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Using Graphical Methods in Assessing Measurement Invariance in Inventory Data

Most measurements of psychological constructs are performed using inventories or tests in which it is assumed that the observed interdependencies among the item responses are accounted for by a set of unobserved variables representing the psychological constructs being measured. Using test scores, researchers often attempt to detect and describe differences among groups to draw inferences about actual differences in the psychological constructs measured by their instruments. However, direct comparisons using tests scores are not meaningful unless these are commensurable or invariant across populations. Most researchers simply assume that measurement invariance holds. However, the extent to which this assumption is a reasonable one for specific measures and specific populations should be tested empirically. Using item response theory, the present study discusses the difficulties faced to evaluate measurement invariance when, as is most common, a psychological construct is assessed by means of a test or inventory composed of categorical items. In this context, graphical methods (fitplots) can be a useful auxiliary tool that we believe has been overlooked. An example is provided to illustrate the use of fitplots in assessing measurement invariance in inventory data.