Calculating non-centrality parameter for power analysis under structural equation modelling: An alternative

Abstract

Identifying the most parsimonious model in structural equation modelling (SEM) is of utmost importance and the appropriate power estimation methods minimize the probabilities of Type I and Type II errors. The power of a test depends on the sample size, Type I error, degrees of freedom and effect size. The effect size choice for power analysis under SEM is so critical. The estimate of the population discrepancy function (F^0), which is based on the sample discrepancy function, is usually used in power computations instead of the sample discrepancy function ( ^ F). Although the sample discrepancy function measures the actual difference between the model implied covariance matrix and covariance matrix of the data, it was considered as a biased estimator to be used as an effect size for power analysis. In this study, a modified approach of using the sample discrepancy function as an effect size in calculating the noncentrality parameter for power is proposed. This is compared to the approach in MacCallum et al. (1996) at different degrees of freedom and sample size specifications—taken from 50 to 2000. The relative efficiency of ^ F was derived, and its asymptotic unbiasedness for calculating the non-centrality parameter for power analysis was assessed. As the sample size and degrees of freedom increased, the difference between the power of a test for both methods reduced to zero. The results showed that the values for the power of a test are the same for the modified and traditional approaches for large sample sizes and degrees of freedom. The findings also revealed that the sample discrepancy function ( ^ F) is asymptotically unbiased for power analysis.