General linear models for the analysis of single subject data and for the comparison of individuals

Abstract

In longitudinal person-oriented and idiographic research, individual-specific parameter estimation is strongly preferred over estimation that is based on aggregated raw data. In this article, we ask whether methods of the General Linear Model, that is, repeated measures ANOVA and regression, can be used to estimate individual-specific parameters. Scenarios and corresponding design matrices are presented in which the shape of temporal trajectories of individuals is parameterized. Real world data examples and simulation results suggest that, for series of sufficient length, trajectories can be well described for individuals. In addition, scenarios are presented for the comparison of two individuals. Here again, trajectories can be well described and the statistical comparison of individuals is possible. However, in contrast to the power for the description of individual series, which is satisfactory, the power for the comparison of individuals is low (except when effect sizes are large). In all simulated scenarios, the power of tests increases only up to a certain number of observation points, and reaches a ceiling at this number. The fact that all parameters cannot always be estimated is also discussed, and options are presented that go beyond what standard general purpose software packages offer.