供需結構是可能的影響機制，包括高教擴張提升技術勞動供給以及服務業低薪工作增加等，但多種外部因素的影響機制仍需後續研究深入探討。 Article Full-text available This study presents a comprehensive assessment of what Millennials think about U.S. correctional policy. Using a 2017 national-level sample (N = 1,000), Millennials’ correctional policy opinions across 13 outcomes are assessed and compared to the views of other generations. The main findings are twofold. First, Millennials are only modestly punitive but clearly supportive of progressive policies. Thus, Millennials favor a rehabilitative correctional orientation, believe in offender redeemability, and prefer policies to protect ex-felons’ civil rights and to expunge criminal records for minor offenses. Second, generational differences in public support for correctional policies are mostly limited. Americans of all generations tend to endorse inclusionary policies—a finding indicating that the future of American corrections might see a lengthy era of progressive reform. Article Background Grip strength is a popular and valuable measure in studies of physical functional capabilities in old-age. The influence of historical trends and differential period-specific exposures can complicate the interpretation of biomarkers of aging and health and requires careful analysis and interpretation of ageing, birth cohort, and period effects. The current study evaluates the effects of aging, period, and cohort on grip strength in a population of adults and older adults. Methods We use >27,000 observations for individuals ≥50 years of age, born in approximately 1910-1960, from the English Longitudinal Study of Aging to examine a variety of multilevel and cross-classified modeling approaches to evaluate age, period, and cohort effects. Our results extended Hierarchical Age Period Cohort modeling and compared our results with a set of nine sub-models with explicit assumptions to determine the most reliable modeling approach. Results Findings suggest grip strength is primarily related to age, with minimal evidence of either period and/or cohort effects. Each year’s increase in a person’s age was associated with a 0.40-kilogram decrease in grip strength, though this decline differs by gender. Conclusions We conclude that as a population ages, grip strength declines at a systematic and predictable rate equal to -0.40-kilograms per year (approximately -.50-kg for men and -.30-kg for women) in residents of England aged 50 and older. Age-effects were predominant and most consistent across methodologies. While there was some evidence for cohort effects, such effects were minimal and therefore indicative that grip strength is a consistent physiological biomarker of aging. Article We examined mainland Chinese immigrants’ economic integration by looking at the earnings gap between locals and immigrants (both permanent and newly arrived) during and after the period of the Hong Kong handover from 1991 to 2016. During this period, Hong Kong experienced a further process of deindustrialization and an increased connection with mainland China. Using 5% Hong Kong population census/by‐census data (1991‐2016), we found that although mainland Chinese immigrants with college or above education still earned less than their local counterparts throughout the years, the income gap rapidly narrowed and their income levels converged in the more recent period. Meanwhile, the gap for those with high school degrees or below only slightly narrowed over time. Moreover, for those with high school degrees or below, the income gap between the permanent immigrants and the newly arrived ones remained constant over time, while a converging trend was observed among those with college or above degrees. Our findings suggest that immigrant economic integration may be accelerated when the socioeconomic linkage is closer between the origins and destination of migration, although some groups may benefit more than others. Article Background: Adults should perform ≥150 minutes per week of moderate-intensity equivalent physical activity for substantial health benefits and >300 minutes per week for additional benefits. The authors analyzed 21 years of National Health Interview Survey data to better understand trends in aerobic physical activity participation among US adults. Methods: The authors estimated the annual prevalence (1998-2018) of self-reported leisure-time physical inactivity, insufficient activity, meeting only the minimal aerobic guideline, and meeting the high aerobic guideline overall and by selected characteristics. Prevalence differences between 1998 and 2018 were compared across subgroups and periods of significant change were identified using JoinPoint regression. Results: The prevalence of inactivity decreased from 40.5% (1998) to 25.6% (2018) while the prevalence of meeting the high aerobic guideline increased from 26.0% to 37.4%. Increases in meeting the high guideline were similar across age groups, racial/ethnic groups, levels of education, and Census regions. Increases in insufficient activity and meeting the minimal guideline were statistically significant but of relatively small magnitude. Conclusions: The prevalence of inactivity decreased and meeting the high aerobic guideline increased overall and for all subgroups from 1998 to 2018. Physical activity promotion strategies may aim to continue these trends while also narrowing persistent disparities in participation across subgroups. Article Methodological advances in demographic research, especially age-period-cohort (APC) analysis, primarily focus on developing new models yet often fail to consider practical concerns in empirical analysis. We propose a mixed approach that integrates multiple data imputation and structural change analysis in time series so that scholars can (i) construct pseudo age groups based on more coarsely grouped age data and (ii) identify temporal anomalies. This approach is illustrated using multiple waves of Canadian Population Census data (1981–2016). We construct pseudo age groups based on more coarse age information available in the Census data and identify a local anomaly in the temporal trajectory of homeownership in Canada's less populous provinces and territories. These findings are assessed and validated in comparison with results from more populous Canadian provinces. This research broadens the methodological repertoire for demographers, geographers, and social scientists in general and extends the literature on homeownership in an understudied area. Article Full-text available There has been a growing concern among researchers and media commentators that men in the United States may be increasingly less sexually active, creating a form of a “sex recession.” Using 14 years of survey data from men in the National Survey of Family Growth (2006–2019), this study assesses whether such concerns are warranted. Cross-classified mixed-effects models are estimated to ascertain whether there is evidence of a population-wide sex recession among men due to secular conditions specific to different time periods, or if birth cohorts that comprise the male population at any given point in time are exhibiting distinct patterns of sexual behavior. The analysis finds no evidence of a population-wide