Analysis of ordinal longitudinal data using semi-parametric mixed models

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.


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