Structured latent curve models for the study of change in multivariate repeated measures

Abstract

This article considers a structured latent curve model for multiple repeated measures. In a structured latent curve model, a smooth nonlinear function characterizes the mean response. A first-order Taylor polynomial taken with regard to the mean function defines elements of a restricted factor matrix that may include parameters that enter nonlinearly. Similar to factor scores, random coefficients are combined with the factor matrix to produce individual latent curves that need not follow the same form as the mean curve. Here the associations between change characteristics in multiple repeated measures are studied. A factor analysis model for covariates is included as a means of relating latent covariates to the factors characterizing change in different repeated measures. An example is provided.