sex recession among men. Rates of sexual inactivity among men have been constant across the time series, but those born between 2000 and 2004 had significantly higher rates of sexual inactivity than previous birth cohorts did at the same age. Additionally, men who are unemployed and/or living at home with their parents are more likely to refrain from sexual intercourse than their peers who are employed and/or living independently of their parents. Article The linear dependence of age, period, and birth cohort is a challenge for the analysis of social change. With either repeated cross-sectional data or conventional panel data, raw change cannot be decomposed into over-time differences that are attributable to the effects of common experiences of alternative birth cohorts, features of the periods under observation, and the cumulation of lifecourse aging. This article proposes a rolling panel model for cohort, period, and aging effects, suggested by and tuned to the treble panel data collected for the General Social Survey from 2006 through 2014. While the model does not offer a general solution for the identification of the classical age-period-cohort accounting model, it yields warranted interpretations under plausible assumptions that are reasonable for many outcomes of interest. In particular, if aging effects can be assumed to be invariant over the course of an observation interval, and if separate panel samples of the full age distribution overlap within the same observation interval, then period and aging effects can be parameterized and interpreted separately, adjusted for cohort differences that pulse through the same observation interval. The estimated cohort effects during the observation interval are then interpretable as effects during the observation interval of entangled period and cumulated aging differences from before the observation interval. Thesis In this thesis we propose models for estimating and projecting mortality rates using adaptive splines. Mortality modelling has various applications from social planning to insurance. However, raw mortality data often exhibits irregular patterns due to randomness. The data at the oldest ages are also very scarce and unreliable as there are only very little survivors at these ages, adding difficulty to estimation. Graduation refers to the act of smoothing crude mortality rates, during which extrapolation to older ages where data is non-existent is usually also performed. We first propose a flexible and robust model for mortality graduation of static life tables using adaptive splines. Male and female mortality rates are graduated jointly, as opposed to previous English Life Tables (ELTs) where they were smoothed independently. Therefore our model borrows information across sexes, which is especially helpful at the oldest ages. Often when male and female mortality rates are estimated independently, implausible age patterns may occur, such as intersecting male and female mortality schedules. This has been addressed using rather ad hoc procedures in previous ELTs, for example, by calculating the weighted average of the estimated mortality rates starting at the age where they intersect or by discarding data at the oldest ages. By utilising the locality of B-spline basis, constraints can be imposed effectively such that female mortality rates are always lower than or equal to male mortality rates at all ages, even at extrapolation ages, hence does not involve subjective adjustments. We then extend the model to forecast mortality rates. Building upon models by Dodd et al. (2020) and Hilton et al. (2019), we jointly model and project male and female mortality rates of England Wales and Scotland. The joint sex model produces more reasonable long term male and female mortality projections that are non intersecting. Information is borrowed at the highest ages where exposures are small. By doing so the extrapolation to higher ages beyond data range gives more plausible estimates, especially for the mortality improvement rates for females at the oldest ages where a worsening mortality is otherwise projected. We also jointly model mortality rates of the same sex across the two countries, as they are expected to have similar mortality structures for the same sex. England Wales populations have a wider age range with available data, therefore the joint country model provides a way for the smaller Scottish populations to borrow information and learn from the bigger English Welsh populations. The joint country model is able to produce non-divergent long term projections between the countries for both males and females. Finally, a joint model for all of the four populations is proposed. The model combines features of the joint sex and joint country models, and borrows strength across sexes and countries.<br/ Book Full-text available The edited volume Age and Work: Advances in Theory, Methods, and Practice presents a systematic collection of key advances in theory, methods, and practice regarding age(ing) and work. This cutting-edge collection breaks new ground by developing novel and useful theory, explaining underutilized but important methodological approaches, and suggesting original practical applications of emerging research topics. The book begins with a prologue by the World Health Organization’s unit head for aging and health, an introduction on the topic by the editors, and an overview of past, current, and future workforce age trends. Subsequently, the frst main section outlines theoretical advances regarding alternative age constructs (e.g., subjective age), intersectionality of age with gender and social class, paradoxical age-related actions, generational identity, and integration of lifespan theories. The second section presents methodological advances regarding behavioral assessment, age at the team and organizational levels, longitudinal and diary methods, experiments and interventions, qualitative methods, and the use of archival data. The third section covers practical advances regarding age and job crafting, knowledge exchange, the work/nonwork interface, healthy aging, and absenteeism and presenteeism, and organizational meta-strategies for younger and older workers. The book concludes with an epilogue by an eminent scholar in age and work. Written in a scientifc yet accessible manner, the book ofers a valuable resource for undergraduate and graduate students, academics in the felds of psychology and business, as well as practitioners working in the areas of human resource management and organizational development. Article Full-text available Objective We examined the formal and informal advance care planning (ACP) patterns of older couples and determined how these patterns are associated with individual and spousal characteristics. Methods Using data from the 2014 and 2016 Health and Retirement Study, we performed latent class analysis to identify ACP patterns and multinomial regression models to describe characteristics of older couples ( N = 2195 couples). Results We identified four ACP patterns: high engaging couple (47%); high engaging husband—low engaging wife (11%); high engaging wife—low engaging husband (11%); and low engaging couple (31%). High