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Don't birth cohorts matter? A commentary and simulation exercise on Reither, Hauser and Yang's (2009) age-period-cohort study of obesity

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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.
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Don’t birth cohorts matter? A
commentary and simulation exercise
on Reither, Hauser and Yang’s (2009)
age-period-cohort study of obesity
Andrew Bell a b and Kelvyn Jones a b
aSchool of Geographical Sciences
University of Bristol
University Road
Bristol
BS8 1SS
UK
bCentre for Multilevel Modelling
University of Bristol
2 Priory Road
Bristol
BS8 1TX
UK
Draft please do not cite without permission
Last updated: 2nd September 2013
Corresponding Author:
Andrew Bell
School of Geographical Sciences
University of Bristol
University Road
Bristol
BS8 1SS
UK
Email: andrew.bell@bristol.ac.uk
Acknowledgements: Thanks to Dewi Owen and Ron Johnston for their help; neither is responsible for
what we have written.
2
Abstract
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.
Research Highlights
Reither et al’s HAPC study suggest rises in obesity are caused by period effects
Simulations suggest that this result may be erroneous
Identical results were found with data simulated from an entirely different process
Results show the pitfalls of using APC models without critical forethought.
Keywords
Age-period-cohort models, Obesity, Collinearity, Model identification
3
1 Introduction
The desire to separate age, period and cohort (APC) effects has been a key feature of both the
medical and social sciences for a number of decades (Ryder, 1965). For at least the same period,
levels of obesity have been rising at a continuous rate, to the point that in 1997 it was classified by
the World Health Organisation as a global epidemic (Caballero, 2007). In 2009, Reither et al. (2009)
used the recently developed Hierarchical Age-Period-Cohort (HAPC) model (Yang & Land, 2006) to
assess the relative importance of periods and cohorts in the development of the obesity epidemic.
Whilst they found some significant cohort effects, the implication of their results was “that period
effects were principally responsible for the obesity epidemic” (Reither et al., 2009:1445), and this
result was repeated by Yang and Land (2013:215-222).
However, the possibility of separating APC effects is beset by an ‘identification problem’ due to the
fact that age, period and cohort when taken together are perfectly collinear. In this paper we show
that the HAPC model does not solve this identification problem, and therefore that the results found
by Reither et al. should be treated with some scepticism.
The purpose of this paper is twofold. The first substantive contribution is to add to the growing
debate in epidemiology regarding the causes of, and therefore possible solutions to, the obesity
epidemic. Whether periods or cohorts are responsible for changes in obesity is of profound
importance because it should affect how policy interventions are targeted. The second,
methodological, contribution is to assess the capabilities of age-period-cohort models, and the
dangers of using these models without critical forethought regarding their limits. In this we are
building on previous work (Bell & Jones, 2013a, b, c; Glenn, 2005; Luo, 2013; Luo & Hodges, 2013)
questioning the capabilities of the HAPC model and other methodological innovations to disentangle
APC effects.
We first outline the identification problem and Yang and Land’s proffered solution to it. Second we
briefly review the literature on the development of the obesity epidemic. Third we outline our
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simulation design which we use to show that the results found by Reither et al. could have been
created by a different data generating process (DGP). Finally, we discuss the implications of this
both within obesity research and beyond, considering ways forward for researchers wishing to use
techniques like the HAPC model to make robust conclusions regarding APC effects.
2 The APC identification problem and Yang and Land’s HAPC Model
The conceptual distinction between age, period and cohort is well known (Bell & Jones, 2013a;
Suzuki, 2012). However despite this, there remains the problem of statistically modelling the three
effects because of the mathematical dependency between them:
  
(1)
As such, if we know the value of two of the terms, we will always know the value of the third. From
an ‘experimental’ standpoint, therefore, it is impossible to hold two of APC constant whilst varying
the third. Because of this, each of the following DGPs (and an infinite number more) would produce
identical values for a dependent variable Y:
          
(2a)
      
(2b)
   
(2c)
Given such data, therefore, it would not be possible to tell which DGP actually produced the data.
These three instances presented here have very different substantive meanings, yet it would not be
5
possible to tell which of the three actually produced the data at hand1. It is for this reason that
many see a solution to the identification problem to be a logical impossibility:
“The continued search for a statistical technique that can be mechanically applied always to
correctly estimate the effects is one of the most bizarre instances in the history of science of
repeated attempts to do the logically impossible.”
