Hybrid logistic and confined exponential growth models : estimation using SEM software

Abstract

The logistic and confined exponential curves represent growth over time in various contexts such as learning and technology transfer. Logistic growth operates as a contagion process in a population of interest, while the confined exponential curve represents the diffusion of an external process on a system, such as the transfer of information through communication channels. Prior work (e.g., Grimm and Ram, 2009) has shown that such nonlinear curves can be estimated using structural equation modeling (SEM) software, allowing model comparison. As an alternative to binary choice between such models, this paper shows how a hybrid model representing a weighted combination of the two models may be specified. In order to assess whether the hybrid model can be successfully estimated using SEM software and conditions under which it can be successfully differentiated from the stand-alone logistic and confined exponential alternatives, Monte Carlo simulations varying the number of measurement occasions (5, 10, and 15), internal consistency ([alpha] = .5, .7, and .8), and sample size (N = 1,000, 500, and 300) were conducted. Convergence failures appeared appreciable only when the estimated hybrid models were the special cases of logistic or confined exponential curves. The hybrid model was successfully preferred over the stand-alone models when 10 or 15 measurement occasions are employed and when internal consistency is moderate ([alpha] = .7 or .8) across all sample sizes but not when only five measurement occasions are used or when internal consistency is low ([alpha] = .5). Implications for the application of the hybrid model to learning, growth, and psychopathology are discussed.