Marginalizable conditional model for clustered ordinal data

TL;DR

This paper presents a flexible mixed effects model for clustered ordinal data that provides interpretable marginal odds ratios, robust estimation, and accommodates complex correlation structures, demonstrated through simulations and real data analyses.

Contribution

It introduces a novel marginalizable conditional model for clustered ordinal data with robust estimation and flexible correlation modeling, improving interpretability and efficiency.

Findings

Robust estimation with low efficiency loss compared to maximum likelihood

Consistent marginal parameter estimation under model misspecification

Effective modeling of complex correlation structures

Abstract

We introduce a flexible parametric mixed effects model for correlated binary data, with parameters that can be directly interpreted as marginal odds ratios. This leads to a robust estimation equation with an optimal weighting matrix being the inverse of a genuine model-based covariance matrix. Flexible correlation structures can be imposed by correlated random effects, and correlation parameters can be estimated by solving a composite likelihood score function. Marginal parameters are consistently estimated even when the conditional parametric model is misspecified, and the robust estimation procedure has low estimation efficiency loss compared to the maximum likelihood estimation under a correct model specification. Simulations, analyses of the Madras longitudinal schizophrenia study and British social attributes panel survey were carried out to demonstrate our method.