(Glenn, 2005:6)
Despite this, numerous supposed solutions to the identification problem have been proposed, each
of which imposes some kind of constraint on the model (Mason et al., 1973; Sasaki & Suzuki, 1987;
Tu et al., 2011; Yang et al., 2008). The problem arises when these constraints are not clearly stated,
are applied arbitrarily on the basis of statistical necessity, and are not grounded in any kind of
substantive theory. The models are generally very sensitive to such constraints and as such can
provide extremely misleading results when those constraints are not precisely justified and
appropriate.
Yang and Land’s proposed solution is to use a cross-classified multilevel model, which treats age as a
fixed effect and periods and cohort groups as random effects contexts in which individuals reside.
The model can thus be specified (in the continuous Y case) as:
   
 
   
 
  
  
(3)
The dependent variable,  is measured for individuals i in period j1 and cohort j2. The ‘micro’
model has linear and quadratic age terms, with coefficients and respectively; a constant
() that varies across both periods and cohorts; and a level 1 residual error term (). The
1 The technical consequence of this is that a regression with age, period and cohort as linear independent
variables will not be estimable (at least with OLS) because the design matrix XTX cannot be inverted.
6
macro model defines the intercept in the micro model by a non-varying overall intercept , and a
residual term for each of period and cohort. The period, cohort and level-1 residuals are all assumed
to follow Normal distributions, each with variances that are estimated.
Putting age in the fixed part and period and cohort in the random part is conceptually attractive; but
also, it is argued by Yang and Land that this distinction solves the identification problem:
"An HAPC framework does not incur the identification problem because the three effects are
not assumed to be linear and additive at the same level of analysis"
(Yang & Land, 2013:191)
In addition to this, Yang and Land suggest that the inclusion of the quadratic term for age helps to
further resolve the identification problem:
the underidentification problem of the classical APC accounting model has been resolved by
the specification of the quadratic function for the age effects.
(Yang & Land, 2006:84)
However, it has been shown elsewhere that this methodological advance in fact amounts to another
constraint (Luo & Hodges, 2013), and simulation studies have shown that the use of this model,
without critical forethought, can lead to misleading results (Bell & Jones, 2013a).
3 The Obesity Epidemic
Historically, obesity was a rare affliction, predominantly affecting those of high socio-economic
status (Caballero, 2007). However, levels of obesity increased throughout the twentieth century,
particularly amongst those of lower socio-economic status and education levels (Visscher et al.,
2010). A number of reasons for this have been proposed, including the more sedentary lifestyle
associated with the technological advances of the modern world (Rokholm et al., 2010), and the
7
greater availability, portion size and fat content of food (Hill & Peters, 1998). However, the question
remains as to whether it is via periods or cohorts that these changes occur. If the former, it would
suggest that changes in lifestyle have affected all age groups equally, resulting in bad diets and low
levels of exercise for all individuals. In contrast, the latter would suggest that these cultural changes
particularly affect people in their formative years, and these changes have affected their behaviour
and possibly their physiological resistance to obesity throughout their subsequent life-course. In the
same vein, interventions to the obesity epidemic should be similarly targeted to the groups most
affected. If cohorts are responsible for changes in obesity, then policy interventions should be
focused on children in their formative years because interventions targeted at adults are likely to be
ineffectual.
Reither et al. argue that the obesity epidemic is the result predominantly of periods, and their
results are shown graphically in the third column of figure 1. They argue that “the pattern of
predicted probabilities for U.S. adults shows a monotonic increase over time, with no sign of
abatement in recent periods of observation” (Reither et al., 2009:1443). Similarly, Allman-Farinelli
et al. (2008) find that period effects are the driving force of changes in their APC analysis of obesity
in Australia, whilst Rokholm et al. (2010:843) argue that the slight levelling off of the obesity
epidemic observed in recent years “occurred at approximately the same time for different age
groups”. However, other studies find evidence that cohorts have the greater influence on obesity:
for example Olsen et al. (2006) find that non-linearities in cohort trends match for different age
groups, but do not match for periods. However, we argue that all of the methods used above have
flaws, relying on un-testable assumptions (explaining why the results that have been found are so
contradictory). The next section takes the results found by Reither et al (2009) and shows that those
results could have been found with a very different data generating process (DGP).
