ABSTRACT
This chapter discusses the second-order latent curve model to handle nonlinear response functions for the latent variables by allowing model parameters to enter nonlinearly. It provides an extension of the structured latent curve model to handle multiple indicators of a latent variable whose mean may follow a nonlinear function. The model, like its predecessors, may also include a common factor model for covariates observed at either the level of the measurement occasion or at the level of the individual. Factorial invariance in longitudinal investigations generally concerns the comparability of factor structure across measurement occasions. An alternative to directly specifying a form of change, such as by a linear or piecewise linear spline, is to consider a latent basis curve model. The latent basis curve model is appropriate for situations in which individuals have been observed at the same times, though naturally there is allowance for missing data.
