ArticlePDF Available

Should age-period-cohort analysts accept innovation without scrutiny? A response to Reither, Masters, Yang, Powers, Zheng, and Land


Abstract and Figures

Post-print version available at This commentary clarifies our original commentary (Bell & Jones, 2014c) and illustrates some concerns we have regarding the response article in this issue (Reither et al., 2015). In particular, we argue that (a) linear effects do not have to be produced by exact linear mathematical functions to behave as if they were linear, (b) linear effects by this wider definition are extremely common in real life social processes, and (c) in the presence of these effects, the Hierarchical Age Period Cohort (HAPC) model will often not work. Although Reither et al. do not define what a ‘non-linear monotonic trend’ is (instead, only stating that it isn’t a linear effect) we show that the model often doesn’t work in the presence of such effects, by using data generated as a ‘non-linear monotonic trend’ by Reither et al. themselves. We then question their discussion of fixed and random effects before finishing with a discussion of how we argue that theory should be used, in the context of the obesity epidemic.
No caption available
Content may be subject to copyright.
Should age-period-cohort analysts accept
innovation without scrutiny? A response
to Reither, Masters, Yang, Powers, Zheng
and Land
Andrew Bell a b and Kelvyn Jones a b
aSchool of Geographical Sciences
University of Bristol
University Road
bCentre for Multilevel Modelling
University of Bristol
2 Priory Road
Corresponding Author:
Andrew Bell
School of Geographical Sciences
University of Bristol
University Road
Acknowledgements: Thanks to Ron Johnston for his helpful advice.
This commentary clarifies our original commentary (Bell & Jones, 2014c) and illustrates some concerns
we have regarding the response article in this issue (Reither et al., 2015). In particular, we argue that
(a) linear effects do not have to be produced by exact linear mathematical functions to behave as if
they were linear, (b) linear effects by this wider definition are extremely common in real life social
processes, and (c) in the presence of these effects, the Hierarchical Age Period Cohort (HAPC) model
will often not work. Although Reither et al. do not define what a ‘non-linear monotonic trend’ is
(instead, only stating that it isn’t a linear effect) we show that the model often doesn’t work in the
presence of such effects, by using data generated as a non-linear monotonic trend by Reither et al.
themselves. We then question their discussion of fixed and random effects before finishing with a
discussion of how we argue that theory should be used, in the context of the obesity epidemic.
Research Highlights
We clarify the nature of the identification problem in all APC analysis
The Hierarchical APC model will sometimes work, but sometimes is not enough
Simulations using plausible data structures show the model often does not work
Relying in theory is problematic, but this is often all researchers can do
Age-period-cohort models, obesity, collinearity, model identification, cohort effects, multilevel
We thank the Social Science & Medicine editors for allowing us to respond to the above article and
allowing the debate regarding age-period-cohort (APC) identification to be furthered. In their article,
Reither et al. (2015, henceforth RMYPZL) argue the following:
Only when period and cohort effects are exactly linear does the Hierarchical APC (HAPC)
model give fallacious results.
In the real world, period and cohort effects are never exactly linear.
Thus, in the real world, the HAPC model will work.
The HAPC model should only be used when goodness-of-fit statistics (such as AIC and BIC)
suggest a simpler model (including only one or two APC dimensions) would be insufficient.
We address each of these arguments in turn below, showing that each of them is flawed, and that our
original critique of the HAPC model (Bell & Jones, 2014c) remains justified.
What is a linear trend, and what is a non-linear monotonic trend?
