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Hutchinson, Susan R.

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Measurement invariance is crucial for making valid comparisons across different groups (Kline, 2016; Vandenberg, 2002). To address the challenges associated with invariance testing such as large sample size requirements, the complexity of the model, etc., applied researchers have incorporated parcels. Parcels have been shown to alleviate skewness, improve reliability, reduce the number of indicators, and produce a more stable solution (Bandalos & Finney, 2001; Matsunaga et al., 2021; Nasser & Takahashi, 2003). Despite these benefits, limited methodological research has been conducted on the effects of parcels on tests of measurement invariance. This dissertation investigated the effects of different total sample sizes, types of indicator variables (including indicator variable techniques), and ratio of group sample sizes on tests of measurement invariance between gender and race. Empirical data from eighth-grade U.S. students' responses on four different math attitude subscales using a Likert-type rating scale from TIMSS 2015 were used to build a CFA model (Tang & Averett, 2018). The study found that using a smaller number of items as indicators with the highest factor loadings can better assess measurement invariance tests, providing a middle way for applied researchers to conduct tests of measurement invariance without the need for extremely large sample sizes or the use of parcels. Furthermore, the study found that item-based models detected a lack of invariance better than parcel-based models. Three-item indicator models provided stronger evidence of configural invariance than nine-item indicator and parcel-based models, with all three-item indicator models exhibiting full configural invariance. Higher CFI and TLI values and lower chi-square and SRMR values supported the use of three-item indicator models in tests of configural invariance. Three-item indicator models-based analyses were found to be better at identifying items with significant differences in factor loadings than parcel-based analyses. These findings provide researchers with a way to conduct tests of measurement invariance without requiring extremely large sample sizes and address the challenges associated with testing measurement invariance, making it more accessible for applied researchers. However, further research is required to determine the optimal number of items with highest factor loadings to use as indicators that can improve and facilitate the testing of measurement invariance for applied researchers.


274 pages

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