Latent Markov Model
The SAGE Encyclopedia of Social Science Research Methods · 2004
The latent Markov model (LMM) can either be seen as an extension of the latent class model for the analysis of longitudinal data or as an extension of the discrete-time Markov chain model for dealing with measurement error in the observed variable of interest. It was introduced in 1955 by Wiggins and also referred to as latent transition or hidden Markov model. The LMM used to separate true systematic change from spurious change resulting from measurement error and other types of randomness in the behavior of individuals. Suppose a single categorical variable of interest is measured at T occasions, and that Yt denote the response at occasion t, 1 ≤ t ≤ T . This could, for example, be a respondent’s party preference measured at 6-month intervals. Let D denote the number of levels of each Yt, and yt a particular level, 1 ≤ yt ≤ D. Let Xt denote an occasion-specific latent variable, C number of categories of Xt, and xt a particular LC class at occasion t, 1 ≤ xt ≤ C. The corresponding LMM has the form