Formulating State Space Models in R with Focus on Longitudinal Regression Models
Claus Dethlefsen, Claus Dethlefsen, Søren Lundbye‐Christensen, Søren Lundbye‐Christensen · RePEc: Research Papers in Economics · 2005
Introduction Generalized linear models, see McCullagh and Nelder (1989), are used when analyzing data where response-densities are assumed to belong to the exponential family. Time series of counts may adequately be described by such models. However, if serial correlation is present or if the observations are overdispersed, these models may not be adequate, and several approaches can be taken. The book by Diggle, Heagerty, Liang, and Zeger (2002) gives an excellent review of many approaches incorporating serial correlation and overdispersion in generalized linear models. Dynamic generalized linear models (DGLM), often called state space models, also address those problems and are treated in a paper by West, Harrison, and Migon (1985) in a conjugate Bayesian setting. They have been subject to further research by e.g. Zeger (1988) using generalized estimating equations (GEE), Gamerman (1998) using Markov chain Monte Carlo (MCMC) methods and Durbin and Koopman (1997) using iterated exten