RMYPZL argue that the HAPC model will only fail to produce accurate results in the presence of linear
effects, and we agree with this. But what is a linear effect? One answer, and that suggested by
RMYPZL, is that it is a process produced by an exact linear algebraic association: y=mx+c. However, in
the real world data are generated by social processes, not equations, meaning RMYPZL are right to
claim that such effects never occur exactly in real life. However, our definition of a linear trend is wider
than this: we argue that a linear trend exists when, if an algebraically linear expression is removed
from the data at hand, this would have the effect of flattening that trend. It would be difficult to argue
that social processes never produce data that fills these criteria. Furthermore, there need only be a
linear component to the data generating process to fulfil this definition. Other effects (stochastic,
quadratic, or whatever else) can also be present, so long as there is also a linear component, defined
as above. Whilst the HAPC model will sometimes work under these circumstances, as shown by the
simulations in RMYPZL, we argue that it will often not work. We also argue that a model that only
works some of the time is not a particularly useful model to social scientists, and at least needs to be
applied with care and awareness of its limitations.
As for what a ‘non-linear monotonic trend’ is, the answer is less clear. RMYPZL state what it is not, but
do not say what it is. This is convenient for their argument: it means that there is no possibility of
questioning the model with simulations because any simulated DGP which the HAPC model fails to
replicate can be dismissed as being unrealistically linear. All that we have to go on are the six trends
(period and cohort trends from each of equations 2-4 in RMYPZL) which we must therefore assume
are examples that are consistent with ‘real life’ situations.
Some counter-simulations
However, RMYPZL’s argument does not even stand up for these six trends. We generated data where
the period trend was the same as that in RMYPZL’s equation 2, the age trend was the same as that in
RMYPZL’s equation 4, and the cohort trend was based on the period trend in figure 4 (we took every
other period effect so the numbers matched the numbers necessary for 7-year cohort groupings).
Thus, the DGP used was as follows:
Logit[Pr(Y=1)] = -1.988 + (0.059*Age-gm) + (-0.001*(Age-gm)2) + (-.474*C1) + (-.423*C2) + (-.362*C3)
+ (-.314*C4) + (-.214*C5) + (-.135*C6) + (-.054*C7) + (.029*C8) + (.172*C9) + (.256*C10) + (.410*C11)
+ (0.529*C12) + (0.605*C13) + (-.02*P1) + (.03*P2) + (.04*P3) + (.04*P4) + (.02*P5) + (-.03*P6) + (-
.03*P7) + (-.05*P8) + (-.05*P9) + (-.05*P10) + (-.05*P11) + (-.05*P12) + (-.06*P13) + (-.05*P14) + (-
.05*P15) + (-.02*P16) + (0*P17) + (.02*P18) + (-.02*P19) + (-.02*P20) + (0*P21) + (-.02*P22) +
(.02*P23) + (.05*P24) + (.08*P25) + (.1*P26) + (.1*P27) + Uc + Up
Uc ~ N(0,.01), Up ~ N(0,.01)
We fitted these data to the HAPC model 100 times, specifying 5-year groupings in the model. If
RMYPZL are correct, unbiased results should be produced because the DGP contains, by their own
definition, no linear effects and only ‘non-linear monotonic trends’ for periods and cohorts.
The results are shown in figure 1. As can be seen, the model fails to pick up the cohort trend, finds a
period trend where there is none, and underestimates the strength of the age trend; in sum, the
HAPC gets it radically wrong in not identifying the true patterns.
[Figure 1 about here]
The use of fit statistics
RMYPZL argue that fit statistics should be used to check that all of the elements of APC are required.
Whilst some of the authors have stated this in the past with regard to the Intrinsic Estimator (e.g. Yang
& Land, 2013:126), in neither their articles nor their book (as far as we are aware) have they stated
that this is necessary before using the HAPC model. Indeed they have regularly claimed that the HAPC
approach “completely avoids the identification problem(Yang & Land, 2013:70) without any such ifs
or buts. Thus, many researchers will (and have) used the HAPC model without taking this step.
Consequently, we welcome this important clarification.
However, there is a problem with this. In each of the models presented in table 1 of RMYPZL, there
are age, period and cohort effects present in the DGPs, even if those effects are only random variation
(generated by the Uc and Up coefficients). As such, in all four of the simulated cases, the model fit
statistics find the incorrect answer. Moreover, in two cases, different model fit statistics give different
answers. This is unsurprising given our previous arguments about the APC identification problem (Bell
& Jones, 2013, 2014a): model fit statistics will never be able to solve the identification problem,
because they cannot tell the difference between DGPs with different linear (by our definition) APC
effects. Model fit statistics showing the full APC model is preferable only suggests that there is
significant non-linear variation present in each of the three dimensions it does not make it possible
to assign linear (by our definition) trends correctly.
