Introduction

Quantitative statisticians often encounter situations where the collected data fail to comply with the assumptions underlying the method that they are using. For instance, in the social sciences, the assumption that variables are normally distributed is rarely satisfied (e.g., Gierl & Mulvenon, 1995; Harlow, 1985; Micceri, 1989). In the case of structural equation modeling (SEM), although recommended standards exist to address violation of assumptions, its reliability has not yet been formally determined. For example, researchers typically use maximum likelihood estimation (MLE) as the standard method for estimating the parameters of structural equations (e.g., Baumgartner & Homburg, 1996; Martínez-López, Gázquez-Abad, & Sousa, 2013). Nonetheless, this estimator's properties are known only asymptotically.1 As a result, some common rules of thumb—such as the recommended sample size of 100 or 150 observations (e.g., Boomsma, 1982) or 5 to 10 observations per estimated parameter (Bentler & Chou, 1987)—may be unsuitable when applying SEM, particularly for models that differ greatly from the original model being tested.