8
4 Simulation exercise
Reither et al (2009) found a strong, approximately linear trend in periods, and very little in terms of a
trend in cohorts (see figure 1). However, we have argued that, because of the identification
problem, these results could have arisen from a very different DGP. In order to test this, we ran the
model used by Reither et al using the following DGP:
            
 for cohorts,  for periods
(4)
Here, Y will equal 1 for an individual who is obese, and 0 otherwise. The period and cohort residuals
were generated to be Normally distributed, with a variance of 0.01. Crucially, in this DGP we include
a linear cohort effect2 of 0.04, and an age effect that is 0.04 larger than that found by Reither et al
(2009). We do not include the period trend found by Reither et al, so this part of the DGP is just
random fluctuations from year to year.
This data, generated with this known functional form, was then fitted to a logistic version of Yang
and Land’s HAPC model:

     
   
 
  
(5)
2 It could be argued that it is unlikely that such a cohort (or period) trend would never be generated in real life
in this way, because periods and cohorts are intrinsically random (in contrast to age which has a fixed range
and so should be treated as a fixed covariate). However, the model is unable to tell whether a trend is the
result of a ‘random’ and fleeting upward fluctuation or a consistent linear trend over all possible time
periods/cohorts, since the resulting data sample would be much the same. This is especially the case when the
trend found (by Reither et al.) is very much linear in appearance and interpreted as such (“a monotonic
increase over time” Reither et al 2009:1443). As such a linear trend is an appropriate means of generating
the data for this situation.
9
It is implicitly being assumed that any period or cohort trend is appropriately picked up by the period
or cohort residuals, since no fixed effect is specified for such trends.
Reither et al. (2009:1442) use 5-year groups to define their cohorts in the models that they fit. This
is “conventional in demography”, but Reither et al. argue that a further advantage of this grouping is
that they “function as equality constraints” which help to identify the model. In previous work (Bell
& Jones, 2013a) it has been shown that the HAPC model is able to correctly estimate trends when
groupings exactly match groupings in the data generating process, but not when those groupings are
chosen by arbitrary convention as they appear to have been here. It is therefore important to
evaluate the possible effect that this grouping has on the question at hand. We therefore examined
three grouping scenarios:
No grouping (i.e. 1 year birth cohorts) in either the DGP or the fitted HAPC model
No grouping in the DGP, but HAPC model fitted with 5-year birth cohorts
7-year birth cohorts in the DGP but HAPC model fitted with 5-year birth cohorts.
Since it is unlikely that we would ever know the exact cohort groups in the DGP (if they are present
at all), we do not test a model where the groupings in the DGP and the fitted models match.
The simulations were conducted in a similar way to those in Bell and Jones (2013a), using Bayesian
MCMC methods (Browne, 2009) in MLwiN version 2.28 (Rasbash et al., 2013), through Stata using
the runmlwin command (Leckie & Charlton, 2013). True values from the DGP were used as starting
values as non-informative priors, and the model was run for 20,000 iterations, following a 1000
iteration burn-in. In order to assess convergence of the chains, a sample of parameter trajectories
were visually inspected. In addition, a version of the Potential Scale Reduction Factor (Bell & Jones,
2013a; Brooks & Gelman, 1998) and Effective Sample Size were calculated for all parameters. The
Stata code for these simulations can be found in the online appendix.
10
For each grouping scenario 1000 separate simulations were conducted. We have reported the
results from the model with the median value for the coefficient associated with age for the scenario
where cohorts were grouped in 7-year intervals and modelled with 5-year intervals. We did this,
rather than averaging over all 1000 simulations, because the mean results could not have been
estimated from a single dataset generated by our DGP (for example, random variation in residuals
would be averaged out). The results found are, however, typical of all simulations in all grouping
scenarios3.
The results are shown in the second column of figure 1, alongside the true DGP (column 1) and the
results found by Reither et al (column 3). As can be seen, the typical median result does not match
the DGP at all. No cohort trend is found, an erroneous period trend is found, and the age effect is
underestimated. In fact, the results found very closely resemble those found by Reither et al. The
implications of this, of course, is that the same DGP could have generated Reither et al.’s data, and
the results that they found could be as misleading as the results found in the simulation.
[Figure 1 about here]
5 Discussion
To be clear: we are not saying that the results found by Reither et al. are necessarily incorrect.
However, Reither et al. (2009:1444) argue that their results are “unambiguous” and it is with this
that we take issue. There is no reason to think that Reither et al’s results are the true DGP, rather
than the DGP we used to generate our data here. This is important for policy makers considering
possible interventions to the obesity epidemic. Whilst Reither et al’s results suggest that
interventions should be targeted to all age groups, the alternative explanation offered by us would
suggest that interventions would be better targeted at children in their formative years.
