| This dissertation compared the statistical power for detecting an interaction versus quadratic effect using ordinary least squares (OLS) regression of scale scores or structural equation modeling of latent variables. Models investigated included two exogenous predictors and either their interaction or a quadratic function of one predictor. In OLS, the interaction term has greater reliability than the quadratic term; thus the power for the interaction exceeds that for the quadratic effect. Given that the latent variable approach corrects for unreliability, the latent variable approach was predicted to yield equal power for the interactive and quadratic effects; the power of the latent variable approach was predicted to exceed that of OLS. Analytic work and a simulation study examined these predictions. In the simulation study, (a) three population models were employed: (1) interaction model, (2) quadratic model with unstandardized coefficient for the quadratic term equal to that for the interaction term (quadratic model 1), and (3) a second quadratic model with the squared semi-partial correlation of the quadratic term equal to that of the interaction term (quadratic model 2). (b) Two estimation methods were implemented: maximum likelihood (ML) using the mean-centered constrained product indicator method and three indicators per latent construct, and OLS regression with mean-centered average composites of observed indicators. (c) Four levels of correlation between the latent exogenous variables were examined: 0.0, 0.3, 0.5, 0.8. (d) Two sample sizes, 200 and 1000, were employed. For all three models, at both sample sizes, and at all four levels of correlation, OLS had greater power than ML. For both estimation methods, quadratic model 1 had greater power than both the interaction model and quadratic model 2. For ML, power of the interaction model slightly exceeded that of quadratic model 2. For OLS, the relative power for the interaction model versus quadratic model 2 varied across conditions. Overall, power increased with increasing correlation and sample size. Outcomes were explained in terms of choice of effect size measures, reliability of the nonlinear term, nonnormality of the nonlinear term, and deviation between theoretical versus empirical standard errors. |
