Detecting sigmoidal trajectories in structured latent curve models : a fit measure performance and parameter recovery simulation study.

This simulation study examined parameter estimate recovery and model selection of structured latent curve models under varying conditions to provide recommendations on how to properly format longitudinal research when there is an a priori hypothesis of sigmoidal growth. To examine model selection, sigmoidal models were generated using the first order Taylor series approximation method detailed in Browne and du Toit (1991) and analyzed as sigmoidal, linear, quadratic, and cubic. Eleven fit measures were assessed to determine their performance in selecting true sigmoidal models over competing incorrect models. The information criteria examined were the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Bayesian Information Criterion with the Sclove sample size penalty adjustment (aBIC), Consistent AIC (CAIC), Draper Information Criterion (DIC), the Hannan and Quinn adjustment of AIC (HQ), and Sugiura's adjustment of the AIC (AICc). Other fit measures investigated were the Comparative Fit Index (CFI), the Tucker-Lewis Index (TLI), the Root Mean Square Error of Approximation (RMSEA), and the Standardized Root Mean Residual (SRMR). Parameter estimates were recovered from converged correctly specified sigmoidal models to assess the amount of bias present. Manipulated design factors for this study included sample size (50, 100, 200, 500, 1,000, and 1,500), the number of repeated measures (six, eight, and 10), the location of the inflection point within the measurement window (δ*= .25, .375, .5), and the rate of change at the inflection point (ρ* = .125, .1875, .25). In addition to model selection and parameter estimate bias, convergence proportions, coverage, and standard error bias were also investigated. Results and recommendations are provided within.