engaging couples were more likely to be older, educated, and financially better off, whereas high ACP engagement in discordant ACP patterns was associated with health and wives’ constraints. Discussion A couple-based approach was recommended to promote the merits of ACP where spouses were older, had limited resources, or where one or both partners were suffering from poor health. Article This article examines the trends and patterns of returns to college education in Hong Kong in the context of educational expansion. Using the data from nine waves of population censuses/by-censuses from 1976 to 2016, we employ age–period–cohort models to investigate the trends in college wage premium in Hong Kong. The descriptive statistics show that, for those aged 22–26, college wage premium declined over time. In addition, there are substantial variations in college wage premiums among different birth cohorts, which cannot be explained by age and period main effects. More specifically, college wage premiums declined almost monotonically for those born after 1950, and two younger birth cohorts (1975–1979 and 1980–1984) experienced cumulative disadvantage in terms of the college premium over the life course. We discuss social and political ramifications of these findings. Article We examine changes in the level of physical health using longitudinal data on people aged 50+ from nine European countries covering the years from 2004 to 2017. For this purpose we develop a novel approach to identify age, period and cohort effects, which, in contrast to methods relying on mechanical restrictions, uses a step-wise estimation combining information on physical health with data on cognitive abilities. The approach relies on two important assumptions. First, we estimate relative differences between cohorts in cognitive abilities assuming that only age and cohort effects are responsible for their evolution. We then use the estimated proportional cohort differences to restrict the differences between cohorts in health development. The method is applied to the dynamics of four measures of poor health: weak grip strength, limitations in mobility, in activities of daily living (ADL) and in instrumental activities of daily living (IADL). Our results suggest insignificant or adverse period effects for the evolution of physical health. For example, the difference in likelihood of poor health as measured through weak grip strength between 2004 and 2017 is 2.1 percentage points, p.p., (95% CI -4.3, 8.4), and the corresponding numbers for the other three measures are respectively: 2.0 p.p. (CI -1.6, 5.6); 2.2 p.p. (CI -0.2, 4.7) and 3.0 p.p. (CI 0.3, 5.8). These estimates, which reflect the implications of time over the period of 14 years, are relatively low, but they highlight the surprising fact that any improvements in health in the examined period have been driven essentially by cohort effects. Our evidence is consistent with some earlier studies and sheds new light on recent (pre-pandemic) trends in life expectancy. It also raises questions concerning efficacy of healthcare and equal access to high quality care – the factors one would consider as important determinants of period effects in health. Article The advent of the Internet has brought great changes in media use, yet little is known about how media use has changed in China and what leads to the overall media-use changes. Using three waves of the China General Social Survey from 2005 to 2015, this study examines age, period, and cohort effects on transitions in Internet, television, and newspaper use. It also tracks the substitution dynamics between the Internet and existing media. The results evidence that (1) cohorts maintain their formative media-use habits in later life. (2) They also adjust media use by the interplay of evolving media structure and life-course phases. (3) The media-use adjustment is also a dynamic process balancing between the emerging and existing media use, based on their compatibility. In summary, the life courses of different cohorts are embedded in the evolving media structure, resulting in the distinguished media-use patterns of digital natives, intermediates, and immigrants. The overall media-use changes could happen through cohort succession or the profound impact of media structure transitions in a certain period. Article Full-text available Les AA. examinent de facon critique l'article de Norval D. Glenn : «Further Discussion of the Evidence for an Intercohort Decline in Education-Adjusted Vocabulary» et l'article de Duane F. Alwin et Ryan J. McCammon : «Aging versus Cohort Interpretations of Intercohort Differences in GSS Vocabulary Scores», publies tous deux en 1999. Les AA. rappellent que l'enquete par cohortes menees, aux Etats-Unis, entre 1974 et 1990 dans le cadre de la General Social Survey a mis en evidence une reduction des connaissances en terme de vocabulaire entre les cohortes nees avant 1920 et les cohortes nees apres 1920. Pour Glenn cette reduction n'est pas due a une baisse de la qualite de l'education mais a une diminution de la pratique de la lecture. Ils reconnaissent avec Alwin et McCammon que l'education affecte la connaissance verbale. Ils affirment que l'evolution du systeme educatif explique ce declin. Ils estiment que la methode de modelisation adoptee par Alwin et McCammon n'est pas adaptee. Ils examinent l'impact des changements linguistiques et plus particulierement de l'obsolescence du vocabulaire. Ils considerent qu'il convient de separer effet de l'âge, periode de l'enquete et cohorte de naissance dans l'analyse des donnees Article Full-text available Has there been a long-term intercohort decline in verbal ability beginning in the early part of this century? Recent analyses by Alwin and Glenn using data from the General Social Survey (GSS) strongly support such a trend. This decline, however, is not consistent with a substantial literature on adult cognitive development. We argue that Alwin's and Glenn's analyses confuse cohort effects with aging effects, apparently because of (1) a reliance on outdated assumptions, or 'side information,' regarding the relationship between age and verbal ability; (2) the treatment of the relationship between age and verbal ability as linear rather than curvilinear; and (3) the high degree of collinearity between age and cohort in the GSS data. The observed trend in the GSS data appears to be explained best by a positive relationship between age and verbal ability rather than by a decline in ability across cohorts. Because the GSS data involve a set of national probability samples conducted over a 22-year period, our analyses complement and strengthen the credibility of the literature on adult cognitive development. Article Full-text available We consider the asymptotic behavior ofregression estimators that minimize the residual sum of squares plus a penalty proportional to\sum|\beta_j|^{\gamma}$. for some$\gamma > 0$. These estimators include the Lasso as a special case when$\gamma = 1\$. Under appropriate conditions, we show that the limiting distributions can have positive probability mass at 0 when the true value of the parameter is 0.We also consider asymptotics for “nearly singular” designs.
