| In biomedical or public health research, outcomes of interest are often clustered ordinal variables. For instance, in longitudinal studies with multiple ordinal outcomes, multiple outcomes (level-1) are nested within measurement occasions (level-2), which are nested within individuals (level-3). Here, a model allowing a measurement model for the multiple outcomes (e.g., a factor analysis model) with multiple random subject effects to account for the longitudinal aspect of the design is needed. Such a model is possible for continuous outcomes, but not for categorical outcomes.; In this research, a three-level mixed-effects model for longitudinal multivariate ordinal outcome is developed. Specifically, an item response theory (IRT) measurement model (which is essentially a categorical version of a factor analysis model) accounts for the multiple ordinal outcomes at a given timepoint. This model allows these ordinal outcomes to have different factor loadings. A latent factor score is derived for each subject at each timepoint. To relate changes in these latent factor scores across the multiple timepoints, the model includes multiple random effects at the subject level (e.g., intercepts and slopes). This model also allows for a general form of covariates, thus covariates can be at any level. Parameter estimation is based on full-information maximum marginal likelihood estimation (MMLE) using multidimensional quadrature to numerically integrate over the distribution of random effects. An iterative Fisher-scoring solution, which converges faster than the EM algorithm, is used.; The accuracy of the parameter estimation of the proposed three-level mixed-effects model was investigated by a simulation study. To illustrate the application of the model, a substance-use data set of African American fifth- to eighth-graders from the ABAN AYA prevention study is used. In this study, multiple ordinal items of substance use behavior (cigarette use, alcohol use, marijuana use, and getting drunk and high) were repeatedly measured over the years. For both the simulation study and the data analysis, results show that the proposed model is superior to simpler models. |
