A model for incomplete longitudinal multivariate ordinal data.

In studies where multiple outcome items are repeatedly measured over time, missing data often occur. A longitudinal item response theory model is proposed for analysis of multivariate ordinal outcomes that are repeatedly measured. Under the MAR assumption, this model accommodates missing data at any level (missing item at any time point and/or missing time point). It allows for multiple random subject effects and the estimation of item discrimination parameters for the multiple outcome items. The covariates in the model can be at any level. Assuming either a probit or logistic response function, maximum marginal likelihood estimation is described utilizing multidimensional Gauss-Hermite quadrature for integration of the random effects. An iterative Fisher-scoring solution, which provides standard errors for all model parameters, is used. A data set from a longitudinal prevention study is used to motivate the application of the proposed model. In this study, multiple ordinal items of health behavior are repeatedly measured over time. Because of a planned missing design, subjects answered only two-third of all items at a given point. Copyright 2008 John Wiley & Sons, Ltd.