The Latent Markov Chain with Multivariate Random Effects

An analytically tractable latent Markov chain with correlated random effects from Gamma distributions is developed by combining techniques developed in latent class modeling and random effects modeling of survival and recurrent binary events data. Continuous unobserved heterogeneity in both classification error and latent class membership is allowed for. The model is used to compare a number of instruments that measure male labor market status in the British Household Panel Survey. Instrument specific, correlated random effects for classification errors are specified. Although the presented methodology is limited to binary events and specific distributional forms for the random effects, the analysis illustrates the importance of trying to understand and allow for potential complexities in classification error processes, if measurement error adjustments are to be relied on. The standard result of such analyses, that nontreatment of dependent classification errors leads to underestimation of the number of “changers,†is emphasized here.