Rejoinder on: Latent Markov models: a review of a general framework for the analysis of longitudinal data with covariates

Abstract

First of all, we thank all the Discussants and the four Referees for their contribution. They helped us to clarify some of the features of the methodology and to answer questions we had in writing the paper; they also stimulated us to consider new interesting issues. All Discussants mention additional important applications, including interesting examples in areas like language processing, psychology, and finance. Their contribution strengthen our original message about the mathematical and analytical flexibility of the proposed Latent Markov (LM) framework, and especially about the usefulness in many areas of application in which LM models can be seen to arise as observation-driven models (Cox, 1981). Furthermore, their comments confirm that generalizations of current LM models can often be directly obtained with minor adjustments to inference. In the following we comment on some of the issues raised by the Discussants. Bockenhold and McShane mention a very interesting and parsimonious extension of the first-order model, which can also include non-memoryless holding times. This is potentially very interesting as in many cases persistency in latent states is stronger than the model predicts, and related to the literature on semi-Markov models and hidden semi-Markov models, which are also mentioned by Visser and Speekenbrink.