Misspecification and flexible random effect distributions in logistic mixed effects models applied to panel survey data

Abstract

Logistic mixed models for binary longitudinal panel data typically assume normal distributed random effects, and appropriately account for correlated data, unobserved heterogeneity and missing data due to attrition. However, this normality assumption may be too restrictive to capture unobserved heterogeneity. The motivating case study is a longitudinal analysis of women's employment participation using data from the Household Income and Labour Force Dynamics in Australia (HILDA) survey. Multimodality of the random effects was identified, potentially due to an underlying mover-stayer scenario.This study focuses on logistic mixed models applied to the HILDA case study and simulation studies motivated by the case study, and aims to investigate:1. robustness of random intercept logistic models to the assumed normal random effects distribution when the true distribution is multimodal 2. whether relaxing the parametric assumption of the random effects distribution can provide a practical solution to reduce the impact of distributional misspecification 3. impact of misspecification and performance of logistic mixed models in the presence of missing data due to attrition.Random intercept logistic models applied to the case study demonstrate that the assumed normal distribution may not adequately capture the underlying heterogeneity due to a potential moverstayer scenario. An asymmetric three component mixture of normal distributions provided a more appropriate fit, potentially representing three sub-populations: those with an extremely low, moderate, or extremely high propensity to be constantly employed.Two simulation studies motivated by the HILDA study considered a three component mixture of normal distributions for the random intercept. The inferential impact of incorrectly assuming a normal distribution was dependent on the severity of departure of the true distribution from normality. In the first study, simulating a potential mover-stayer scenario, misspecification produced biased estimates of the intercept constant and random effect variance. More severely asymmetric and skewed multimodal distributions produced larger bias. The second study considered a range of true symmetric multimodal distributions, with increasing severity in departures from normality. The random intercept logistic model assuming normality was robust to minor deviations. However, for larger departures characterised by three distinct modes, ii misspecification produced biased parameter estimates and poor coverage rates for the intercept constant, time-invariant explanatory variables and those time-varying explanatory variables exhibiting minimal within-individual variability. For both simulation studies, estimates of the random effect variance were extremely sensitive to distributional misspecification, resulting in biased parameter estimates, poor coverage rates and inaccurate standard errors.Non-parametric estimation techniques, which leave the distribution completely unspecified, reduced the risks associated with misspecification o...