Modelling inter-individual differences in latent within-person variation: The confirmatory factor level variability model

Psychological theories often produce hypotheses that pertain to individual differences in within-person variability. To empirically test the predictions entailed by such hypotheses with longitudinal data, researchers often use multilevel approaches that allow them to model between-person differences in the mean level of a certain variable and the residual within-person variance. Currently, these approaches can be applied only when the data stem from a single variable. However, it is common practice in psychology to assess not just a single measure but rather several measures of a construct. In this paper we describe a model in which we combine the single-indicator model with confirmatory factor analysis. The new model allows individual differences in latent mean-level factors and latent within-person variability factors to be estimated. Furthermore, we show how the model's parameters can be estimated with a maximum likelihood estimator, and we illustrate the approach using an example that involves intensive longitudinal data.