<p>Hidden Markov models (HMMs) are gaining popularity for analyzing multivariate longitudinal datasets wherein state switching of subjects is desirable; however, over-parameterization remains an issue. Thus, parsimonious HMMs are essential for the analysis of such data. In model-based clustering, it is common to introduce parsimony via a series of constraints on decomposed state covariance matrices. This approach for handling over-parameterization is applied to HMMs for longitudinal data. Specifically, two families of HMMs are developed: one arising from an eigen-decomposition of the state covariance matrices and another resulting from a latent Gaussian mixture. In the latter case, further parsimony is introduced by imposing constraints on the resulting factor analysis covariance structure. The performance of the introduced approaches is compared on various simulated and real datasets.</p>