| This study empirically investigated the issues in growth modeling concerning the effect of the unmodeled residual heteroscedasticity and correlation on parameter estimates and model fit indexes. A Monte Carlo simulation design was used, and four design factors were manipulated: residual heteroscedasticity levels, residual collinearity level, number of repeated measurements, and sample size.; The results of this study showed that the misspecification of the residual covariance structure did not have the substantial impact on the estimates of the intercept and slope of the growth trajectory, but did affect the estimates of the intercept variance, the slope variance and the intercept-slope covariance. Additionally, the slope variance was more sensitive to the residual misspecification than other parameter estimates of the growth trajectory. Among the four design factors of this simulation study, the sample size had no significant effect on the bias of parameter estimates, but it had some effect on the RMSE of the parameter estimates. Other design factors (residual heteroscedasticity level, residual collinearity level, and number of repeated measurement) had a constant effect on the bias and the RMSE of the estimates of the variance parameters (intercept variance, slope variance and intercept-slope covariance).; It was found that model fit indexes were differentially sensitive to misspecified residual structure: CFI, NFI and NNFI were the least sensitive to misspecified residual structure, and RMSEA was the most sensitive to misspecified residual structure. |
