Simple State-Space Models in a Mixed Model Framework

Abstract

State-space models play a central role in time series analysis. Biological time series, which present trend, seasonal, and cyclic fluctuations, can be well described by such models. In addition, biological experiments and surveys often have a relatively complex design structure calling for special attention. It is straightforward to account for design effects in a mixed linear model framework. This article shows how simple state-space models can be cast as a standard mixed model, provided the transition matrix of the state equation has a simple form. This opens up the opportunity for refined modeling of time series data involving complex blocking and treatment structures. Conversely, the state-space model gives rise to a special class of variance-covariance structures. Thus, integrating state-space components into a mixed model broadens the class of variance-covariance structures that may be employed to model serial correlation in longitudinal data. The approach is illustrated using several biological examples.