## A note on normal theory power calculation in SEM with data missing completely at random. Structural Equation Modeling-A (2005)

Venue: | Multidisciplinary Journal |

Citations: | 2 - 0 self |

### BibTeX

@ARTICLE{Dolan05anote,

author = {Conor Dolan and Sophie Van Der Sluis and Raoul Grasman and Van Der Sluis},

title = {A note on normal theory power calculation in SEM with data missing completely at random. Structural Equation Modeling-A},

journal = {Multidisciplinary Journal},

year = {2005},

volume = {12},

pages = {245--262}

}

### OpenURL

### Abstract

We consider power calculation in structural equation modeling with data missing completely at random (MCAR). Muthén and Muthén (2002) recently demonstrated how power calculations with data MCAR can be carried out by means of a Monte Carlo study. Here we show that the method of Satorra and Saris (1985), which is based on the nonnull distribution of the (normal theory) log-likelihood ratio test, can also be used. Compared to a Monte Carlo study, this method is computationally less intensive. We discuss 2 ways to calculate power when data are MCAR, one based on multigroup analysis and summary statistics, the other based on transformed raw data. The latter method is quite simple to carry out. Four examples are presented. This article is limited to data MCAR. Generally MCAR is a strong assumption. We demonstrate that results of power analyses based on the MCAR assumption are not informative if the data are actually missing at random. In structural equation modeling (SEM), power calculation based on the normal theory likelihood ratio test (LRT) has been developed and discussed by Satorra and Saris (1985; Saris & Satorra, 1993). In this method, power is calculated by integrating the nonnull distribution of the LRT. This method is quite easy to carry out, but is based on the various assumptions associated with the normal theory LRT, such as large samples and multivariate normality (Azzelini, 1996; Bollen, 1989) and small to moderate misspecification (Curran, Bollen, Paxton, Kirby, & Chen, 2002). An alternative approach to power calculation is based on the empirical, rather than the theoretical distribution of the test statistic (Lei & Dunbar, 2004;