Analysis of ordinal longitudinal data using semi-parametric mixed models

Abstract

A spline mixed item response theory model that allows for three-level multivariate ordinal
outcomes and accommodates multiple random subject effects is proposed for analysis of
ordinal outcomes in longitudinal studies. Assuming cumulative logit model with proportional
odds, maximum marginal likelihood estimation for model parameters is proposed
utilizing Monte Carlo Metropolis Hastings Newton Raphson (MCMHNR) algorithm. An
iterative Fisher scoring solution, which provides standard errors for all model parameters,
is considered. The performance of the estimates of the model parameters in finite samples
has been looked into. A longitudinal orthodontic data set, where plaque content in teeth is
repeatedly measured over time, is used to illustrate application of the proposed model.