Title: Application of ordered latent class regression model in educational assessment
Description: Latent class analysis is a useful tool to deal with discrete multivariate response data. Croon (1990) proposed the ordered latent class model where latent classes are ordered by imposing inequality constraints on the cumulative conditional response probabilities. Taking stochastic ordering of latent classes into account in the analysis of data gives a meaningful interpretation, since the primary purpose of a test is to order students on the latent trait continuum. This study extends Croon's model to ordered latent class regression that regresses latent class membership on covariates (e.g., gender, country) and demonstrates the utilities of an ordered latent class regression model in educational assessment using data from Trends in International Mathematics and Science Study (TIMSS). The benefit of this model is that item analysis and group comparisons can be done simultaneously in one model. The model is fitted by maximum likelihood estimation method with an EM algorithm. It is found that the proposed model is a useful tool for exploratory purposes as a special case of nonparametric item response models and cross-country difference can be modeled as different composition of discrete classes.

Simulations is done to evaluate the performance of information criteria (AIC and BIC) in selecting the appropriate number of latent classes in the model. From the simulation results, AIC outperforms BIC for the model with the order-restricted maximum likelihood estimator.