Concomitant-Variable Latent-Class Models

Abstract This article introduces and illustrates a new type of latent-class model in which the probability of latent-class membership is functionally related to concomitant variables with known distribution. The function (or so-called submodel) may be logistic, exponential, or another suitable form. Concomitant-variable models supplement latent-class models incorporating grouping by providing more parsimonious representations of data for some cases. Also, concomitant-variable models are useful when grouping models involve a greater number of parameters than can be meaningfully fit to existing data sets. Although parameter estimates may be calculated using standard iterative procedures such as the Newton—Raphson method, sample analyses presented here employ a derivative-free approach known as the simplex method. A general procedure for imposing linear constraints on the parameter estimates is introduced. A data set involving arithmetic test items in a mastery testing context is used to illustrate fitting and comparison of concomitant-variable models.