Care Needed When Using Latent Basis Functions of Change
A common challenge when modeling repeated measures data is finding the linear or nonlinear shape that best characterizes the observed pattern of change over time. The SEM-based latent curve model offers several options for modeling nonlinearity, and a particularly flexible method is to freely estimate a subset of factor loadings to define a “latent basis curve”. Although commonly used in practice, there are very important proportionality assumptions that must be met for proper interpretation of the means and variances of the latent basis factors. A recent paper by Wu and Lang (2016) clearly demonstrates that when the proportionality assumption is violated the latent basis model will force the individual trajectories to conform to the assumption and this in turn biases the model estimates. The authors recommend a strategy in which multiple alternative nonlinear functions are evaluated in addition to the latent basis models so that the optimal functional form can be identified for a given sample of data.
Wu, W., & Lang, K. M. (2016). Proportionality Assumption in Latent Basis Curve Models: A Cautionary Note. Structural Equation Modeling: A Multidisciplinary Journal, 23, 140-154.