A class of linear spectral models and analyses for the study of longitudinal data

Longitudinal data can always be represented by a time series with a deterministic trend and randomly correlated residuals, the latter of which do not usually form a stationary process. The class of linear spectral models is a basis for the exploratory analysis of these data. The theory and techniques of factor analysis provide a means by which one component of the residual series can be separated from an error series, and then partitioned into a sum of randomly scaled metameters that characterize the sample paths of the residuals. These metameters, together with linear modelling techniques, are then used to partition the nonrandom trend into a determined component, which is associated with the sample paths of the residuals, and an independent inherent component. Linear spectral models are assumption-free and represent both random and nonrandom trends with fewer terms than any other mixed-effects linear model. Data on body-weight growth of juvenile mice are used in this paper to illustrate the application of linear spectral models, through a relatively sophisticated exploratory analysis.