Constraints in Random Effects Age-Period-Cohort Models

by   Liying Luo, et al.

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.


varTestnlme: Variance Components Testing in Linear and Nonlinear Mixed-effects Models

The issue of variance components testing arises naturally when building ...

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

Social scientists have frequently sought to understand the distinct effe...

Inference for high-dimensional linear mixed-effects models: A quasi-likelihood approach

Linear mixed-effects models are widely used in analyzing clustered or re...

Spiked covariances and principal components analysis in high-dimensional random effects models

We study principal components analyses in multivariate random and mixed ...

Consistent Fixed-Effects Selection in Ultra-high dimensional Linear Mixed Models with Error-Covariate Endogeneity

Recently, applied sciences, including longitudinal and clustered studies...

Gaussian linear approximation for the estimation of the Shapley effects

In this paper, we address the estimation of the sensitivity indices call...