Fixed and Random effects
A theme that runs through RMYPZL’s article is the question of whether one should use fixed (FE) or
random (RE) effects models. We want to emphasise that this is a separate issue to the identification
problem and RMYPZL conflate the two in their article, which distracts from the issue at hand. We
agree with the conceptual treatment of cohorts and periods as random effects. But an appropriate
conceptual treatment does not mean the model works in practice. RMYPZL claim that we “assume”
the classical APC accounting/linear regression model where “the effects of all three temporal
dimensions are fixed [effects]” (RMYPZL:6). This is not the case; indeed this claim does not really make
sense. Statistical models are not assumed; they are used to appropriately represent the social
processes that produced the data at hand. Our argument is simply that in many situations the model
used by RMYPZL fails to accurately represent these processes. Should we use FE or RE? Whilst in other
scenarios we have actually argued strongly for the latter (Bell & Jones, 2015b), if we are looking for an
automatic, general solution to the identification problem, the answer is that we should use neither.
The problem is that RMYPZL are completely wrong when they say that the identification problem “is
not data specific, but model specific” (RMYPZL:4) if linear trends (by our definition) exist in the
dataset, you will encounter problems regardless of what model you use, whether a RE HAPC, a FE
accounting model, or whatever else.
Solid Theory
Finally, we want to thank RMYPZL for their discussion of solid theory which, in general, we agree with.
In our article we did not give an opinion one way or another regarding which of period or cohort
effects are more likely to be responsible for the obesity epidemic. Our point was simply that this
question cannot be answered using the data and methods of Reither et al. (2009). We therefore
welcome RMYPZL’s theoretically informed review of previous studies of obesity. Indeed that is exactly
what we called for in our original commentary (Bell & Jones, 2014c).
In particular, RMYPZL cite two papers (Flegal et al., 2002; Lee et al., 2011) which find a non-linear trend
in periods: obesity/BMI appears relatively flat until about 1980 and then increases from there. It is
unlikely that such a nonlinearity could be the result of cohort effects. We do not dispute this logic
except to make two points. First, another study, albeit in a different cultural context, have used a
similar analysis of non-linearities, and found that cohorts fit best (Olsen et al., 2006). Second, the non-
linearities were not, and could not, be found by Reither et al’s study, because their data only went as
far back as 1976 and so no such non-linearities were present.
Our point about strong theory was not that it is a solution to the APC identification problem. We agree
that “compelling speculation can never replace evidence in any field of scientific inquiry (RMYPZL:22).
However this doesn’t mean that any evidence will do, and where the choice is between compelling
speculation and misleading evidence dressed up as science, we would always choose the former.
RMYPZL ask the question “Should APC studies return to the methodologies of the 1970s?” The answer
to this rather loaded question is clearly no. However that previous methods don’t work does not mean
that new innovations do, and this discussion should guide readers in making their own minds up about
whether the HAPC model is appropriate for their purposes. We have argued before that there are
some situations where the HAPC model could be used (e.g. when periods and cohorts have no
continuous trends) and it can easily be adapted to incorporate theory where appropriate (Bell, 2014;
Bell & Jones, 2014b, 2015a). However the model does not work as a general purpose APC model; no
model does. Our concerns mirror those of others regarding another the Intrinsic Estimator (Luo, 2013;
Pelzer et al., 2014) and we agree with Fienberg (2013:1983) that “the search for methodological
solutions to the APC identity is an endless and fruitless quest. It is surely time to move onto
substantively focused considerations of the meaning of the three components in settings of interest.”
Bell, A. (2014). Life course and cohort trajectories of mental health in the UK, 1991-2008: a multilevel
age-period-cohort analysis. Soc Sci Med, 120, 21-30.
