Power of latent growth curve models to detect piecewise linear trajectories

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. This simulation study was designed to investigate the Type I error rates, rates of nonconvergence, and the power of LCMs to detect piecewise linear growth and mean differences in the slopes of the 2 joined longitudinal processes represented by the piecewise model. The impact of 7 design factors was examined: number of time points, growth magnitude (slope mean), interindividual variability, sample size, position of the turning point, and the correlation of the intercept and the second slope as well between the 2 slopes. The results show that previous results based on linear LCMs cannot be fully generalized to a nonlinear model defined by 2 linear slopes. Interestingly, design factors specific to the piecewise context (position of the turning point and correlation between the 2 growth factors) had some effects on the results, but these effects remained minimal and much lower than the effects of other design factors. Similarly, observed rates of inadmissible solutions are comparable to those previously reported for linear LCMs. The major finding of this study is that a moderate sample size (N = 200) is needed to detect piecewise linear trajectories, but that much larger samples (N = 1,500) are required to achieve adequate statistical power to detect slope mean difference of small magnitude.