Assessing Invariance of Factor Structures and Polytomous Item Response Model Parameter Estimates
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The purpose of the present study was to examine the invariance of the factor structure and item response model parameter estimates obtained from a set of 27 items selected from the 2002 and 2003 forms of Your First College Year (YFCY). The first major research question of the present study was: How similar/invariant are the factor structures obtained from two datasets (i.e., identical items, different people)? The first research question was addressed in two parts: (1) Exploring factor structures using the YFCY02 dataset; and (2) Assessing factorial invariance using the YFCY02 and YFCY03 datasets. After using exploratory and confirmatory and factor analysis for ordered data, a four-factor model using 20 items was selected based on acceptable model fit for the YFCY02 and YFCY03 datasets. The four factors (constructs) obtained from the final model were: Overall Satisfaction, Social Agency, Social Self Concept, and Academic Skills. To assess factorial invariance, partial and full factorial invariance were examined. The four-factor model fit both datasets equally well, meeting the criteria for partial and full measurement invariance. The second major research question of the present study was: How similar/invariant are person and item parameter estimates obtained from two different datasets (i.e., identical items, different people) for the homogenous graded response model (Samejima, 1969) and the partial credit model (Masters, 1982)? To evaluate measurement invariance using IRT methods, the item discrimination and item difficulty parameters obtained from the GRM need to be equivalent across datasets. The YFCY02 and YFCY03 GRM item discrimination parameters (slope) correlation was 0.828. The YFCY02 and YFCY03 GRM item difficulty parameters (location) correlation was 0.716. The correlations and scatter plots indicated that the item discrimination parameter estimates were more invariant than the item difficulty parameter estimates across the YFCY02 and YFCY03 datasets.
Reyes, Jennifer McGee (2010). Assessing Invariance of Factor Structures and Polytomous Item Response Model Parameter Estimates. Doctoral dissertation, Texas A&M University. Available electronically from