Article
Full-text available
Narrowly defined, demography deals with the measurement of vital events (birth, death, and marriage) and migration, studies the factors that influence the rate at which those events occur, and, to a lesser extent, investigates the consequences of the patterns of these events. In this paper, we adopt this narrow definition of the field and consider only the first three events so that by limiting the scope of our review, we can examine these selected topics in detail.
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The literature on the determinants of earnings suggest an earnings function for individual i which depends on age ai, year t, “vintage” or “cohort” schooling level si, and experience ei. Adopting a linear function to facilitate exposition we may write $${Y_i}(t,{a_i},{c_i},{e_i},{s_i}) = {\alpha _0} + {\alpha _1}{a_i} + {\alpha _2}t + {\alpha _3}{e_i} + {\alpha _4}{s_i} + {\alpha _5}{c_i}$$ (1) where ei is experience, usually defined for males as age minus schooling, (ei = ai – si),1 and Yi may be any monotone transformation of earnings.
Chapter
Our purpose is both substantive and methodological. Substantively, we crystallize the results of prior research and expectations into an extended rationale for the application of the age-period-cohort accounting framework to the problem of understanding historical variability in the rate of tuberculosis mortality. This framework is then used to analyze a ninety year data series of tuberculosis mortality rates for the State of Massachusetts and a similar forty year series for the United States. The age-period-cohort accounting framework yields age effects with an expected pattern not well understood, period effects consistent with the advent of successful chemotherapeutic regimes after World War II, and steadily declining cohort effects whose interpretation has yet to be verified. In an attempt to pin down a possible interpretation, we show that cohort nativity composition affects the trend of cohort mortality in the Massachusetts series, and both level and trend in the United States series.
Article
In their article, Wilson and Gove do not sufficiently consider the implications of the fact that education-adjusted GSS vocabulary scores in the total U.S. adult population declined to an important extent during the period covered by the GSS data. It is improbable that this decline resulted only from period influences: The declines in scores for different age levels over time are inconsistent with the usual tendency for period influences to affect the psychological characteristics of younger persons more than those of older persons. Furthermore, the GSS data show no increases in vocabulary scores within cohorts during middle age, as should have occurred if the intercohort differences shown by the data reflected only age effects. That an intercohort decline in time spent reading has contributed to an intercohort decline in education-adjusted vocabulary scores remains a reasonable hypothesis.
Article
We investigate the plausibility of aging versus cohort interpretations of cohort-linked differences in vocabulary knowledge using data from 13 GSS surveys over a 22-year period, 1974 to 1996. We argue that one way to assess the effects of aging in these surveys is to examine the diachronic data within cohorts and to assume minimal period effects. Holding cohort constant in this fashion reveals detectable effects of aging that are not likely to be due to period influences between 1974 and 1996. Aging, however, explains only a tiny portion of the variation in the data, and aging effects are of insufficient magnitude to account for the larger intercohort patterns in the GSS vocabulary test data. Even when taking into account the effects of aging, the results of a cohort analysis support the argument that unique cohort experiences make important contributions to variation in GSS vocabulary test scores, especially among cohorts educated in the post-World War II era.
Article
This study found that an intercohort decline in vocabulary at all or most educational levels in the United States in recent years was closely related to an intercohort decline in newspaper reading. The decline in newspaper reading, in turn, may have resulted largely from an increase in television watching, but other influences, such as those from women's increased participation in the labor force, seem to have been involved as well. Other types of reading apparently declined in tandem with newspaper reading, and thus differences in reading are the most promising explanation for differences in the verbal ability of the various cohorts.
