Combined Logistic and Confined Exponential Growth Models: Estimation Using SEM Software

Abstract

The logistic and confined exponential curves are frequently used in studies of growth and learning. These models, which are nonlinear in their parameters, can be estimated using structural equation modeling software. This paper proposes a single combined model, a weighted combination of both models. Mplus, Proc Calis, and lavaan code for the model are provided. Monte Carlo simulations varying the number of measurement occasions (5, 10, and 15), internal consistency (α = 0.5, 0.7, and 0.8), and sample size (N = 1,000, 500, and 300) were examined to understand whether the model can be successfully fit with SEM software. Convergence failures were appreciable when model parameters were equal to special cases of logistic or confined exponential curves. At least ten measurement occasions and a moderate degree of reliability (α > 0.7) were required to identify the model as superior to its stand-alone alternatives.