Using a Multilevel Structural Equation Modeling Approach to Explain Cross-Cultural Measurement Noninvariance

Davidov, Eldad; Dülmer, Hermann; Schlüter, Elmar; Schmidt, Péter; Meuleman, Bart

doi:10.1177/0022022112438397

Cited by 125 publications

(108 citation statements)

References 48 publications

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“…They have been reported in previous (recent and older) studies (see, e.g., Cheung and Au 2005;Davidov et al 2012;Jak et al 2014a, b;Hox 2010;Muthén 1989Muthén , 1994Muthén , 2011Rabe-Hesketh et al 2004). However, even though several researchers have underlined the importance of explaining non-invariance rather than only testing for it, we…”

Section: Introductionsupporting

confidence: 78%

“…Cheung and Au 2005;Hox 2010;Muthén 1985Muthén , 1994, its further development has been the focus of more recent empirical investigation (Cheung and Au 2005;Davidov et al 2012;Jak et al 2014a, b;Hox 2010;Muthén 1989Muthén , 1994Muthén , 2011Rabe-Hesketh et al 2004). However, its application has become more accessible to applied researchers in recent years only after its inclusion in structural equation modeling software packages such as Mplus Muthén 1998-2014).…”

Section: Measurement Invariancementioning

confidence: 99%

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Explaining Measurement Nonequivalence Using Multilevel Structural Equation Modeling

Davidov

Dülmer

Cieciuch

et al. 2016

Sociological Methods & Research

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It is necessary to test for equivalence of measurements across groups to guarantee that comparisons of regression coefficients or mean scores of a latent factor are meaningful. Unfortunately, when tested, many scales display non-equivalence. Several researchers have suggested that non-equivalence may be used as a useful source of information as to why equivalence is biased and proposed employing a multilevel structural equation modeling (MLSEM) approach to explain why equivalence is not given. This method can consider a latent between-level factor and/or single contextual variables and use them to explain items' non-equivalence. In the current study we show that this method may also be useful for social science studies in general and for survey research and sociological comparative studies in particular when one fails to establish cross-group equivalence. We utilize data from the International Social Survey Program (ISSP) national identity module (2003) to test for the cross-country equivalence of a scale measuring attitudes toward granting citizenship rights to immigrants. As expected, the scale fails to achieve scalar equivalence. However, we explain a significant part of the most non-equivalent intercept by a latent between-level factor and one contextual variable, namely, the percentage of foreigners in the country relying on group threat theory. We show that the method does not necessarily rectify non-equivalence but it can help to explain why it is absent. It is necessary to test for equivalence of measurements across groups to guarantee that comparisons of regression coefficients or mean scores of a latent factor are meaningful.Unfortunately, when tested, many scales display non-equivalence. Several researchers have suggested that non-equivalence may be used as a useful source of information as to why equivalence is biased and proposed employing a multilevel structural equation modeling (MLSEM) approach to explain why equivalence is not given. This method can consider a latent between-level factor and/or single contextual variables and use them to explain items' non-equivalence. In the current study we show that this method may also be useful for social science studies in general and for survey research and sociological comparative studies in particular when one fails to establish cross-group equivalence. We utilize data from the International Social Survey Program (ISSP) national identity module (2003) to test for the cross-country equivalence of a scale measuring attitudes toward granting citizenship rights to immigrants. As expected, the scale fails to achieve scalar equivalence. However, we explain a significant part of the most non-equivalent intercept by a latent between-level factor and one contextual variable, namely, the percentage of foreigners in the country relying on group threat theory. We show that the method does not necessarily rectify non-equivalence but it can help to explain why it is absent.

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Section: Introductionsupporting

confidence: 78%

Section: Measurement Invariancementioning

confidence: 99%

Explaining Measurement Nonequivalence Using Multilevel Structural Equation Modeling

Davidov

Dülmer

Cieciuch

et al. 2016

Sociological Methods & Research

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“…It is also possible to extend the models further to aim to explain the non-equivalence, essentially by modeling with explanatory variables the cross-group variation in measurement parameters (see e.g. Soares et al 2009;Davidov et al 2012). …”

Section: Using Modeling To Detect and Allow For Non-equivalence Of Mementioning

confidence: 99%

Nonequivalence of measurement in latent variable modeling of multigroup data: A sensitivity analysis.

Kuha¹,

Moustaki²

2015

Psychological Methods

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MEASUREMENT NON-EQUIVALENCE: A SENSITIVITY ANALYSIS 2In studies of multiple groups of respondents, such as cross-national surveys and cross-cultural assessments in psychological or educational testing, an important methodological consideration is the comparability or "equivalence" of measurement across the groups. Ideally full equivalence would hold, but very often it does not. If non-equivalence of measurement is ignored when it is present, substantively interesting comparisons between the groups may become distorted. We consider this question in multigroup latent variable modeling of multiple-item scales, specifically latent trait models for categorical items. We use numerical sensitivity analyses to examine the nature and magnitude of the distortions in different circumstances, and the factors which affect them. The results suggest that estimates of multigroup latent variable models can be sensitive to assumptions about measurement, in that non-equivalence of measurement does not need to be extreme before ignoring it may substantially affect cross-group comparisons. We also discuss the implications of such findings on the analysis of large comparative studies.

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“…Hence, if the goal of the analysis is not an overall test on the presence of measurement bias, but one wants to differentiate between the two types of bias, other methods may be more appropriate. One could, for example, use multigroup analysis as presented by Davidov et al (2012), random item effects modeling (Verhagen & Fox, 2012), or tests of approximate invariance (Muthén & Asparouhov, 2013). It has to be noted that, for all bias detection methods, it would be a problem if all items would be affected by the same biasing factor to the same degree.…”

Section: Advantages and Disadvantages Of The Approachmentioning

confidence: 99%

“…Moreover, the use of multilevel factor analysis facilitates the investigation of the relation of latent variables (as opposed to composite scores) with observed country-level variables like general income level or literacy level. Davidov et al (2012) presented a procedure to test factorial invariance across countries using multigroup factor analysis, after which they use MLSEM to explain the bias across countries. The researchers stress the importance of explaining possible bias using country-level variables, as such an analysis will give deeper insight into the differences across countries.…”

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confidence: 99%

Testing and Explaining Differences in Common and Residual Factors Across Many Countries

Jak

2016

Journal of Cross-Cultural Psychology

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To make valid comparisons across countries, a measurement instrument needs to be measurement invariant across countries. The present article provides a nontechnical exposition of a recently proposed multilevel factor analysis approach to test measurement invariance across countries. It is explained that strong factorial invariance across countries implies equal factor loadings across levels and zero residual variance at the country level in a two-level factor model. Using two-level factor analysis, the decomposition of the variance at each level can be investigated, measurement invariance can be tested, and country-level variables can be added to explain differences in the common or residual factors. The approach is illustrated using two examples. The first example features data about well-being from the European Social Survey and the second example uses data about mathematical ability from the Programme for International Student Assessment (PISA) study. The input-files and annotated output-files for both examples are provided in the supplementary files.

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Using a Multilevel Structural Equation Modeling Approach to Explain Cross-Cultural Measurement Noninvariance

Cited by 125 publications

References 48 publications

Explaining Measurement Nonequivalence Using Multilevel Structural Equation Modeling

Explaining Measurement Nonequivalence Using Multilevel Structural Equation Modeling

Nonequivalence of measurement in latent variable modeling of multigroup data: A sensitivity analysis.

Testing and Explaining Differences in Common and Residual Factors Across Many Countries

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