3 A small minority (~5%) of results for the scenarios with mismatched groupings (between the DGP and the
fitted model) produced different results, including results that were correct according to the DGP. However
this did not occur when the cohorts were ungrouped. We have not reported these, given that a model that is
right less than 10% of the time is not particularly useful.
11
Reither et al are not alone in finding results that may be misleading using the HAPC model.
Dassonneville (2012) finds a period trend in voter turnout volatility, going against the literature
which tends to find cohort effects to be most significant. Much like the period trend found by
Reither et al, this could be an incorrect finding. Other studies (Piontek et al., 2012; Schwadel, 2010)
similarly use the HAPC model to find period and cohort trends which may be over-interpretations of
their data.
So what should the researcher of APC effects do? Where there are no trends in the periods or
cohorts, the HAPC model works well, meaning that it can be used to assess random variation in
periods and cohorts. This assumes that there are not equal and opposite linear period and cohort
trends (which, would cancel each other out, with the model estimating a spurious age effect rather
than the true period and cohort trends), but this is an assumption that researchers are often willing
to make. Furthermore, there remains the possibility that cohort and/or period residuals remain
autocorrelated, even when there is no trend; the model can be extended to incorporate this
autocorrelation into the model (Stegmueller, 2013).
Where trends do exist, one option would be to make a decision based on theory as to which of
periods or cohorts are most likely to have generated the data, and include that term in the HAPC
model as a linear fixed effect (Bell & Jones, 2013a). This decision cannot, however, be made on the
basis of the data, since a model with period and age fixed linear trends will fit the data as well as one
with age and cohort fixed linear trends. This is confirmed by simulations using the same DGP as
above, (but with a period or cohort linear term included in the fixed part of the fitted model). The
results of these are displayed in Table 1.
[Table 1 about here]
In the case of this study, where the purpose of the research is to examine which of period and
cohort are most likely to be the cause of the epidemic, researchers could assess the age trend that is
12
found and decide whether it seems likely. In the case of the modelled results here, we would argue
that the age effect that we generated is more plausible than that found by Reither et al (2009).
Whilst we would expect some decline in obesity at older ages due to physiological reasons and
survival bias (Villareal et al., 2005) we would not expect it to be as large or as early in life as that
found by Reither et al. (Villareal et al., 2005; Visscher et al., 2010). Of course it is also possible that
the rise of obesity is the result of a mixture of period and cohort effects, in which case the true DGP
would be somewhere in between those found in figure 1. Where there are very good theoretical
(e.g. physiological) reasons to believe the age trend is known, such belief could be incorporated into
the model (e.g. see Tilley & Evans, 2013) potentially in a Bayesian way using strong informative
priors (Browne, 2009; Jackman, 2009). However, that would involve a theoretical judgement which,
again, cannot be confirmed simply on the basis of the data.
Overall, we hope that this commentary will push researchers towards engaging in more critical
forethought regarding APC effects. With appropriate constraints, based on theoretical plausibility
rather than statistical necessity, techniques like the HAPC model can be useful in modelling possible
APC combinations, so long as those constraints are explicitly stated by the authors. When those
constraints are unclear, or not known about in the first place, misleading results may be produced.
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Figure 1: Age (row 1) cohort (row 2) and period (row 3) effects on obesity, according to the true self-
generated DGPa (column 1), the median simulation result (column 2) and the result found by Reither
et al., 2009 (column 3).
a Simulation here is from the scenario where cohorts were grouped in 7-year intervals in the DGP and 5-year
intervals in the fitted model. However the results of the other grouping scenarios were substantively similar.
16
Table 1: Mean fixed effects and model fit criterion (DIC - see Spiegelhalter et al., 2002) for simulation
results with a model using (1) age and cohort, and (2) age and period, as fixed linear effects. It can
be seen that, if anything, the DIC supports the incorrect specification.
Truth
1. Age and Cohort
β
Upper
Bound
Lower
Bound
Β
Upper
Bound
Lower
Bound
Cons
-2
-2.000
-1.901
-2.102
-2.001
-1.902
-2.101
Age
0.1
0.097
0.106
0.088
0.060
0.065
0.056
Age2
-0.001
-0.00099
-0.00077
-0.00120
-0.00099
-0.00077
-0.00120
aCohort
0.04
0.037
0.045
0.029
-
-
-
Period
0
-
-
-
0.039
0.047
0.031
DIC
13681.61
a Cohorts here were grouped by 7-year intervals in the DGP and by 5-year intervals in the model (but the
results were substantively similar to the other grouping scenarios tested).