Bell, A., & Jones, K. (2013). The impossibility of separating age, period and cohort effects. Soc Sci Med,
93, 163-165.
Bell, A., & Jones, K. (2014a). Another 'futile quest'? A simulation study of Yang and Land's Hierarchical
Age-Period-Cohort model. Demographic Research, 30, 333-360.
Bell, A., & Jones, K. (2014b). Current practice in the modelling of Age, Period and Cohort effects with
panel data: a commentary on Tawfik et al (2012), Clarke et al (2009), and McCulloch (2012).
Qual Quant, 48, 2089-2095.
Bell, A., & Jones, K. (2014c). Don't birth cohorts matter? A commentary and simulation exercise on
Reither, Hauser and Yang's (2009) age-period-cohort study of obesity. Soc Sci Med, 101, 176-
Bell, A., & Jones, K. (2015a). Bayesian Informative Priors with Yang and Land’s Hierarchical Age-Period-
Cohort model. Qual Quant, 49, 255-266.
Bell, A., & Jones, K. (2015b). Explaining Fixed Effects: Random effects modelling of time-series-cross-
sectional and panel data. Polit Sci Res Methods, 3, 133-153.
Fienberg, S.E. (2013). Cohort analysis' unholy quest: a discussion. Demography, 50, 1981-1984.
Flegal, K.M., Carroll, M.D., Ogden, C.L., & Johnson, C.L. (2002). Prevalence and trends in obesity among
US adults, 1999-2000. JAMA, 288, 1723-1727.
Lee, H., Lee, D., Guo, G., & Harris, K.M. (2011). Trends in Body Mass Index in Adolescence and Young
Adulthood in the United States: 1959-2002. J Adolescent Health, 49, 601-608.
Luo, L. (2013). Assessing Validity and Application Scope of the Intrinsic Estimator Approach to the Age-
Period-Cohort Problem. Demography, 50, 1945-1967.
Olsen, L.W., Baker, J.L., Holst, C., & Sorensen, T.I.A. (2006). Birth cohort effect on the obesity epidemic
in Denmark. Epidemiology, 17, 292-295.
Pelzer, B., te Grotenhuis, M., Eisinga, R., & Schmidt-Catran, A.W. (2014). The Non-uniqueness Property
of the Intrinsic Estimator in APC Models. Demography, online.
Reither, E.N., Hauser, R.M., & Yang, Y. (2009). Do birth cohorts matter? Age-period-cohort analyses of
the obesity epidemic in the United States. Soc Sci Med, 69, 1439-1448.
Reither, E.N., Masters, R.K., Yang, Y.C., Powers, D.A., et al. (2015). Should age-period-cohort studies
return to the methodologies of the 1970s? Soc Sci Med, online.
Yang, Y., & Land, K.C. (2013). Age-Period-Cohort Analysis: New models, methods, and empirical
applications. Boca Raton, FL: CRC Press.
Figure 1: The DGP (black) and results (grey) from fitting the HAPC model to 100 datasets generated as
in equation 1.
... Nonetheless, researchers building on our work should examine whether different findings emerge with non-presidential measures of political rhetoric. Fourth, there is an ongoing debate about how best to deal with the identification problem in age-period-cohort models (Bell and Jones, 2015;Fienberg, 2013;Luo, 2013;Yang and Land, 2013). Studies should thus explore whether similar findings emerge using alternative modeling approaches. ...
... HAPC modeling has a number of limitations (see reviews byLuo and Hodges, 2016;Bell and Jones, 2015;O'Brien, 2017).Therefore, we provide a series of supplemental analyses where we implement several alternative APC models to examine the age, period and cohort effects on crime salience. Some of these alternative analyses are presented in Appendix G1-G3, other supplementary analyses are available upon request. ...
