Interaction Effects in Latent Growth Models: Evaluation of Alternative Estimation Approaches

Abstract

The purpose of this investigation is to compare and evaluate 2 approaches for estimating interaction effects in latent growth models (LGMs): the unconstrained approach and the latent moderated structural equations (LMS) approach. To reduce the complexity of modeling interactions in LGMs, we created difference-product indicators to replace the traditional product indicators used in the unconstrained approach because these differences in original indicators represent changes over time. Our focus was to verify the performance of this simplified interaction model of LGMs with difference-product indicators by using the unconstrained approach and comparing it with the LMS approach. Our simulation study showed that the LMS approach generally resulted in smaller biases in the estimated parameters and was consistently more precise than the unconstrained approach under normal conditions, particularly when the sample size was small. When normality assumptions were violated, however, the unconstrained approach was shown to be more robust than the LMS approach in terms of the bias of estimation. In summary, we generally recommend both the unconstrained approach and the LMS approach if the indicators are normally distributed and when the sample size is large enough (e.g., not less than 500). Under normal conditions, the LMS approach is preferred. If normality assumptions are violated, however, the unconstrained approach is recommended. Under the most stringent conditions when normality assumptions are severely violated and the sample size is small, the results from both the unconstrained approach and the LMS approach should be treated with caution, and alternative procedures might be considered.

Keywords:

• initial level
• interaction effect
• latent growth model
• latent moderated structural equation
• rate of change
• unconstrained approach

Notes

1. ¹For the calculations, please refer to Wen et al. (2002, Formulas 4–6). If the means of and are zero, the interaction effect term accounts for 5.4% of .