ABSTRACT
This chapter addresses some methodological issues that may arise when researchers conduct the structural equation modelling (SEM) analysis of factorial invariance. It introduces the concept of factorial invariance, reviews the levels of invariance, and also introduces the concept of differential item functioning (DIF), which refers a lack of invariance at the item level. Means and covariance structure analysis analysis for DIF detection assumes that the responses on a given set of items reflect a single common construct. The concept of factorial invariance also underlies the concept of DIF; a concept originated from the item response theory literature. The chapter describes several SEM-based DIF analyses, and summarizes certain Monte Carlo studies that examine the effects of employing different scaling designs, analytic strategies, and test statistics. It provides general procedural guidelines for evaluating invariance of a scale. The chapter attempts to provide the cross-cultural measurement literature by cautioning researchers against the use of the conventional analytic approach in DIF analysis.