Article
Do birth-cohort differences in family configuration brought about by post-World War II increases in fertility explain declines in verbal test scores of young people in the 1960s and 1970s? Data from nine representative samples of the U.S. population in the General Social Survey data file confirm systematic declines in verbal scores for cohorts born in the post-World War II era, but reveal a trend beginning much earlier, at least with cohorts born prior to 1920, and one sustained through cohorts born in the 1960s. Despite the significance of these intercohort patterns, within-cohort factors are much more important in producing variation in verbal scores. Social and economic characteristics of the respondent's family of origin and amount of schooling are associated with the largest differences in vocabulary knowledge. Sibship size has a significant influence on the development of verbal skills, but is relatively less important than other family background factors. Birth order, however, is not independently linked to verbal scores. Finally, owing in part to the relatively weak role of family configuration in producing variation in verbal scores, there is no support for the hypothesis that cohort differences in family experiences account for the trends in verbal ability across cohorts in the U.S. population.
Article
Hierarchical linear models have found widespread application when the data have a nested structure-for example, when students are nested within classrooms (a two-level nested structure) or students are nested within classrooms and classrooms are nested within schools (a three-level nested structure). Often, however, the data will have a more complex nested structure. In Example 1, students are nested within both neighborhoods and schools; however, a school can draw students from multiple neighborhoods, and a neighborhood can send students to multiple schools. In Example 2, children are nested within classrooms during the first year of the study; however, each child finds himself or herself with a new teacher and a new set of classmates during each subsequent year of the study. By combining Lindley and Smith's (1972) concepts of exchangeability between and within regressions, this article formulates a crossed random effects model that applies to such data, provides maximum likelihood estimates via the EM algorithm, and illustrates application to study (a) neighborhood and school effects on educational attainment in Scotland and (b) classroom effects on mathematics learning during the primary years in the United States.
Article
This special issue of SMR is about the analysis of data collected at different levels of observation such cu: groups and individuals within these groups, and about the methodological problems that are present when natural experimentation and observations nested within existing social groups are the object of study. The methodological problems are summarized in the term multilevel problems. A multilevel problem is a problem that inquires into the relationships between a set of variables that are measured at a number of different levels of a hierarchy. This article discusses some traditional approaches to the analysis of multilevel data and their statistical shortcomings. The random coefficient linear model is presented, which resolves many of these problems, and the currently available software is discussed. Next, some more general developments in multilevel modeling are discussed. The authors end with an overview of this special issue.
Article
Cohort analyses in which the joint effects of aging, historical change and birth cohort membership are estimated for some dependent variable are often desirable on substantive grounds. Unless two of these three variables are viewed as indexing identical unmeasured causal factors, any analysis which makes estimates for only two of the three variables is subject to spurious results. But three-way cohort analysis is problematic because age, time period and birth cohort are linearly dependent on each other. Although this confounding makes estimation of some three-way cohort models impossible, this paper demonstrates that estimation is feasible in a number of such models. By exploring estimates derived for some of these models from hypothetical data for which the underlying effects are known, this paper also shows that meaningful three-way cohort analysis is difficult unless the researcher entertains relatively strong hypotheses about the nature of aging, period and cohort effects.
Article
This article compares the estimates produced by a number of solutions to the identifiability problem in age-period-cohort models using a series of disease rates with known structure. The results suggest that only those methods that are based on the estimable functions such as curvatures can be recommended for use in all circumstances. The other common approaches that give parameter estimates that are easier to interpret all have induced bias in the estimates. In particular methods based on the minimization of a penalty function to achieve identifiability are only of use if there is no change in the rates with time. Any drift in the rates tends to be expressed as a cohort-based trend. The methods based on individual records introduce a bias if there is a strong age effect in the direction of a decreasing cohort trend and a compensating increase based on period effects. The nonparametric testing method has little power to detect trends in the rates in small tables but ascribes a strong drift in the rates to both period and cohort trends. With careful interpretation, all methods estimate nonlinear components correctly.
Article
This paper discusses the specific problems of age-period-cohort (A-P-C) analysis within the general framework of interaction assessment for two-way cross-classified data with one observation per cell. The A-P-C multiple classification model containing the effects of age groups (rows), periods of observation (columns), and birth cohorts (diagonals of the two-way table) is characterized as one of a special class of models involving interaction terms assumed to have very specific forms. The so-called A-P-C identification problem, which results from the use of a particular interaction structure for detecting cohort effects, is shown to manifest itself in the form of an exact linear dependency among the columns of the design matrix. The precise relationship holding among these columns is derived, as is an explicit formula for the bias in the parameter estimates resulting from an incorrect specification of an assumed restriction on the parameters required to solve the normal equations. Current methods for modeling A-P-C data are critically reviewed, an illustrative numerical example is presented, and one potentially promising analysis strategy is discussed. However, gien the large number of possible sources for error in A-P-C analyses, it is strongly recommended that the results of such analyses be interpreted with a great deal of caution.
