| Through a series of related studies, the research attempted to identify better estimation approaches and modeling techniques for latent interaction and quadratic effects. The literature review provided a conceptual framework for the unconstrained approach which was recommended for its simplicity and robustness. Three other approaches, namely, the constrained, the partially constrained (i.e., the generalized appended product indicator, GAPI), and the quasi-maximum likelihood (QML) approaches were selected and compared with the unconstrained approach.; Six simulation studies, four for the latent interaction models, and two for the latent quadratic models were conducted to compare the performances of the four approaches. Results generally showed that the QML approach and the constrained approach behaved similarly, while the performance of the unconstrained approach was close to that of the GAPI approach. Under the normal distribution condition, the QML approach performed the best among the four approaches in terms of lack of bias, precision, and power. However, with moderate and large sample sizes (N=200 or above), the differences among the four approaches were systematically smaller, with similar bias and precision. Under nonnormal conditions, the unconstrained approach was more robust, with a smaller bias and predictable type I error rate (near the significant level), and its precision and power increased as the sample size increased. These results supported the use of the unconstrained approach for the analyses of latent interaction and quadratic models.; Concepts and issues related to standardized solutions for the latent interaction model were discussed. Quasi-standardized solution was proposed and formulated by using the estimates of the original solution and the ordinary standardized solution. Some properties of the quasi-standardized solution were mathematically derived and proved, which included the demonstration that the main and interaction effects were scale free, so were the loading and the Chi-square of model fit, while t statistics of main and interaction effects were approximate scale free.; A real empirical study was conducted to illustrate the application of the unconstrained approach. The genuine study focused on the interaction effect of music self-concept and music-domain importance on the global self-concept. The result showed that structural equation analysis was advantageous over the traditional regression analysis, while such superiority of the structural equation modeling approach was more prominent in higher-order structural equation models. As expected, the estimated main and interaction effects in the quasi-standardized solution obtained using the centered data coincided with those using the standardized data in different order structural models.; The unconstrained approach was extended to estimate interaction effects in latent growth models. With the indicators of the interaction term formed by the products of differences (rather than using the usual indicator product strategy), a simplified full interaction model for the latent growth model was proposed. The model was further simplified when only the interaction between change rates was considered. Importantly, the unconstrained approach was an appropriate method for analyses of such simplified full interaction model for latent growth model, which also constituted a unique contribution of this dissertation. |
