Latent Growth Modeling for Logistic Response Functions

Throughout much of the social and behavioral sciences, latent growth modeling (latent curve analysis) has become an important tool for understanding individuals' longitudinal change. Although nonlinear variations of latent growth models appear in the methodological and applied literature, a notable exclusion is the treatment of growth following logistic (sigmoidal; S-shape) response functions. Such trajectories are assumed in a variety of psychological and educational settings where learning occurs over time, and yet applications using the logistic model in growth modeling methodology have been sparse. The logistic function, in particular, may not be utilized as often because software options remain limited. In this article we show how a specialized version of the logistic function can be modeled using conventional structural equation modeling software. The specialization is a reparameterization of the logistic function whose new parameters correspond to scientifically interesting characteristics of the growth process. In addition to providing an example using simulated data, we show how this nonlinear functional form can be fit using transformed subject-level data obtained through a learning task from an air traffic controller simulation experiment. LISREL syntax for the empirical example is provided.