An application of Measurement error evaluation using latent class analysis

‎Latent class analysis (LCA) is a method of evaluating non sampling errors‎, ‎especially measurement error in categorical data‎. ‎Biemer (2011) introduced four latent class modeling approaches‎: ‎probability model parameterization‎, ‎log linear model‎, ‎modified path model‎, ‎and graphical model using path diagrams‎. ‎These models are interchangeable‎. ‎Latent class probability models express likelihood of cross-classification tables in term of conditional and marginal probabilities for each cell‎. ‎In this approach model parameters are estimated using EM algorithm‎. ‎To test latent class model chi-square statistic is used as a measure of goodness-of-fit‎. ‎In this paper we use LCA and data from a small-scale survey to estimate misclassification error (as a measurement error) of students who had at least a failing grade as well as misclassification error of students with average grades below 14‎.