A framework for power analysis using a structural equation modelling procedure

BACKGROUND This paper demonstrates how structural equation modelling (SEM) can be used as a tool to aid in carrying out power analyses. For many complex multivariate designs that are increasingly being employed, power analyses can be difficult to carry out, because the software available lacks sufficient flexibility. Satorra and Saris developed a method for estimating the power of the likelihood ratio test for structural equation models. Whilst the Satorra and Saris approach is familiar to researchers who use the structural equation modelling approach, it is less well known amongst other researchers. The SEM approach can be equivalent to other multivariate statistical tests, and therefore the Satorra and Saris approach to power analysis can be used. METHODS The covariance matrix, along with a vector of means, relating to the alternative hypothesis is generated. This represents the hypothesised population effects. A model (representing the null hypothesis) is then tested in a structural equation model, using the population parameters as input. An analysis based on the chi-square of this model can provide estimates of the sample size required for different levels of power to reject the null hypothesis. CONCLUSIONS The SEM based power analysis approach may prove useful for researchers designing research in the health and medical spheres.