The Age-Period-Cohort-Interaction Model for Describing and Investigating Inter-cohort Deviations and Intra-cohort Life-course Dynamics

Luo, Liying; Hodges, James S.

doi:10.1177/0049124119882451

Cited by 56 publications

(83 citation statements)

References 101 publications

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“…Many methods have been proposed, some relying on technical assumptions (see, e.g., Robertson and Boyle 1998; Yang et al 2008) and others based on social theory (Fosse and Winship forthcoming; Mason and Fienberg 1985; O’Brien 2000) or hypothesized mechanisms or proxy variables through which causal factors affect the outcome measures (Heckman and Robb 1985; Winship and Harding 2008). In the end, what researchers can hope to accomplish depends on what they intend the statistical method to do (Luo 2013b; Luo and Hodges forthcoming). In many demographic and social science applications, statistical models are useful for summarizing information in the data in a concise way.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Constraints in Random Effects Age-Period-Cohort Models

Luo

Hodges

2020

Sociological Methodology

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Random effects (RE) models have been widely used to study the contextual effects of structures such as neighborhood or school. The RE approach has recently been applied to age-period-cohort (APC) models that are unidentified because the predictors are exactly linearly dependent. However, it has not been fully understood how the RE specification identifies these otherwise unidentified APC models. We address this challenge by first making explicit that RE-APC models have greater-not less-rank deficiency than the traditional fixed-effects model, followed by two empirical examples. We then provide intuition and a mathematical proof to explain that for APC models with one RE, treating one effect as an RE is equivalent to constraining the estimates of that effect's linear component and the random intercept to be zero. For APC models with two RE's, the effective constraints implied by the model depend on the true (i.e., in the data-generating mechanism) non-linear components of the effects that are modeled as RE's, so that the estimated linear components of the RE's are determined by the true non-linear components of those effects. In conclusion, RE-APC models impose arbitrary though highly obscure constraints and thus do not differ qualitatively from other constrained APC estimators.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Constraints in Random Effects Age-Period-Cohort Models

Luo

Hodges

2020

Sociological Methodology

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“…Cohort differentiation is generated by events in particular periods, and resulting effects can have a pronounced latency periods. Moreover, this rationalization contradicts the emergent position, detailed in Keyes et al (2010) and Luo and Hodges (2020b), that age effects must be understood as always varying by period, at least potentially, or else the cohort differentiation that generates cohort effects cannot itself emerge.…”

Section: Characterization Of the Estimands Of Interestmentioning

confidence: 93%

A Rolling Panel Model of Cohort, Period, and Aging Effects for the Analysis of the General Social Survey

Morgan¹,

Lee²

2021

Preprint

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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 (GSS) from 2006 through 2014. While the model does not offer a general solution for the identification of the classical age-period-cohort (APC) 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.

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“…I review below four models that are not on the line of solutions, and suggest why they will typically have results that approximate the estimable functions noted in this article. I begin with two‐factor models that use residuals to estimate the third factor's effects 27,28 Then I discuss the factor‐characteristic models, 29,30 the mixed model age‐period‐cohort (MMAPC) approach, 31,32 and Bayesian age‐period‐cohort models 33,34 …”

Section: Which Apcmc Models Produce Estimable Functionsmentioning

confidence: 99%

“…These models are identified, since they do not include the third factor in the equation. Hobcraft et al 27 and Luo and Hodges 28 treat cohorts as the left out factor. They then estimate cohort effects as the mean of the residuals along the cohort diagonals.…”

Section: Which Apcmc Models Produce Estimable Functionsmentioning

confidence: 99%

A simplified approach for establishing estimable functions in fixed effectage‐period‐cohortmultiple classification models

O’Brien

2020

Statistics in Medicine

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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.”

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The Age-Period-Cohort-Interaction Model for Describing and Investigating Inter-cohort Deviations and Intra-cohort Life-course Dynamics

Cited by 56 publications

References 101 publications

Constraints in Random Effects Age-Period-Cohort Models

Constraints in Random Effects Age-Period-Cohort Models

A Rolling Panel Model of Cohort, Period, and Aging Effects for the Analysis of the General Social Survey

A simplified approach for establishing estimable functions in fixed effectage‐period‐cohortmultiple classification models

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