Full-text available
The public salience of crime has wide-ranging political and social implications; it influences public trust in the government and citizens’ everyday routines and interactions, and may affect policy responsiveness to punitive attitudes. Identifying the sources of crime salience is thus important. Two competing theoretical models exist: the objectivist model and the social constructionist model. According to the first, crime salience is a function of the crime rate. According to the second, crime salience is a function of media coverage and political rhetoric, and trends in crime salience differ across population subgroups due to differences in their responsiveness to elite initiatives. Both theories emphasize period-level effects. However, variation in crime salience may also reflect age and cohort effects. Using data from 422,504 respondents interviewed between 1960 and 2014, we first examine the nature of crime salience using hierarchical age-period-cohort (HAPC) models and then analyze period-level predictors using first differences. We find that: (1) crime salience varies mostly at the period level, (2) crime salience trends are parallel (cointegrated) across demographic, socioeconomic, and partisan groups, and (3) the constructionist model best explains crime salience trends within every population subgroup. The crime rate does not exert a significant effect in any subgroup.
... The results were very similar to those we present that allow for direct comparison of effects of predictors of both types of crime, in the same metric. the variation, or changes in some predictor variables across time within the municipalities, is modest, and differences in crime rates are also likely to be due to differences between municipal units, we also estimate random effects models (Bell & Jones, 2015). The random effects model provides estimates of the effects of the predictor variables that are a weighted average of the within and between-unit effects. ...
Full-text available
There is very little research that provides a truly sociological assessment of the structural correlates of animal crime. There is also no comparative, community-level research on animal crimes in countries other than the U.S. In this exploratory study, we examine correlates of animal crime across Finland. Taking advantage of Finnish data on reported animal crime for 294 municipalities over a 10-year period, we (1) compare community-level predictors of violent and animal crime and (2) examine whether there is a relationship between violent crime and animal crime. While several economic, structural, and cultural variables are related to violent crime, we find that poverty is a common correlate of both violent and animal crime in Finland. We also find that, in contrast to the U.S., violent crime and animal crime are not related in Finland at the community level. We discuss implications for future research and the ways animal crime differs in the U.S. and Finland.
... In sum, different constraints can produce different results and the results will be meaningful only if the constraints are valid (Bell and Jones 2015;Glenn 2005). This state of affairs is often overlooked in applied research and prior studies of American attitudes to homosexuality do not constitute an exception. ...
Full-text available
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.
... Debates regarding the pros and cons of Yang and Land's HAPC model continue (Bell and Jones, 2015c;Feinberg, 2013;Reither et al., 2015). This study involves selecting a more prudent approach. ...
... Recent studies drawing on simulation exercises (Bell & Jones, 2014a, 2014b, 2015Luo, 2013) and mathematical proofs (Luo, Hodges, Winship, & Powers, 2016;Pelzer, te Grotenhuis, Eisinga, & Schmidt-Catran, 2015) demonstrate that purely statistical solutions to the APC problem fail because the confounding lies in the very nature of the linear dependency between APC. Therefore, several scholars agree that instead of trying to solve the APC problem by purely statistical constraints, scholars must employ solid theory and external information to choose an identification restriction (Bell & Jones, 2015;Chauvel & Schröder, 2015;Fienberg, 2013;Glenn, 2005;Heckman & Robb, 1985;Rodgers, 1982). ...
... Recent studies drawing on simulation exercises (Bell & Jones, 2014a, 2014b, 2015Luo, 2013) and mathematical proofs (Luo, Hodges, Winship, & Powers, 2016;Pelzer, te Grotenhuis, Eisinga, & Schmidt-Catran, 2015) demonstrate that purely statistical solutions to the APC problem fail because the confounding lies in the very nature of the linear dependency between APC. Therefore, several scholars agree that instead of trying to solve the APC problem by purely statistical constraints, scholars must employ solid theory and external information to choose an identification restriction (Bell & Jones, 2015;Chauvel & Schröder, 2015;Fienberg, 2013;Glenn, 2005;Heckman & Robb, 1985;Rodgers, 1982). ...
