Rasch and IRT Approaches

For unidimensional constructs with dichotomous or ordered categorical items, the Rasch model and the 2-parameter logistic IRT model are commonly used (see Embretson & Reise, 2000). The Rasch model has one parameter (bp for each item representing its difficulty (level), whereas the two-parameter IRT model has both a difficulty parameter (b.) and a discrimination (slope) parameter (a) for each item. Assessment of measurement invariance across time involves checking that the item parameters a. and bj have not changed over time. If the data fit the Rasch model, a. = 1 for each item so only the set of bjs will be checked. For measures with multiple ordered categories, the item parameters corresponding to each possible response category will need to be checked for each item. These procedures work very well for unidimensional scales that are often developed for the assessment of abilities. Unfortunately, current measures of many psychological constructs (e.g., many attitudes; traits) are very often multidimensional, consisting of several underlying factors or a major factor and several minor factors. The use of Rasch and IRT procedures for the assessment of measurement invariance is not as well studied for multidimensional psychological scales.

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