Proportionality Assumption in Latent Basis Curve Models: A Cautionary Note

Abstract

Latent basis curve models (LBCMs) have been popular in modeling change when the change trajectories are unknown or nonlinear. The estimated change trajectories from LBCMs are often viewed as optimal and used as reference points against which other change trajectories are tested. However, there is a proportionality assumption underlying LBCMs that has received little attention from researchers. This study uses a Monte Carlo simulation to show that violation of this assumption can potentially result in substantially biased estimates of the means and variances of changes and covariate effects on these changes, leading to incorrect statistical inference. The implications of the simulation study are discussed and alternatives to LBCMs are suggested for use when the proportionality assumption is likely to be violated.

Keywords:

• latent basis curve model
• level and shape model
• proportionality assumption
• growth curve

Notes

¹ In the original study, the covariance between the intercept and the linear slope was –3.69, the covariance between the intercept and the quadratic slope was –1.36, and the covariance between the linear and quadratic slopes was –4.96. We found the covariance between the linear and quadratic slopes caused convergence problems for the LBCM (251 out of 1,000 replications failed to converge). Fixing this covariance to 0 or changing it from negative to positive (i.e., 4.96) solved the convergence problem. This implies that the LBCM might be poorly suited to capturing certain covariance patterns, particularly when the proportionality assumption is violated. Future work is needed to further investigate this issue. Excluding the covariances between growth parameters did not affect the major results of our study, so we chose to fix these covariances to 0 in the interests of parsimony.

² The mean intercept, mean linear slope, and mean quadratic slope were 2, –1, and 0.2, respectively, with variances of 1, 0.01, and 0.01, respectively. The residual variances were constrained to be equal to 1 across time. The growth parameters were not correlated.