Dynamic analysis of multivariate panel data with nonlinear transformations

Many models for multivariate data analysis can be seen as special cases of the linear dynamic or state space model. Contrary to the classical approach to linear dynamic systems analysis, the model presented here is developed from the social science framework of approximation, data reduction and interpretation, where generalization is required not only over time points but over subjects as well. Borrowing concepts from the theory on mixture distributions, the linear dynamic model can be viewed as a multilayered regression model, in which the output variables are imprecise manifestations of an unobserved continuous process. An additional layer of mixing makes it possible to incorporate non-normal as well as ordinal variables. Using the EM-algorithm, we find estimates of the unknown mode parameters, simultaneously providing stability estimates. We illustrate the applicability of the obtained procedure through an empirical example.