... Ordinary least square regression analysis is further used as recommended by Rekker (2018). Using multi-level models for assessing generation and age effects has been criticised since a simulation study demonstrated that the hierarchical model often showed untrue significant findings (Bell and Jones 2014). Nor are they recommended for assessing regional effects since the analyses include fewer than 50 cases at the higher, contextual, level (Mehmetoglu 2017: 213). ...
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The underlying mechanisms of the association between education and socio-cultural liberal attitudes have received much attention from scholars within public opinion. Despite sharp increases in the proportion of highly educated in recent decades, the influence of a generational replacement has been widely overlooked in research. The central hypothesis in this article is that generational differences constitute one explanation for the average strength of the education effect on socio-cultural values. Also, the importance of education for forming attitudes could be weaker in generations that grew up when higher education was widespread and the societal climate was more liberal. Results from the ‘age-period-cohort’ (APC) analysis, using the European Social Survey 2002–2018, confirm that a substantial part of the liberalising education effect is generational in origin and that its strength depends on the generation. They further show that this dependency varies across different European regions. The findings shed new light on the mechanisms and political significance of the education effect.
... In the field of political participation, Caren et al. (2011) and Quaranta (2016) have applied this technique to identify cohort and period effects on protest in the United States and in Italy. Bell and Jones (2014a, 2014b, however, have demonstrated through simulations that Yang and Land's method leads to biased results if period or cohort effects exhibit a linear or nonlinear trend. Biases appear, for example, if the period or cohort trend correlates with age (but see . ...
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.
... As an example, let ik = −2 + 0.1i − 0.001i 2 + 0.04k as in Bell and Jones (2014). This could arise from θ defined by i = −2 + 0.1i − 0.001i 2 , k = 0.04k, j = = 0; or equally from * defined by * i = −1.96 ...
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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.
... In 1971-2006 NHANES data on both children and adults, Keyes et al. [15] used three different APC modeling approaches and reported a positive cohort effect from only one of these. As they and others [49] argue, interpretation depends on the choice of model and often boils down to conceptual, as opposed to statistical, context. In our case, hypotheses were about cohort effects on obesity disparities. ...
Article
Full-text available
Background Children belonging to the same birth cohort (i.e., born in the same year) experience shared exposure to a common obesity-related milieu during the critical early years of development—e.g., secular beliefs and feeding practices, adverse chemical exposures, food access and nutrition assistance policies—that set the stage for a shared trajectory of obesity as they mature. Fundamental cause theory suggests that inequitable distribution of recent efforts to stem the rise in child obesity may exacerbate cohort-based disparities over time. Methods Data were from electronic health records spanning 2007–2016 linked to birth records for children ages 2–19 years. We used hierarchical age-period-cohort models to investigate cohort effects on disparities in obesity related to maternal education. We hypothesized that maternal education-based disparities in prevalence of obesity would be larger among more recent birth cohorts. Results Sex-stratified models adjusted for race/ethnicity showed substantial obesity disparities by maternal education that were evident even at young ages: prevalence among children with maternal education < high school compared to maternal college degree was approximately three times as high among girls and twice as high among boys. For maternal education < high school, disparities compared to maternal college degree were higher in more recent birth cohorts. Among girls, this disparity cohort effect was evident at younger ages (at age 4, the disparity increased by 4 [0.1–8] percentage points per 5 birth years), while among boys it was larger at older ages (at age 16, the disparity increased by 7 [1–14] percentage points per 5 birth years). Conclusions There may be widening maternal education-based disparities in child obesity by birth cohort at some ages.
... Accompanying the article was a comment and a reply by two of the article's authors that discussed the merits of using age-period-cohort (APC) methods to identify cohort-based trends [2,3]. The exchange exemplified the contentious spirit that characterizes most discussions about APC methods (e.g., see [4][5][6][7][8][9][10][11][12]). The back-and-forth was unsatisfactory as the exchange provided little practical advice for users of APC methods. ...
