Penalized likelihood estimation and iterative kalman smoothing for non-gaussian dynamic regression models

Dynamic regression or state space models provide a flexible
framework for analyzing non-Gaussian time series and longitudinal
data, covering for example models for discrete longitudinal
observations. As for non-Gaussian random coefficient models, a
direct Bayesian approach leads to numerical integration problems,
often intractable for more complicated data sets. Recent Markov
chain Monte Carlo methods avoid this by repeated sampling from
approximative posterior distributions, but there are still open
questions about sampling schemes and convergence. In this article
we consider simpler methods of inference based on posterior modes
or, equivalently, maximum penalized likelihood estimation. From the
latter point of view, the approach can also be interpreted as a
nonparametric method for smoothing time-varying coefficients.
Efficient smoothing algorithms are obtained by iteration of common
linear Kalman filtering and smoothing, in the same way as
estimation in generalized linear models with fixed effects can be
performed by iteratively weighted least squares estimation. The
algorithm can be combined with an EM-type method or
cross-validation to estimate unknown hyper- or smoothing
parameters. The approach is illustrated by applications to a binary
time series and a multicategorical longitudinal data set.