Article
For the past 80 years or more, social scientists have attempted to analyze cross-time data, using as explanatory variables age and time (or phenomena that are time-specific). When such data are analyzed in aggregate forms, age and time are typically grouped and polytomized. More recently, some investigators have adopted an analytic focus in which cohort membership, as defined by the period and age at which an individual observation can first enter an age-by-period data array, is held to be more important than age or period for substantive understanding. This focus has led to age-cohort and period-cohort models, as distinguished form age-period models. This paper is concerned with models for situations in which all three of age, period, and cohort are potentially relevant for the study of a substantive phenomenon.
Article
Ridge estimator of a singular design is considered for linear and gener¬alized linear models. Ridge penalty helps determine a unique estimator in singmar uesign. me tuning parameter o± tue penalty is seiecteu via gener¬alized cross-validation (GCV) method. It is proven that the ridge estimator lies in a special sub-parameter space and converges to the intrinsic estimator, an estimable function in singular design, as the shrinkage penalty diminishes. The expansion of the ridge estimator and its variance are also obtained. Thismethod is demonstrated through an application to age-period-cohort (APC) analysis of the incidence rates of cervical cancer in Ontario women 1980-1994
Article
Age-period-cohort (APC) accounting models have long been objects of attention in statistical studies of human populations. It is well known that the identification problem created by the linear dependency of age, period, and cohort (Period = Age + Cohort or P = A + C) presents a major methodological challenge to APC analysis, a problem that has been widely addressed in demography, epidemiology, and statistics. This paper compares parameter estimates and model fit statistics produced by two solutions to the identification problem in age-period-cohort models—namely, the conventional demographic approach of constrained generalized linear models (Fienberg and Mason 1978, 1985; Mason and Smith 1985) and the intrinsic estimator method recently developed by Fu (2000; Knight and Fu 2000; Fu, Hall, and Rohan 2004). We report empirical analyses of applications of these two methods to population data on U.S. female mortality rates. Comparisons of parameter estimates suggest that both constrained generalized linear models and the intrinsic estimator method can yield similar estimates of age, period, and cohort effects, but estimates obtained by the intrinsic estimator are more direct and do not require prior information to select appropriate model identifying constraints. We also describe three statistical properties of the estimators: (1) finite-time-period bias, (2) relative statistical efficiency, and (3) consistency as the number of periods of observed data increases. These empirical analyses and theoretical results suggest that the intrinsic estimator may well provide a useful alternative to conventional methods for the APC analysis of demographic rates.
Chapter
Assessing the effects of growing older has always been a central task of scholars and researchers in the academic specialties that focus on age-related phenomena. Although effects have rarely been attributed to chronological aging or the mere passage of time after birth, such age-related changes as the accumulation of experience, role changes, and biological maturation and decline have been thought to bring about changes in attitudes, values, behavior, affective states, cognitive ability, and relations with other people. A fairly typical hypothesis about attitudinal change and aging, for instance, is that accommodation and adaptation to existing social arrangements tend to make aging persons more conservative in the sense of being resistant to change (Glenn, 1974). An example of a hypothesis concerning aging and behavior is that declines in energy and risk-taking propensities associated with biological aging tend to diminish participation in conventional crime (Hirschi & Gottfredson, 1983).
Article
Age Period Cohort Characteristic (APCC) models provide a powerful method for testing theories that involve age, period, and cohort effects, but much of that power remains unrecognized. Studies that use this method almost always focus on a single explanatory cohort characteristic and control for only age groups and periods. Even with this simple model, we note that the relationship between the dependent variable and the cohort characteristic is controlled not only for historical period and for age, but also for the period in which the cohort was born. The APCC models can accommodate controls for “contemporaneous” variables such as age/period-specific measures of percentage Black as well as for additional cohort characteristics. Autocorrelated errors, due to cohort residuals, can arise in APCC models, and we derive methods to detect and deal with this autocorrelation. OLS or WLS typically are employed to estimate the parameters in APCC models; we note that other estimation techniques, e.g., Poisson regression or logistic regression may at times be more appropriate. An empirical example illustrates these refinements and extensions using a substantively important data set.
Article
Incl. bibl., index.
Article
Longitudinal trends can be analysed in terms of the effect of age, birth cohort or year of diagnosis. All three temporal effects are thought to be useful by epidemiologists, but they are not identifiable when assessed simultaneously. Partitioning the effects in terms of linear and curvature components is one approach to understanding the problem and finding a reasonable summary of trends. Other solutions can be expressed in terms of these components, and they can also be used to understand both subgroup and temporal interactions. One approach that may offer a way of understanding the effect of risk factor trends on population based rates is to use models that incorporate an effect due to the risk factors. These methods are discussed using lung cancer incidence and mortality to illustrate the underlying concepts.
