Multisample Analysis of Multivariate Ordinal Categorical Variables

We study a multiple group model with ordinal categorical observed variables that are manifestations of underlying normal variables. When the objective of an analysis is to compare the locations and dispersions of the underlying continuous variables in different groups, traditional approaches use exact linear constraints on thresholds across groups to identify the model. Though the resultant model facilitates interpretation in multiple group analysis, in some cases the exact linear relationships on thresholds are not appropriate for describing the reality. However, these constraints must be imposed to identify the model. In view of this, we propose to apply across group stochastic constraints on thresholds to identify the model. Stochastic constraints are more practical and flexible than exact constraints, and subsume exact constraints as a special case, and therefore enable the structure of the data to be described in a more realistic way. Using stochastic constraints, we can achieve an identified model that allows the comparison of underlying continuous variables in different groups relatively, and at the same time accommodate the possible differences in thresholds. A Bayesian approach is employed to analyze the model, and prior knowledge can be incorporated into the analysis. It is demonstrated that the parameter estimates can be produced conveniently using the Mx software program, and an illustrative sample Mx input script is presented. A real data set is analyzed with the proposed approach, and results are compared to those obtained by using other prevailing approaches.