Journal of Medical Internet Research - International Scientific Journal for Medical Research, Information and Communication on the Internet

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.

A version of the nonlinear mixed-effects model is presented that allows random effects only on the linear coefficients. Nonlinear parameters are not stochastic. In nonlinear regression, this kind of model has been called conditionally linear. As a mixed-effects model, this structure is more flexible than the popular linear mixed-effects model, while being nearly as straightforward to estimate. In addition to the structure for the repeated measures, a latent variable model ( Browne, 1993 ) is specified for a distinct set of covariates that are related to the random effects in the second level. Unbalanced data are allowed on the repeated measures, and data that are missing at random are allowed on the repeated measures or on the observed variables of the factor analysis sub-model. Features of the model are illustrated by two examples.