Article
Most investigations of trends in cancer rates are based on a cross-sectional approach, i.e., an examination of trends in rates by year of diagnosis or death. When there are longitudinal effects (i.e., trends in rates with successive birth cohorts), interpretation of cross-sectional trends can be misleading. Based on cross-sectional comparisons, U.S. breast cancer mortality rates have been reported to be decreasing over the last 20 years in younger women but to be increasing during the same period in older women. To examine the impact of longitudinal effects on the divergence of cross-sectional trends in breast cancer mortality with age, we examined breast cancer mortality rates from 1969 to 1988 by birth cohort for White women in the United States. By using a novel, nonparametric, permutational method to analyze 2-year, age-specific mortality rates for women aged 30-89 years, we identified trends in rates with successive birth cohorts. The divergence in trends with age is shown to be consistent with an increase in breast cancer risk with successive birth cohorts from 1900 to 1916 and with a decrease in breast cancer risk with successive birth cohorts beginning around 1926. Longitudinal effects have a significant impact on cross-sectional trends in breast cancer mortality. Continuation of the birth cohort trend in younger women, which could correspond to changes in reproductive patterns accompanying the "baby boom," would result in decreasing cross-sectional trends in women 60-69 years of age over the next decade and in women 70-79 years of age in the subsequent decade. Longitudinal effects must be taken into consideration when monitoring and evaluating the effects of early detection, treatment, and intervention programs using national rates.
Article
Our first paper reviewed methods for modelling variation in cancer incidence and mortality rates in terms of either period effects or cohort effects in the general multiplicative risk model. There we drew attention to the difficulty of attributing regular trends to either period or cohort influences. In this paper we turn to the more realistic problem in which neither period nor cohort effects alone lead to an adequate description of the data. We describe the age-period-cohort model and show how its ambiguities surrounding regular trends 'intensify'. We recommend methods for presenting the results of analyses based upon this model which minimize the serious risk of misleading implications and critically review previous suggestions. The discussion is illustrated by an analysis of breast cancer mortality in Japan with special reference to the phenomenon of 'Clemmesen's hook'.
Article
Descriptive and statistical age-period-cohort (APC) analysis methods have received considerable attention in the literature. The statistical modeling of APC data often involves the popular multiple classification model, a model containing the effects of age groups (rows), periods of observation (columns), and birth cohorts (diagonals of the age-by-period table). The identifiability problem inherent to this model is discussed, and its adverse effects on the results of APC modeling exercises are illustrated numerically. Potential problems attendant with the use of two-factor models are described, and other possible modeling approaches currently in use are discussed. Interpretational limitations due to certain innate characteristics of typical APC data sets are also detailed. Given all the documented potential sources for error, the current state-of-the-art regarding the statistical modeling of APC data should be considered to be at an early stage of development.
Article
Society persists despite the mortality of its individual members, through processes of demographic metabolism and particularly the annual infusion of birth cohorts. These may pose a threat to stability but they also provide the opportunity for societal transformation. Each birth cohort acquires coherence and continuity from the distinctive development of its constituents and from its own persistent macroanalytic features. Successive cohorts are differentiated by the changing content of formal education, by peer-group socialization, and by idiosyncratic historical experience. Young adults are prominent in war, revolution, immigration, urbanization and technological change. Since cohorts are used to achieve structural transformation and since they manifest its consequences in characteristic ways, it is proposed that research be designed to capitalize on the congruence of social change and cohort identification.
Article
We develop the application of age, period and cohort models to the representation of tables of age- and period-specific rates. A derivation is given by way of a familiar graphical technique. The identifiability problem is discussed, identification techniques are reviewed and a new approach is recommended that is based upon the success of the three two-variable submodels. Other constraints are introduced that enhance interpretation. Examples are given for two sites of cancer. This approach is contrasted with other methods designed to demonstrate trends. Finally, standard errors of the parameters and tests of goodness of fit are discussed.
Article
Sex differences in central tendency, variability, and numbers of high scores on mental tests have been extensively studied. Research has not always seemed to yield consistent results, partly because most studies have not used representative samples of national populations. An analysis of mental test scores from six studies that used national probability samples provided evidence that although average sex differences have been generally small and stable over time, the test scores of males consistently have larger variance. Except in tests of reading comprehension, perceptual speed, and associative memory, males typically outnumber females substantially among high-scoring individuals.
Article
Age-Period-cohort models are widely used by epidemiologists to analyse trends in disease incidence and mortality. The interpretation of such models is fraught with difficulty in view of the exact linear dependency between the three variables. It is the purpose of this paper to review, compare and contrast some of the more common approaches to this problem based on Poisson regression and a linear model for the log rates. Also the results of using the different approaches on a single series of data on breast cancer incidence among females in Scotland from 1960-1989 are presented for comparison. Recommendations as to the merits and drawbacks of the approaches are also given in the conclusions. Models which are based upon the estimable contrasts such as local curvatures and deviations from linearity are most suitable.
Article
This article compares the estimates produced by a number of solutions to the identifiability problem in age-period-cohort models using a series of disease rates with known structure. The results suggest that only those methods that are based on the estimable functions such as curvatures can be recommended for use in all circumstances. The other common approaches that give parameter estimates that are easier to interpret all have induced bias in the estimates. In particular methods based on the minimization of a penalty function to achieve identifiability are only of use if there is no change in the rates with time. Any drift in the rates tends to be expressed as a cohort-based trend. The methods based on individual records introduce a bias if there is a strong age effect in the direction of a decreasing cohort trend and a compensating increase based on period effects. The nonparametric testing method has little power to detect trends in the rates in small tables but ascribes a strong drift in the rates to both period and cohort trends. With careful interpretation, all methods estimate nonlinear components correctly.
