A Comparison of Methods for Estimating Relationships in the Change Between Two Time Points for Latent Variables

Collection and analysis of longitudinal data is an important tool in understanding growth and development over time in a whole range of human endeavors. Ideally, researchers working in the longitudinal framework are able to collect data at more than two points in time, as this will provide them with the potential for a deeper understanding of the development processes under study and a much broader array of statistical modeling options. However, in some circumstances data collection is limited to only two time points, perhaps because of resource limitations, issues with the context in which the data are collected, or the nature of the trait under study. In such instances, researchers may still want to learn about complex relationships in the data, such as the correlation between changes in latent traits that are being measured. However, with only two data points, standard approaches for modeling such relationships, such as growth curve modeling, cannot be used. The current simulation study compares the performance of two methods for estimating the correlations among changes in latent variables between two points in time, the two-wave latent change score model and the latent difference factor model. Results of the simulation study showed that both methods yielded generally accurate estimates of the correlation between changes in a latent trait, with relatively small standard errors. Estimation bias and standard errors were lower with larger samples, larger factor loading magnitudes, and more indicators per factor. Further comparisons between the methods and implications of these results are discussed.