A framework for power analysis using a structural equation modelling procedure

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.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.The SEM based power analysis approach may prove useful for researchers designing research in the health and medical spheres.Structural equation modelling (SEM) was developed from work in econometrics (simultaneous equation models; see for example Wansbeek and Meijer [2]) and latent variable models from factor analysis [3,4]. Structural equation modelling is an enormously flexible technique – it is possible to use a structural equation modelling approach to carry out direct equivalents of many analyses, including (but not limited to): ANOVA, correlation, ANCOVA, multiple regression, multivariate analysis of variance, and multivariate regression. This flexibility will be exploited in the approach set out in this article.A necessarily very brief introduction to the logic of structural equation modelling is presented here – for a more thorough introduction to the basics of structural equation modelling the reader is directed towards one of the many good introductory texts, (Steiger has recently reviewed several such texts [5]). For more details on the statistical and mathematical aspects of struc