Article
Age-period-cohort analyses of US breast-cancer mortality rates reveal an unexpected decrease in risk for women born after 1948. Hormones are thought to play an important role in the aetiology of breast cancer and female gynaecologic cancers, and thus the evaluation of birth-cohort trends for female gynaecologic cancers may shed light on the declining breast-cancer risk among 'baby-boomers'. Age-period-cohort analyses are applied to US mortality rates for breast cancer, ovarian cancer, endometrial cancer and cervical cancer from 1950 through 1995. Age-period-cohort analyses provide no clues regarding the declining birth-cohort risk for breast cancer in 'baby-boomers'. The birth-cohort curves for ovarian and endometrial cancers are roughly similar, and largely explained by known risk factors. The calendar-period curve for endometrial cancer reveals increased risk between 1960 and 1980, probably due to increased use of oestrogen replacement therapy. Changes in the birth-cohort curve for cervical cancer reflect, for the most part, changes in sexual activity. An unexpected significant increase in the calendar-period curve for ovarian cancer occurred around 1980. Most of the major changes in the calendar-period and birth-cohort curves for breast cancer and female gynaecologic cancers can be explained by documented changes in known risk factors and in medical practice. The decreasing breast-cancer birth-cohort risk among 'baby-boomers' and the increasing ovarian-cancer calendar-period curve after 1980 are recent changes that require further investigation.
Article
Age-related differences in cognitive abilities observed in cross-sectional samples of individuals varying in age may in part be spurious due to the effects of cohort differences in schooling and related factors. This study examined the effects of aging on cognitive function controlling for any and all differences in cohort-based social experiences of different age groups. We examined age-related patterns in a measure of verbal ability using 14 repeated cross-sectional surveys from the General Social Survey (GSS) over a 24-year period. The raw GSS data show the expected age-related growth and decline in vocabulary knowledge, but these age differences are reduced when adjusted for cohort differences. There is evidence of small age-related patterns in vocabulary knowledge within cohorts, but the curvilinear contributions of aging to variation in verbal scores account for less than one-third of 1% of the variance in vocabulary knowledge, once cohort is controlled. Cohort differences in schooling contribute substantially to this effect. Within-age-group variation in vocabulary knowledge is vastly more important than age differences per se, and the complexities of the relationship of verbal skills to historical differences in the experience of schooling present an interesting avenue for future research.
Article
"The analysis of age-specific vital rates is studied, and special attention is given to the problem of decomposing an array of rates into factors related to age, period, and cohort.... The paper focuses on the age and period dimensions and derives an initial description of the matrix's structure with regard to changes only in those two directions. This two-dimensional description is then augmented by a consideration of residual patterns that seem clearly linked to cohorts. The use of a model that is asymmetric in age, period, and cohort is justified by a detailed discussion of the problems of identification in models involving perfectly collinear independent variables. An important conclusion is that traditional modeling approaches that treat age, period, and cohort in a symmetric fashion are fundamentally flawed." Some of these concepts are illustrated using mortality data from France. This is a revised version of a paper originally presented at the 1989 Annual Meeting of the Population Association of America (see Population Index, Vol. 55, No. 3, Fall 1989, pp. 375-6).
Article
The author reexamines the hypothesis developed by Norman Ryder that the birth and death of individuals constitutes a massive process of personnel replacement that holds enormous potential for social change. "In this paper I describe and illustrate six possible ways to estimate cohort (personnel) replacement effects: three based on algebra (Kitagawa's two-component method, forward partitioning, and backward partitioning), and three based on regression (regression standardization, survey metric analysis, and linear decomposition). Assuming monotonic change, regression methods typically are better, because standard algebraic methods are ill suited for analyzing change with regard to birth cohorts that enter or exit during the period studied."
Cohort Analysis Redux Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling
• H L T Smith
• R Bosker
Smith, H. L. 2004. " Cohort Analysis Redux. " Pp. 111–19 in Sociological Methodol-ogy, vol. 34, edited by Ross M. Stolzenberg. Boston, MA: Blackwell Publishing. Snijders, T., and R. Bosker. 1999. Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling. Thousand Oaks, CA: Sage.
NAEP 1999—Trends in Aca-demic Progress: Three Decades of Student Performance
• J R Campbell
• C M Hombo
• J Mazzeo
Campbell, J. R., C. M. Hombo, and J. Mazzeo. 2000. NAEP 1999—Trends in Aca-demic Progress: Three Decades of Student Performance. Washington, DC: Na-tional Center for Education Statistics.
Age-Period-Cohort Analysis and the Study of Deaths from Pulmonary Tuberculosis
• W M Mason
• H L Smith
Mason, W. M. and H. L. Smith. 1985. " Age-Period-Cohort Analysis and the Study of Deaths from Pulmonary Tuberculosis. " Pp. 151–228 in Cohort Analysis in Social Research, edited by W. M. Mason and S. E. Fienberg. New York: Springer-Verlag.