Проверка измерительной инвариантности: случай порядковых переменных (на примере гендерного эгалитаризма в арабских странах)
Аннотация
Современные межстрановые сравнительные исследования позволяют оценивать уровень поддержки тех или иных убеждений в разных странах, однако по мере накопления все большего объема данных сопоставимость стран и волн опросов становится отдельной методологической проблемой. Литературы по этому вопросу все еще недостаточно, особенно для анализа более сложных случаев, таких как работа с порядковыми переменными. Мы хотим продемонстрировать механизм проверки измерительной инвариантности латентного фактора «гендерный эгалитаризм» на примере первой волны проекта «Арабский барометр». С помощью многогруппового конфирматорного факторного анализа конструируется модель, в основе которой лежат 4 порядковые переменные, закодированные по шкале от 0 до 3. Проводится ряд тестов измерительной инвариантности латентного фактора «гендерный эгалитаризм». Результаты моделирования позволяют говорить о достижении частичной сильной инвариантности измерений в 5 изучаемых странах.
Ключевые слова:
инвариантность измерений, гендерный эгалитаризм, Арабский барометр, конфирматорный факторный анализ порядковых переменных
Литература
Davidov E., Meuleman B., Cieciuch J., Schmidt P., Billiet J. Measurement Equivalence in Cross-national Research // Annual Review of Sociology. 2014. Vol. 40. P. 55–75.
Horn J.L., McArdle J.J. A Practical and Theoretical Guide to Measurement Invariance in Aging Research // Experimental aging research. 1992. Vol. 18. No. 3. P. 117–144.
Davidov E., Dülmer H., Schlüter E., Schmidt P., Meuleman B. Using a Multilevel Structural Equation Modeling Approach to Explain Cross-cultural Measure¬ment Noninvariance // Journal of Cross-Cultural Psychology. 2012. Vol. 43. No. 4. P. 558–575.
Руднев М.Г. Инвариантность измерения базовых ценностей по методике Шварца среди русскоязычного населения четырех стран // Социология: методология, методы, математическое моделирование. 2013. №. 37. С. 7–38.
Vandenberg R.J., Lance C.E. A Review and Synthesis of the Measurement Invariance Literature: Suggestions, Practices, and Recommendations for Organizational Research // Organizational Methods Research. 2000. Vol. 3. No. 1. P. 4–70.
Van de Schoot R., Lugtig P., Hox J. A Checklist for Testing Measurement Invariance // European Journal of Developmental Psychology. 2012. Vol. 9. No. 4. P. 486–492.
Davidov E., Datler G., Schmidt P., Schwartz S. Testing the Invariance of Values in the Benelux Countries with the European Social Survey: Accounting for Ordinality // Cross-cultural Analysis: Methods and Applications / Ed. E. Davidov, P. Schmidt, Y. Billiet. N.Y.: Taylor & Francis Group, 2011. P. 149–171.
Kim E.S., Yoon M. Testing Measurement Invariance: A Comparison of Multiple-group Categorical CFA and IRT // Structural Equation Modeling. 2011. Vol. 18. No. 2. P. 212–228.
Liu Y., Millsap R.E., West S.G., Tein J.Y., Tanaka R., Grimm K.J. Testing Measurement Invariance in Longitudinal Data With Ordered-Categorical // Psychological Methods. Advance online publication. 2016.
Millsap R.E., Yun-Tein J. Assessing Factorial Invariance in Ordered-categorical Measures // Multivariate Behavioral Research. 2004. Vol. 39. No. 3. P. 479–515.
Muthén B.O., Asparouhov T. Latent Variable Analysis with Categorical Outcomes: Multiple-Group and Growth Modeling in Mplus // Mplus Web Note. 2002. No. 4.
Sass D.A., Schmitt T.A., Marsh H.W. Evaluating Model Fit With Ordered Categorical Data Within a Measurement Invariance Framework: A Comparison of Estimators // Structural Equation Modeling: A Multidisciplinary Journal. 2014. Vol. 21. No. 2. P. 167–180.
