Understanding Individual-level Change Through the Basis Functions of a Latent Curve Model

Latent curve models have become a popular approach to the analysis of longitudinal data. At the individual level, the model expresses an individual’s response as a linear combination of what are called “basis functions” that are common to all members of a population and weights that may vary among individuals. This article uses differential calculus to define the basis functions of a latent curve model. This provides a meaningful interpretation of the unique and dynamic impact of each basis function on the individual-level response. Examples are provided to illustrate this sensitivity, as well as the sensitivity of the basis functions, to changes in the measure of time.