Parsimonious Hidden Markov of Factor Analyzers models are developed by using a modified factor analysis covariance structure. This framework can be seen as a extension of the Parsimonious Gaussian mixture models (PGMMs) accounting for heterogeneity in a longitudinal setting. In particular, a class of 12 models are in- troduced and the maximum likelihood estimates for the parameters in these models are found using an AECM algorithm. The class of models includes parsimonious models that have not previously been developed. The performance of these models is discussed on a benchmark gene expression data. The results are encouraging and would deserve further discussion.

Parsimonious Hidden Markov of Factor Analyzers models are developedby using a modified factor analysis covariance structure. This framework can be seenas a extension of the Parsimonious Gaussian mixture models (PGMMs) accountingfor heterogeneity in a longitudinal setting. In particular, a class of 12 models are in-troduced and the maximum likelihood estimates for the parameters in these modelsare found using an AECM algorithm. The class of models includes parsimoniousmodels that have not previously been developed. The performance of these modelsis discussed on a benchmark gene expression data. The results are encouraging andwould deserve further discussion.