Misspecification of Multimodal Random-Effect Distributions in Logistic Mixed Models for Panel Survey Data

Abstract

Summary Logistic mixed models for longitudinal binary data typically assume normally distributed random effects, which may be too restrictive if an underlying subpopulation structure exists. The paper illustrates the ease of implementing diagnostic tests and fitting random effects as a mixture of normal distributions to detect and address distributional misspecification of the random effects in a potential mover–stayer scenario. Methods are illustrated by using data from the Household, Income and Labour Dynamics in Australia panel survey. The robustness of the normality assumption to violations characterized by a three‐component mixture of normal distributions was assessed via a simulation study. Adverse inferential impact of incorrectly assuming normality was identified for parameters directly related to the random effects, resulting in biased estimates and poor coverage rates for confidence intervals. The results support the general robustness of fixed effect parameters to non‐extreme distributional violations of the random effects.

Generalized quasi-linear mixed-effects model

“…However, many researchers have been concerned that the incorrect assumption may lead to substantial asymptotic bias in the maximum likelihood estimates of the regression parameters when the assumption for a random effect is violated. [9][10][11][12] Moreover, the type I error and the power for a test associated with regression parameter are also affected. 13,11 Various inferential methods have been developed to address the misspecification issues (for example, see 14,15,10,1 ).…”

Exploratory assessment of treatment‐dependent random‐effects distribution using gradient functions

“…10,11 Verbeke and Molenberghs (2013) illustrated the use of the gradient function method combined with a finite mixture of normals, proposed by Verbeke and Lesaffre (1996), instead of using the simple normality assumption on random-effects distribution. Although mixtures of normals are very flexible and may offer very simple interpretations, 11,12 it is often difficult to obtain stable solutions. Therefore, it was suggested that a finite mixture of normals for random-effects distributions could be incorporated into a general sensitivity analysis.…”

“…Therefore, it was suggested that a finite mixture of normals for random-effects distributions could be incorporated into a general sensitivity analysis. 5 Insights from the gradient function can be utilized in model construction in this framework, 11,12 and can also be applied to research involving joint modeling of longitudinal measurements and survival time. 13 In addition to the normality assumption, dependence of the random-effects variance on covariates is also an important issue.…”