Article
Full-text available
Background Age-period-cohort (APC) models are often used to decompose health trends into period- and cohort-based sources, but their use in epidemiology and population sciences remains contentious. Central to the contention are researchers’ failures to 1) clearly state their analytic assumptions and/or 2) thoroughly evaluate model results. These failures often produce varying conclusions across APC studies and generate confusion about APC methods. Consequently, scholarly exchanges about APC methods usually result in strong disagreements that rarely offer practical advice to users or readers of APC methods. Methods We use research guidelines to help practitioners of APC methods articulate their analytic assumptions and validate their results. To demonstrate the usefulness of the guidelines, we apply them to a 2015 American Journal of Epidemiology study about trends in black-white differences in U.S. heart disease mortality. Results The application of the guidelines highlights two important findings. On the one hand, some APC methods produce inconsistent results that are highly sensitive to researcher manipulation. On the other hand, other APC methods estimate results that are robust to researcher manipulation and consistent across APC models. Conclusions The exercise shows the simplicity and effectiveness of the guidelines in resolving disagreements over APC results. The cautious use of APC models can generate results that are consistent across methods and robust to researcher manipulation. If followed, the guidelines can likely reduce the chance of publishing variable and conflicting results across APC studies.
Article
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This study aims to investigate the age, period, and cohort effects on trends in activities of daily living (ADL) disability among Chinese older adults; and to explore these three temporal effects on gender and residence disparities in disability. We utilized multiple cross-sectional waves of the Chinese Longitudinal Healthy Longevity Survey data (1998–2018), including 89,511 participants aged above 65 years old. Our measurement of disability is the number of ADL items (dressing, bathing, indoor transferring, toileting, eating, and continence) participants can’t perform independently. Hierarchical age-period-cohort cross-classified random effects models were conducted to investigate age, period and cohort trends in ADL disability. Results showed that ADL disability increased with age at an increasing rate. A V-shaped cohort trend and a fluctuated period trend were identified. Females and urban residents were associated with more ADL limitations. When age increased, the gender and residence gaps in disability further increased. The cohort-based gender and residence inequalities in ADL limitations converged with successive cohorts. The period-based residence gap in ADL limitations diverged throughout the 20-year period, while the corresponding period-based change in gender disparity was not significant. These findings suggested that age, period, and cohort had different and independent effects on ADL disability among Chinese older adults. The age effect on trends in ADL is stronger compared to period and cohort effects. The gender and residence disparities in disability increased with age and decreased with successive cohorts. These patterns might help inform healthcare planning and the priorities for medical resource allocation accordingly.
Article
Background: Changes to pertussis vaccination programmes can have impacts on disease burden that should be estimated independently from factors such as age- and period-related trends. We used age-period-cohort (APC) models to explore pertussis incidence in Manitoba over a 25-year period (1992-2017). Methods: We identified all laboratory-confirmed cases of pertussis from Manitoba's Communicable Diseases Database and calculated age-standardized incidence rates. We used APC models to investigate trends in pertussis incidence. Results: During the study period, 2479 cases were reported. Age-standardized rates were highest during a large outbreak in 1994 (55 cases/100 000 person-years), with much lower peaks in 1998, 2012 and 2016. We saw strong age and cohort effects in the APC models, with a steady decrease in incidence with increasing age and increased risk in the cohort born between 1980 and 1995. Conclusions: The highest risk for pertussis was consistently in young children, regardless of birth cohort or time period. The 1981 programme change to an adsorbed whole-cell pertussis vaccine with low effectiveness resulted in reduced protection in the 1981-95 birth cohort and contributed to the largest outbreak of disease during the 25-year study period.
Article
Background and aims Smoking prevalence has been falling in England for over 50 years but remains a prevalent and major public health problem. This study used an Age-Period-Cohort (APC) approach to measure lifecycle, historical and generational patterns of individual smoking behaviour. Design APC analysis of repeated cross-sectional smoking prevalence data obtained from three nationally representative surveys. Setting England (1972 – 2019). Participants Individuals aged 18 to 90 years old. Measurements We studied relative odds of current smoking in relation to age in single years from 18 to 90, 24 groups of 2-year survey periods (1972-1973 to 2018-2019), and 20 groups of 5-year birth cohorts (1907-1911 to 1997-2001). Age and period rates were studied for two groups of birth cohorts: those aged 18 to 25 years and those aged over 25 years. Findings Relative to age 18, the odds of current smoking increased with age until around age 25 (odds ratio (OR): 1.48; 95% confidence interval (CI):1.41 to 1.56) and then decreased progressively to age 90 (OR: 0.06; 95% CI: 0.04 to 0.08). They also decreased almost linearly with period relative to 1972-1973 (for 2018-2019 OR: 0.30; 95% CI: 0.26 to 0.34) and with birth cohort relative to 1902-1906, with the largest decreased observed for birth cohort 1992-1996 (OR: 0.44; 95% CI: 0.35 to 0.46) and 1997-2001 (OR: 0.35; 95% CI: 0.74 to 0.88). Smoking declined in the 18-25 age group by an average of 7% over successive 2-year periods, and by an average of 5% in those aged over 25. Conclusions Smoking in England appears to have declined over recent decades mainly as a result of reduced smoking uptake before age 25, and to a lesser extent to smoking cessation after age 25.
