Marginally specified models for analyzing multivariate longitudinal binary data

TL;DR

This paper introduces a new three-level marginally specified model for analyzing multivariate longitudinal binary data, providing explicit solutions and an R package for practical implementation.

Contribution

It develops a novel three-level model with explicit solutions for complex constraints, and provides an R package for fitting the model to longitudinal binary data.

Findings

Simulation confirms estimator properties

Model effectively analyzes multivariate binary data

R package facilitates practical application

Abstract

Marginally specified models have recently become a popular tool for discrete longitudinal data analysis. Nonetheless, they introduce complex constraint equations and model fitting algorithms. Moreover, there is a lack of available software to fit these models. In this paper, we propose a three-level marginally specified model for analysis of multivariate longitudinal binary response data. The implicit function theorem is introduced to approximately solve the marginal constraint equations explicitly. Furthermore, the use of \textit{probit} link enables direct solutions to the convolution equations. We propose an R package \textbf{pnmtrem} to fit the model. A simulation study is conducted to examine the properties of the estimator. We illustrate the model on the Iowa Youth and Families Project data set.