A Latent Class Covariate Model with Applications to Criterion-Referenced Testing

Abstract

Modern developments of latent class models as pioneered by Lazarsfeld and Henry (1968) and extended by Proctor (1970), Goodman (1974, 1975), Haberman (1974, 1979), Dayton and Macready (1976, 1980a), and others have found a variety of applications in the social and behavioral sciences. An area of special interest has been criterion referenced testing, where latent class models offer an attractive and powerful alternative to latent trait models (Macready & Dayton, 1980). Latent class models can directly represent mastery/nonmastery status and have the advantage of permitting an objective determination of cutting scores for mastery classification (Macready & Dayton, 1977). Recently, there has been interest in extending latent class models to include information from concomitant variables, or covariates. Although categorical concomitant variables (i.e., variables used to group respondents) can be incorporated systematically into current latent class formulations (Clogg & Goodman, 1984, 1985, 1986; Macready & Dayton, 1980) and estimation carried out using available computer programs (e.g., Clogg, 1977), this chapter develops a more general model in which latent class membership is functionally related to one or more categorical and/or continuous concomitant variables (see Dayton & Macready, 1980b for a restricted model of this type).