Wu H., Estabrook R. Identification of Confirmatory Factor Analysis Models of Different Levels of Invariance for Ordered Categorical Outcomes // Psychometrika. 2016. Vol. 81. No. 4. P. 1014–1045.
Xing C., Hall J.A. Confirmatory Factor Analysis and Measurement Invariance Testing with Ordinal Data: An Application in Revising the Flirting Styles Inventory // Communication Methods and Measures. 2015. Vol. 9. No. 3. P. 123–151.
Byrne B., Shavelson R., Muthén B. Testing for the Equivalence of Factor Covariance and Mean Structures: The Issue of Partial Measurement in Variance // Psychological Bulletin. 1989. Vol. 105. No. 3. P. 456–466.
Hu L., Bentler P.M. Cutoff Criteria for Fit Indexes in Covariance Structure Analysis: Conventional Criteria Versus New Alternatives // Structural Equation Modeling: A Multidisciplinary Journal. 1999. Vol. 6. No. 1. P. 1–55.
Browne M.W., Cudeck R. Alternative Ways of Assessing Model Fit // Test¬ing Structural Equation Models / Ed. K. Bollen, J. Long. SAGE Publications, Inc., 1993. P. 136–162.
Chen F.F. Sensitivity of Goodness of Fit Indexes to Lack of Measurement Invariance // Structural Equation Modeling. 2007. Vol. 14. No. 3. P. 464–504.
Oberski D.L. Evaluating Sensitivity of Parameters of Interest to Measurement Invariance in Latent Variable Models // Political Analysis. 2014. Vol. 22. No. 1. P. 45–60.
Saris W.E., Satorra A., Sörbom D. The Detection and Correction of Specifica¬tion Errors in Structural Equation Models // Sociological Methodology / Ed. C.C. Clogg. Washington, 1987. P. 105–129.
Saris W.E., Satorra A., Van der Veld W.M. Testing Structural Equation Models or Detection of Misspecifications? // Structural Equation Modeling. 2009. Vol. 16. No. 4. P. 561–582.
Meuleman B. When Are Item Intercept Differences Substantively Relevant in Measurement Invariance Testing? // Methods, Theories, and Empirical Applica¬tions in the Social Sciences / Ed. S. Salzborn, E. Davidov, J. Reinecke. VS Verlag für Sozialwissenschaften, 2012. P. 351.
Oberski D.L., Vermunt J.K., Moors G.B.D. Evaluating Measurement Invariance in Categorical Data Latent Variable Models with the EPC-interest // Political Analysis. 2015. Vol. 23. No. 4. P. 550–563.
Horn J.L., McArdle J.J. A Practical and Theoretical Guide to Measurement Invariance in Aging Research // Experimental aging research. 1992. Vol. 18. No. 3. P. 117–144.
Davidov E., Dülmer H., Schlüter E., Schmidt P., Meuleman B. Using a Multilevel Structural Equation Modeling Approach to Explain Cross-cultural Measure¬ment Noninvariance // Journal of Cross-Cultural Psychology. 2012. Vol. 43. No. 4. P. 558–575.
Руднев М.Г. Инвариантность измерения базовых ценностей по методике Шварца среди русскоязычного населения четырех стран // Социология: методология, методы, математическое моделирование. 2013. №. 37. С. 7–38.
Vandenberg R.J., Lance C.E. A Review and Synthesis of the Measurement Invariance Literature: Suggestions, Practices, and Recommendations for Organizational Research // Organizational Methods Research. 2000. Vol. 3. No. 1. P. 4–70.
Van de Schoot R., Lugtig P., Hox J. A Checklist for Testing Measurement Invariance // European Journal of Developmental Psychology. 2012. Vol. 9. No. 4. P. 486–492.
