Measurement Invariance (MI) refers to the equivalent functioning of psychometric instruments when applied across different groups. Violations of MI can lead to spurious between-group differences, or obscure true differences, on observed scores, means, and covariances. Chapter 1 introduces the multiple-group confirmatory factor analysis (MGCFA) approach to evaluating MI. The present research seeks to identify overly restrictive assumptions of the MGCFA approach, and to provide alternative

more »

... ndations. Chapter 2 notes that typical MGCFA MI models assume equivalent functioning of each item, while in practice, applied researchers are often primarily interested in equivalent functioning of composite scores. Chapter 2 introduces an approach to assessing MI of composite scores that does not assume MI of all items, by placing between-group equality constraints on measurement parameter totals. Invariance of parameter totals is referred to as "scale-level MI", while the invariance of individual measurement parameters is referred to as "item-level MI." Power analyses of tests of scale-level and item-level MI illustrate that, despite item-level MI models being nested within scale-level MI models, tests of scale-level MI are often more sensitive to violations of MI that affect the between-group comparability of composite scores. Chapter 3 introduces an approach to quantifying between-group differences in classification accuracy when critical composite scores are used for selection and a minimum of partial scalar MI – MI of some, but not all, loadings and intercepts – is retained. Chapter 3 illustrates that different patterns of violations of MI differentially affect classification accuracy ratios for different measures of classification accuracy. Between-group differences on multiple sets of measurement parameters can have compensatory or additive effects on classification accuracy ratios. Finite sample variability of classification accuracy ratios is discussed, and a Bollen-Stine bootstrapping approach for estimating con [...]