Full-text available
A stylized finding on returns to vocational education is that vocational compared to general education generates a differential life course pattern of employability: while vocational education guarantees smooth transitions into the labour market and thus generates initial advantages, these erode with increasing age, leading to late-life reversals in employment chances. We contribute to this research by assessing cohort variations in life-cycle patterns and distinguishing two explanations for late-life reversals in employment chances. The adaptability argument states that this phenomenon is due to the lower adaptability and occupational flexibility of those with vocational education. In contrast, the health argument states that vocational education leads to physically more demanding occupations, faster health deterioration, and, thus, lower employability in later life. Using data from the German Socio-Economic Panel, we employ non-parametric state probability analysis to assess cohort variations in employment patterns, and mediation analysis to assess how much of the late-life reversal of employment patterns is due to a faster health deterioration among the vocationally educated. Results show that the early life advantage of vocational education increases across cohorts. Furthermore, those with vocational education exhibit faster health deterioration, and a small part of the late-life employment disadvantage of this group works through lower levels of health after midlife.
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.
Intermarriage is an important indicator of immigrant integration trajectories and the rigidity of ethnoracial boundaries. Although questions of Middle Eastern and North African (MENA) integration and social exclusion occupy a central place in public discourse, little is known about their marriage patterns. The authors use the 2017 American Community Survey to estimate patterns of coethnic, panethnic, and intergroup marriages for MENA populations. Compared with other immigrant groups, rates of intermarriage are relatively high, and there is little evidence of “panethnic” patterns of marriage. However, more recent marriages have become less exogamous. Hierarchical age-period-cohort models suggest that this is driven by changing patterns among more recent cohorts, with some evidence of a post-2001 period effect among men. Compositional changes in the country of origin account for some, but not all, of these cohort effects. The findings highlight the importance of further research on MENA Americans to understand their unique social experiences of the U.S. ethnoracial hierarchy, particularly in the context of increasing racialized anti-Arab and anti-Muslim discrimination after 2001.
Full-text available
According to theories of cumulative (dis-)advantage, inequality increases over the life course. Labour market research has seized this argument to explain the increasing economic inequality as people age. However, evidence for cumulative (dis-)advantage in subjective well-being remains ambiguous, and a prominent study from the United States has reported contradictory results. Here, we reconcile research on inequality in subjective well-being with theories of cumulative (dis-)advantage. We argue that the age-specific endogenous selection of the (survey) population results in decreasing inequalities in subjective well-being means whereas individual-level changes show a pattern of cumulative (dis-)advantage. Using repeated cross-sectional data from the European Social Survey (N = 15,252) and employing hierarchical age-period-cohort models, we replicate the finding of decreasing inequality from the United States with the same research design for Germany. Using panel data from the German Socio Economic Panel Study (persons = 47,683, person-years = 360,306) and employing growth curve models, we show that this pattern of decreasing inequality in subjective well-being means is accompanied by increasing inequality in intra-individual subjective well-being changes. This pattern arises because disadvantaged groups, such as the low educated and individuals with low subjective well-being show lower probabilities of continuing to participate in a survey and because both determinants reinforce each other. In addition to allowing individual changes and attrition processes to be examined, the employed multi-cohort panel data have further key advantages for examining inequality in subjective well-being over the life course: They require weaker assumptions to control for period and cohort effects and make it possible to control for interviewer effects that may influence the results.
Im Jahr 2006 haben Yang Yang und Kenneth C. Land sogenannte hierarchische Alters-Perioden-Kohorten-Modelle (HAPK) vorgeschlagen. Hierbei werden Einflüsse der Kalenderzeit und der Geburtskohorte als zeitliche Kontextfaktoren auf Ebene 2 eines Mehrebenenmodells aufgefasst. Die vorliegende Arbeit kommt auf Basis einer Simulationsstudie mit Trenddaten (wiederholten Querschnitten) zu dem Schluss, dass das konventionelle HAPK-Modell zu deutlich verzerrten Schätzungen führt. Während der Alters- als auch der Periodeneffekt überschätzt werden, wird der Kohorteneffekt unterschätzt. Abgewandelte HAPK-Modelle, die den Kohorteneffekt im „fixed part“ des Modells ansiedeln, sind dem konventionellen Modell gemäß der Simulationsstudie deutlich überlegen. Der modifizierte HAPK-Ansatz wird anschließend auf ein empirisches Beispiel angewendet, das sich mit dem Wandel der Geschlechtsrollenideologie westdeutscher Frauen beschäftigt.