Davidov E., Datler G., Schmidt P., Schwartz S. Testing the Invariance of Values in the Benelux Countries with the European Social Survey: Accounting for Ordinality // Cross-cultural Analysis: Methods and Applications / Ed. E. Davidov, P. Schmidt, Y. Billiet. N.Y.: Taylor & Francis Group, 2011. P. 149–171.
Kim E.S., Yoon M. Testing Measurement Invariance: A Comparison of Multiple-group Categorical CFA and IRT // Structural Equation Modeling. 2011. Vol. 18. No. 2. P. 212–228.
Liu Y., Millsap R.E., West S.G., Tein J.Y., Tanaka R., Grimm K.J. Testing Measurement Invariance in Longitudinal Data With Ordered-Categorical // Psychological Methods. Advance online publication. 2016.
Millsap R.E., Yun-Tein J. Assessing Factorial Invariance in Ordered-categorical Measures // Multivariate Behavioral Research. 2004. Vol. 39. No. 3. P. 479–515.
Muthén B.O., Asparouhov T. Latent Variable Analysis with Categorical Outcomes: Multiple-Group and Growth Modeling in Mplus // Mplus Web Note. 2002. No. 4.
Sass D.A., Schmitt T.A., Marsh H.W. Evaluating Model Fit With Ordered Categorical Data Within a Measurement Invariance Framework: A Comparison of Estimators // Structural Equation Modeling: A Multidisciplinary Journal. 2014. Vol. 21. No. 2. P. 167–180.
Wu H., Estabrook R. Identification of Confirmatory Factor Analysis Models of Different Levels of Invariance for Ordered Categorical Outcomes // Psychometrika. 2016. Vol. 81. No. 4. P. 1014–1045.
Xing C., Hall J.A. Confirmatory Factor Analysis and Measurement Invariance Testing with Ordinal Data: An Application in Revising the Flirting Styles Inventory // Communication Methods and Measures. 2015. Vol. 9. No. 3. P. 123–151.
Byrne B., Shavelson R., Muthén B. Testing for the Equivalence of Factor Covariance and Mean Structures: The Issue of Partial Measurement in Variance // Psychological Bulletin. 1989. Vol. 105. No. 3. P. 456–466.
Hu L., Bentler P.M. Cutoff Criteria for Fit Indexes in Covariance Structure Analysis: Conventional Criteria Versus New Alternatives // Structural Equation Modeling: A Multidisciplinary Journal. 1999. Vol. 6. No. 1. P. 1–55.
Browne M.W., Cudeck R. Alternative Ways of Assessing Model Fit // Test¬ing Structural Equation Models / Ed. K. Bollen, J. Long. SAGE Publications, Inc., 1993. P. 136–162.
Chen F.F. Sensitivity of Goodness of Fit Indexes to Lack of Measurement Invariance // Structural Equation Modeling. 2007. Vol. 14. No. 3. P. 464–504.
Oberski D.L. Evaluating Sensitivity of Parameters of Interest to Measurement Invariance in Latent Variable Models // Political Analysis. 2014. Vol. 22. No. 1. P. 45–60.
Saris W.E., Satorra A., Sörbom D. The Detection and Correction of Specifica¬tion Errors in Structural Equation Models // Sociological Methodology / Ed. C.C. Clogg. Washington, 1987. P. 105–129.
Saris W.E., Satorra A., Van der Veld W.M. Testing Structural Equation Models or Detection of Misspecifications? // Structural Equation Modeling. 2009. Vol. 16. No. 4. P. 561–582.
Meuleman B. When Are Item Intercept Differences Substantively Relevant in Measurement Invariance Testing? // Methods, Theories, and Empirical Applica¬tions in the Social Sciences / Ed. S. Salzborn, E. Davidov, J. Reinecke. VS Verlag für Sozialwissenschaften, 2012. P. 351.
Oberski D.L., Vermunt J.K., Moors G.B.D. Evaluating Measurement Invariance in Categorical Data Latent Variable Models with the EPC-interest // Political Analysis. 2015. Vol. 23. No. 4. P. 550–563.
