A Latent Markov Model to Correct for Measurement Error

Abstract

In classical test theory the reliability of a test can be estimated by test-retest correlation models. These models do not apply to data of the lowest or nominal measurement level. Instead, models for latent Markov chains may be used to correct for measurement error in panel data from three or more waves. In this article it is shown how to use the E-M algorithm for estimating the parameters of a latent Markov chain. Where previous algorithms performed badly on variables with more than two categories this algorithm performs better, although convergence is often slow. The method is applied to two trichotomous questions from the Dutch civil servants panel survey. Generally the assumptions of the model that is, a latent stationary Markov chain, are reasonably well met by the data. The probability of a correct answer, which can be interpreted as the reliability of a latent response category, is high in most cases (about. 8). Also transition tables are presented that are corrected for measurement error according to the model. Standard errors of model parameters are approximated by a finite difference method.