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Understanding non-linear modeling of measurement invariance in heterogeneous populations

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  • Deana Desa

    (IEA Data Processing and Research Center)

Abstract

This study examined how a non-linear modeling of ordered categorical variables within multiple-group confirmatory factor analysis supported measurement invariance. A four-item classroom disciplinary climate scale used in cross-cultural framework was empirically investigated. In the first part of the analysis, a separated categorical confirmatory factor analysis was initially applied to account for the complex structure of the relationships between the observed measures in each country. The categorical multiple-group confirmatory factor analysis (MGCFA) was then used to conduct a cross-country examination of full measurement invariance namely the configural, metric, and scalar levels of invariance in the classroom discipline climate measures. The categorical MGCFA modeling supported configural and metric invariances as well as scalar invariance for the latent factor structure of classroom disciplinary climate. This finding implying meaningful cross-country comparisons on the scale means, on the associations of classroom disciplinary climate scale with other scales and on the item-factor latent structure. Application of the categorical modeling appeared to correctly specify the factor structure of the scale, thereby promising the appropriateness of reporting comparisons such as rankings of many groups, and illustrating league tables of different heterogeneous groups. Limitations of the modeling in this study and future suggestions for measurement invariance testing in studies with large numbers of groups are discussed.

Suggested Citation

  • Deana Desa, 2018. "Understanding non-linear modeling of measurement invariance in heterogeneous populations," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(4), pages 841-865, December.
    • Handle: RePEc:spr:advdac:v:12:y:2018:i:4:d:10.1007_s11634-016-0240-3
    DOI: 10.1007/s11634-016-0240-3
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    References listed on IDEAS

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    1. Steenkamp, Jan-Benedict E M & Baumgartner, Hans, 1998. "Assessing Measurement Invariance in Cross-National Consumer Research," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 25(1), pages 78-90, June.
    2. William Meredith, 1993. "Measurement invariance, factor analysis and factorial invariance," Psychometrika, Springer;The Psychometric Society, vol. 58(4), pages 525-543, December.
    3. Martijn G. De Jong & Jan-Benedict E. M. Steenkamp & Jean-Paul Fox, 2007. "Relaxing Measurement Invariance in Cross-National Consumer Research Using a Hierarchical IRT Model," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 34(2), pages 260-278, June.
    4. William Meredith & Roger Millsap, 1992. "On the misuse of manifest variables in the detection of measurement bias," Psychometrika, Springer;The Psychometric Society, vol. 57(2), pages 289-311, June.
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