Parameter Identifiability Issues in a‎ ‎Latent Ma‎- ‎rkov Model for Misclassified Binary Responses

Medical researchers may be interested in disease processes‎ ‎that are not‎ ‎directly observable‎. ‎Imperfect diagnostic‎ ‎tests may be used repeatedly to monitor the‎ ‎condition of a patient in the absence of a gold standard.‎ ‎We consider parameter identifiability and estimability‎ ‎in a Markov model for alternating binary longitudinal ‎responses that may be misclassified.‎ ‎Exactly two distinct sets of parameter values are shown to‎ ‎generate the distribution for the data in a common situation and we propose ‎a restriction to distinguishes the two‎. ‎Even with the restriction‎, ‎parameters‎ ‎may not be estimable‎. ‎Issues of sampling and correct model specification ‎are discussed.‎