Complementary and competing factor analytic approaches for the investigation of measurement invariance
Andrea Hildebrandt, Oliver Wilhelm, Alexander Robitzsch · University of Zagreb University Computing Centre (SRCE) · 2009
The scientist is usually looking for invariance whether he knows it or not.Whenever he discovers a functional relationship his next question follows naturally: under what conditions does it hold?"(Stevens, 1951) As pointed out in the quotation by Stevens (1951), the issue of invariance is a highly relevant topic in scientific measurement.Concepts of invariance and the development of methods to determine whether or not specific aspects of equivalence are hold for a given measurement instrument have a long history in psychometrics and can be traced back to Thorndike (1904) and Thurstone (1925Thurstone ( , 1947;; see Engelhard, 1992 for a historical review).There is a bifocal perspective on the concept of invariance in psychometrics, that Thurstone emphasized and that was later immersed by Rasch (1961).One perspective is that of sample invariance of a measure and the other perspective is that of item invariant measurement of individuals (see also Engelhard, 1992).Evidence of sample invariance of a measure or a single test item is given, when subgroup characteristics (like gender, age, social class etc.) do not influence ability estimates or an item scale value.Item invariant measurement refers to the concept of minimizing discrepancies between ability estimates of an individual when using for example two different item pools.In the present paper we will focus on the issue of sample-related invariance.The main goal of this paper is to present and illustrate two analytical approaches for the investigation of measurement invariance.To this end we will first shortly review the concept of cross-group (sample-related) psychometric invariance defined in factor analytical context and name some of the prevailing research questions linked to its investigation.Second will be the description of the commonly used method to study invariance (Multiple-Group Mean and Covariance Structures -MGMCS) and the discussion