Effects of score discreteness and estimating alternative model parameters on power estimation methods in structural equation modeling

The primary purpose of this study was to examine relative performance of 2 power estimation methods in structural equation modeling. Sample size, alpha level, type of manifest variable, type of specification errors, and size of correlation between constructs were manipulated. Type 1 error rate of the model chi-square test, empirical critical values, and empirical power were established through Monte Carlo simulations. The power estimation methods performed similarly. Bias and standard error appeared to relate nonlinearly to the magnitude of "true" power. When the alternative population matrix was estimated, bias leaned toward the middle of the power scale regardless of score level. When the alternative population matrix was known, bias was small for continuous scores throughout the power scale but large for discrete scores with medium-sized power. Standard error was larger in the middle than at the ends of the power scale. Implications of the findings and future directions are discussed.