Mixed models, linear dependency, and identification in age‐period‐cohort models

Abstract

This paper examines the identification problem in age-period-cohort models that use either linear or categorically coded ages, periods, and cohorts or combinations of these parameterizations. These models are not identified using the traditional fixed effect regression model approach because of a linear dependency between the ages, periods, and cohorts. However, these models can be identified if the researcher introduces a single just identifying constraint on the model coefficients. The problem with such constraints is that the results can differ substantially depending on the constraint chosen. Somewhat surprisingly, age-period-cohort models that specify one or more of ages and/or periods and/or cohorts as random effects are identified. This is the case without introducing an additional constraint. I label this identification as statistical model identification and show how statistical model identification comes about in mixed models and why which effects are treated as fixed and which are treated as random can substantially change the estimates of the age, period, and cohort effects. Copyright © 2017 John Wiley & Sons, Ltd.

Dynamics of Anthropometric Indices in a Large Paired Cohort With 10 Years of Follow-Up: Paving the Way to Sarcopenic Obesity

“…The age of the individuals was stratified into the following groups: 18-29 years (only in the 2007-2008 period), 30-39, 40-49, 50-59, 60-79, 80-90, and 90-100 years (only in the 2017-2019 period). Data were also evaluated according to the definition of the elderly proposed by the United Nations, and the cut-off of 60 years was used to refer to the older or elderly persons (17).…”

“…On the other hand, longitudinal studies involve information directly gathered in a survey of households or individuals and follow individual persons over time. Longitudinal studies allow researchers to separate the independent effects of age, period, and cohort from trends in overweight and obesity rates (17). However, large paired cohort investigations assessing anthropometric indices between long periods are scarce.…”

Constraints in Random Effects Age-Period-Cohort Models

“…For example, Bell and Jones (2018) showed that the data structure (e.g., the number of A, P, and C categories included in the data) affects the estimates from the RE-APC models markedly. For another example, O'Brien (2017) conjectured that assuming the effect of A, P, or C to be random produces a result similar to constraining that effect's linear trend to be near zero.…”

Mental Health over the Life Course: Evidence for a U-Shape?

“…The use of parameter restrictions has often been criticized (Bell & Jones, 2013Luo & Hodges, 2016;De Ree & Alessie, 2011;O'Brien, 2017). By relying on arbitrary assumptions to reach identification, all of the studies above are likely to suffer from biases of unknown size.…”