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To investigate temporal patterns, socio-demographic gradients, and structural breaks in adolescent marijuana use in the United States from 1991 to 2018, we used hierarchical Age-Period-Cohort logistic models to separate temporal effects of marijuana use among 8th, 10th, and 12th graders from 28 waves of the Monitoring the Future survey. Structural breaks in period effects were further detected via a dynamic-programing-based method. Net of other effects, we found a clear age-related increase in the probability of marijuana use (10.46%, 23.17%, and 31.19% for 8th, 10th and 12th graders, respectively). Period effects showed a substantial increase over time (from 16.23% in 2006 to 26.38% in 2018), while cohort effects remained stable over the period of study. Risk of adolescent marijuana use varied by sex, racial group, family status, and parental education. Significant structural breaks during 1995–1996, 2006–2008, and 2011–2013 were identified in sub-populations. A steady increase in marijuana use among adolescents over the latter years of this time period was identified. Adolescents who were male, non-Black, lived in non-intact families, and who had less educated parents were especially at risk of marijuana usage. Trends of adolescent marijuana use changed significantly during times of economic crisis.
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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.
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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.
Book
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.
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To examine dynamics of political processes using repeated cross-section data, effects of age, cohort, and time period have to be disentangled. I propose a Bayesian dynamic hierarchical model with cohort and period effects modeled as random walk through time. It includes smoothly time-varying effects of covariates, allowing researchers to study changing effects of individual characteristics on political behavior. It provides a flexible functional form estimate of age by integrating a semi-parametric approach in the hierarchical model. I employ this approach to examine religious voting in the United States using repeated cross-sectional surveys from 1972 to 2008. I find starkly differing nonlinear trends of de- and re-alignment among different religious denominations.
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This paper examines how ageing and generational formative experiences affect vote choices in Britain. Using a combination of panel data and assumptions about party fortunes we estimate ageing effects. These are then entered into a model using cross-sectional data from 1964 to 2010 to estimate generational differences in vote choice. Ageing increases the likelihood of a Conservative vote substantially, but there is no trend towards lower rates of Conservative voting among newer generations. There are however identifiable political generations corresponding with periods of Conservative dominance: voters who came of age in the 1930s, 1950s and 1980s are ceteris paribus somewhat more Conservative. Our method therefore lends some support to theories of political generations, but also demonstrates the considerable impact of ageing on vote choice.
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Political behavior has been changing all over Western Europe and electoral volatility is one of the facets of politics in which this change is apparent. Theories on stabilization of political attitudes and behavior in lifetime and the slow rate at which change in the electoral arena is found to proceed, have led to the assumption of generational replacement as the mechanism driving change. The Netherlands, however, provide a remarkably different case of this trend in electoral volatility. The country has shifted from an example of how cleavages stabilize politics to one of the most electorally volatile countries in Europe. The Dutch surge in electoral volatility thus contrasts with expectations of a slow process driven by generational replacement. Starting from this apparent contradiction between the evolution of volatility in the Netherlands and theories on generational replacement, this article investigates time effects of electoral volatility. The study is based on an age, period and cohort analysis on the repeated cross-sectional data of the Dutch Parliamentary Election Studies, 1971–2010. Based on characteristics of such repeated cross-sectional data, individuals are cross-classified in birth cohorts and election years respectively, which overcomes the identification problem inherent in cohort analyses. Results of a Cross-Classified Random Effects Model (CCREM) indicate that, contrary to the hypothesis of new generations causing the increase in volatility, the Dutch change can be attributed primarily to period effects. As such, the analyses indicate that a general shift in the Dutch electorate has caused the growth in volatility and that supply-side factors should probably be analyzed when trying to explain electoral volatility.