Full-text available
In many different fields, social scientists desire to understand temporal variation associated with age, time period, and cohort membership. Among methods proposed to address the identification problem in age-period-cohort analysis, the intrinsic estimator (IE) is reputed to impose few assumptions and to yield good estimates of the independent effects of age, period, and cohort groups. This article assesses the validity and application scope of IE theoretically and illustrates its properties with simulations. It shows that IE implicitly assumes a constraint on the linear age, period, and cohort effects. This constraint not only depends on the number of age, period, and cohort categories but also has nontrivial implications for estimation. Because this assumption is extremely difficult, if not impossible, to verify in empirical research, IE cannot and should not be used to estimate age, period, and cohort effects.
Full-text available
Previous work (Bell and Jones 2013a, c; Luo and Hodges 2013) has shown that, when there are trends in either the period or cohort residuals of Yang and Land’s Hierarchical Age-Period-Cohort (APC) model (Yang and Land 2006; Yang and Land 2013), the model can incorrectly estimate those trends, because of the well-known APC identification problem. Here we consider modelling possibilities when the age effect is known, allowing any period or cohort trends to be estimated. In particular, we suggest the application of informative priors, in a Bayesian framework, to the age trend, and we use a variety of simulated but realistic datasets to explicate this. Similarly, an informative prior could be applied to an estimated period or cohort trend, allowing the other two APC trends to be estimated. We show that a very strong informative prior is required for this purpose. As such, models of this kind can be fitted but are only useful when very strong evidence of the age trend (for example physiological evidence regarding health). Alternatively, a variety of strong priors can be tested and the most plausible solution argued for on the basis of theory.
Full-text available
Reither et al. (2009) use a Hierarchical Age-Period-Cohort model (HAPC - Yang & Land, 2006) to assess changes in obesity in the USA population. Their results suggest that there is only a minimal effect of cohorts, and that it is periods which have driven the increase in obesity over time. We use simulations to show that this result may be incorrect. Using simulated data in which it is cohorts, rather than periods, that are responsible for the rise in obesity, we are able to replicate the period-trending results of Reither et al. In this instance, the HAPC model misses the true cohort trend entirely, erroneously finds a period trend, and underestimates the age trend. Reither et al.’s results may be correct, but because age, period and cohort are confounded there is no way to tell. This is typical of age-period-cohort models, and shows the importance of caution when any APC model is used. We finish with a discussion of ways forward for researchers wishing to model age, period and cohort in a robust and non-arbitrary manner.
Age-Period-Cohort Analysis: New Models, Methods, and Empirical Applications is based on a decade of the authors’ collaborative work in age-period-cohort (APC) analysis. Within a single, consistent HAPC-GLMM statistical modeling framework, the authors synthesize APC models and methods for three research designs: age-by-time period tables of population rates or proportions, repeated cross-section sample surveys, and accelerated longitudinal panel studies. The authors show how the empirical application of the models to various problems leads to many fascinating findings on how outcome variables develop along the age, period, and cohort dimensions. The book makes two essential contributions to quantitative studies of time-related change. Through the introduction of the GLMM framework, it shows how innovative estimation methods and new model specifications can be used to tackle the "model identification problem" that has hampered the development and empirical application of APC analysis. The book also addresses the major criticism against APC analysis by explaining the use of new models within the GLMM framework to uncover mechanisms underlying age patterns and temporal trends. Encompassing both methodological expositions and empirical studies, this book explores the ways in which statistical models, methods, and research designs can be used to open new possibilities for APC analysis. It compares new and existing models and methods and provides useful guidelines on how to conduct APC analysis. For empirical illustrations, the text incorporates examples from a variety of disciplines, such as sociology, demography, and epidemiology. Along with details on empirical analyses, software and programs to estimate the models are available on the book’s web page.
