Statistical power of latent growth curve models to detect quadratic growth

Latent curve models (LCMs) have been used extensively to analyze longitudinal data. However, little is known about the power of LCMs to detect nonlinear trends when they are present in the data. For this study, we utilized simulated data to investigate the power of LCMs to detect the mean of the quadratic slope, Type I error rates, and rates of nonconvergence during the estimation of quadratic LCMs. Five factors were examined: the number of time points, growth magnitude, interindividual variability, sample size, and the R(2)s of the measured variables. The results showed that the empirical Type I error rates were close to the nominal value of 5 %. The empirical power to detect the mean of the quadratic slope was affected by the simulation factors. Finally, a substantial proportion of samples failed to converge under conditions of no to small variation in the quadratic factor, small sample sizes, and small R-2 of the repeated measures. In general, we recommended that quadratic LCMs be based on samples of (a) at least 250 but ideally 400, when four measurement points are available; (b) at least 100 but ideally 150, when six measurement points are available; (c) at least 50 but ideally 100, when ten measurement points are available.