Social scientists have recognized the importance of age-period-cohort (APC) models for half a century, but have spent much of this time mired in debates about the feasibility of APC methods. Recently, a new class of APC methods based on modern statistical knowledge has emerged, offering potential solutions. In 2009, Reither, Hauser and Yang used one of these new methods – hierarchical APC (HAPC) modeling – to study how birth cohorts may have contributed to the U.S. obesity epidemic. They found that recent birth cohorts experience higher odds of obesity than their predecessors, but that ubiquitous period-based changes are primarily responsible for the rising prevalence of obesity. Although these findings have been replicated elsewhere, recent commentaries by Bell and Jones call them into question – along with the new class of APC methods. Specifically, Bell and Jones claim that new APC methods do not adequately address model identification and suggest that “solid theory” is often sufficient to remove one of the three temporal dimensions from empirical consideration. They also present a series of simulation models that purportedly show how the HAPC models estimated by Reither et al. (2009) could have produced misleading results. However, these simulation models rest on assumptions that there were no period effects, and associations between period and cohort variables and the outcome were perfectly linear. Those are conditions under which APC models should never be used. Under more tenable assumptions, our own simulations show that HAPC methods perform well, both in recovering the main findings presented by Reither et al. (2009) and the results reported by Bell and Jones. We also respond to critiques about model identification and theoretically-imposed constraints, finding little pragmatic support for such arguments. We conclude by encouraging social scientists to move beyond the debates of the 1970s and toward a deeper appreciation for modern APC methodologies.
This article explores an important property of the intrinsic estimator that has received no attention in literature: the age, period, and cohort estimates of the intrinsic estimator are not unique but vary with the parameterization and reference categories chosen for these variables. We give a formal proof of the non-uniqueness property for effect coding and dummy variable coding. Using data on female mortality in the United States over the years 1960-1999, we show that the variation in the results obtained for different parameterizations and reference categories is substantial and leads to contradictory conclusions. We conclude that the non-uniqueness property is a new argument for not routinely applying the intrinsic estimator.
There is ongoing debate regarding the shape of life-course trajectories in mental health. Many argue the relationship is U-shaped, with mental health declining with age to mid-life, then improving. However, I argue that these models are beset by the age-period-cohort (APC) identification problem, whereby age, cohort and year of measurement are exactly collinear and their effects cannot be meaningfully separated. This means an apparent life-course effect could be explained by cohorts. This paper critiques two sets of literature: the substantive literature regarding life-course trajectories in mental health, and the methodological literature that claims erroneously to have 'solved' the APC identification problem statistically (e.g. using Yang and Land's Hierarchical APC-HAPC-model). I then use a variant of the HAPC model, making strong but justified assumptions that allow the modelling of life-course trajectories in mental health (measured by the General Health Questionnaire) net of any cohort effects, using data from the British Household Panel Survey, 1991-2008. The model additionally employs a complex multilevel structure that allows the relative importance of spatial (households, local authority districts) and temporal (periods, cohorts) levels to be assessed. Mental health is found to increase throughout the life-course; this slows at mid-life before worsening again into old age, but there is no evidence of a U-shape--I argue that such findings result from confounding with cohort processes (whereby more recent cohorts have generally worse mental health). Other covariates were also evaluated; income, smoking, education, social class, urbanity, ethnicity, gender and marriage were all related to mental health, with the latter two in particular affecting life-course and cohort trajectories. The paper shows the importance of understanding APC in life-course research generally, and mental health research in particular.
Post-print version available at This commentary discusses the age-period-cohort identification problem. It shows that, despite a plethora of proposed solutions in the literature, no model is able to solve the identification problem because the identification problem is inherent to the real-world processes being modelled. As such, we cast doubt on the conclusions of a number of papers, including one presented here (Page et al., this issue). We conclude with some recommendations for those wanting to model age, period and cohort in a compelling way.