Abstract
Comparisons of means or associations between theoretical constructs of interest in cross-national comparative research assume measurement invariance, that is, that the same constructs are measured in the same way across the various nations under study. While it is intuitive, this assumption needs to be statistically tested. An increasing number of sociological and social psychological studies have been published in the last decade in which the cross-national comparability of various scales such as human values, national identity, attitudes toward democracy, or religiosity, to name but a few, were tested. Many of these studies did not manage to fully achieve measurement invariance. In this study we review, in a nontechnical manner, the methodological literature on measurement invariance testing. We explain what it is, how to test for it, and what to do when measurement invariance across countries is not given in the data. Several approaches have been recently proposed in the literature on how to deal with measurement noninvariance. We illustrate one of these approaches with a large dataset of seven rounds from the European Social Survey (2002–2015) by estimating the most trustworthy means of human values, even when strict measurement invariance is not given in the data. We conclude with a summary and some critical remarks.
Zusammenfassung
Vergleiche von Mittelwerten und von Beziehungen zwischen theoretischen Konstrukten, die im Rahmen international vergleichender Forschung untersucht werden, gehen davon aus, dass diese Konstrukte messinvariant sind, d. h., dass sie in den verschiedenen Ländern identisch gemessen werden. Obwohl diese Annahme plausibel sein kann, muss sie jedoch statistisch getestet werden. Im letzten Jahrzehnt wurde eine zunehmende Zahl von soziologischen, politikwissenschaftlichen und sozialpsychologischen Studien veröffentlicht, in denen die internationale Vergleichbarkeit von verschiedenen Skalen zur Messung von z. B. menschlichen Werten, nationaler Identität, Einstellungen zu Demokratie oder Religiosität überprüft wurde. In vielen dieser Studien konnte Messinvarianz nicht völlig nachgewiesen werden. Die folgende Studie bietet in einer nicht technischen Art und Weise einen Überblick über die methodologische Literatur zur Messinvarianz. Es wird erklärt, was Messinvarianz ist, wie man sie überprüft und was man tun kann, wenn sie in den Daten nicht gegeben ist. In der Literatur wurden in der letzten Zeit verschiedene Ansätze vorgeschlagen, wie man fehlende Messinvarianz behandeln kann. Die Autoren illustrieren eine dieser Herangehensweisen (Alignment) mit einem großen Datensatz, der 7 Befragungsrunden des European Social Survey (2002–2015) beinhaltet, und schätzen den vertrauenswürdigsten Durchschnitt menschlicher Werte, auch wenn strikte Messinvarianz in den Daten nicht vorhanden ist. Abschließend folgen eine Zusammenfassung und einige kritische Anmerkungen.
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Notes
Researchers examine global fit measures and perform chi-square difference tests to determine whether a more highly restricted model is supported by the data, that is if a higher level of invariance is given. However, based on a Monte Carlo study, Chen (2007) proposed an alternative to the chi-square difference test, which leads too easily to a rejection of measurement invariance. He proposed that metric noninvariance is indicated by a change smaller than 0.01 in the comparative fit index (CFI), supplemented by a change smaller than 0.015 in the root mean square error of approximation (RMSEA), or a change smaller than 0.03 in the standardized root mean square residual (SRMR) compared with the configural invariance model. To guarantee scalar invariance, Chen (2007) proposed to inspect whether the change in CFI is smaller than 0.01, the change in RMSEA is smaller than 0.015, or the change in SRMR is smaller than 0.01, when moving from a metric to a scalar invariance model for sample sizes larger than 300 per group.
Measures of the Schwartz values are also included in other international surveys such as the World Values Survey or the U.S. General Social Survey (for further details, see http://www.worldvaluessurvey.org/wvs.jsp; http://www.norc.org/Research/Projects/Pages/general-social-survey.aspx).
The authors excluded the value ‘hedonism’ from this model. According to the theory, this value is located between openness to change and self-enhancement. Including this value in either of the models resulted in a significant reduction in model fit.
The scale of latent variables is unknown, and hence their variance is also unknown (by definition, these variables are unobserved). Therefore, in order to identify the model, researchers need to apply some restriction for the estimation: either restricting the variance of the latent variable to an arbitrary value (typically it is then restricted to 1 in all groups), or fixing the scale of the latent variable by restricting the factor loading of one of the items (the so-called anchor item) to 1 in all groups. When doing so, it is important to guarantee that such a restriction fits the data at hand. In the former case, the restriction implies an implicit assumption that the latent variance is equal across groups. In the latter case, the restriction implies that the factor loading of the anchor item is indeed equal across groups. In both cases, researchers need to make sure that the assumption holds, for example by inspecting which of these parameters (factor loading of one of the items or the latent variable variance) are indeed most similar across groups, and choose the restriction which best corresponds with the data at hand (see also Brown 2015, p. 271).
Many studies evidenced that intercepts were not equal across groups, and that it was easier to guarantee equal factor loadings than equal intercepts when comparing different countries (see e. g. Davidov et al. 2014). In other words, it was often easier to establish metric invariance than scalar invariance. Different intercepts may also reflect different country-specific survey strategies, which in turn may result in different response patterns across countries.
Tables that display more highly specific information about the (non)invariance pattern for each higher-order value may be obtained from the first author on request. They present the number of noninvariant loadings and intercepts for each item and country. One way to estimate the amount of bias, discussed in Oberski (2014), is to perform a sensitivity analysis.
Methodologists also discuss the topic of isomorphism, which refers to equivalent construct meaning across levels of analysis. In other words, it refers to the presence or absence of measurement invariance across levels, for example across individuals and countries. However, examining isomorphism in cross-national data settings is beyond the scope of the present study (for a further discussion, see e. g. Guenole 2016; Muthén 1994; or Ruelens et al. 2016).
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Acknowledgements
The work of the first, second and fourth authors was supported by the University Research Priority Program Social Networks of the University of Zurich. The work of the third author was supported by the Alexander von Humboldt Polish Honorary Research Fellowship granted by the Foundation for Polish Science for the international cooperation between Peter Schmidt and Jan Cieciuch. The authors would like to thank Lisa Trierweiler and Neil Mussett for the English proof of the manuscript.
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Cieciuch, J., Davidov, E., Schmidt, P. et al. How to Obtain Comparable Measures for Cross-National Comparisons. Köln Z Soziol 71 (Suppl 1), 157–186 (2019). https://doi.org/10.1007/s11577-019-00598-7
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DOI: https://doi.org/10.1007/s11577-019-00598-7
Keywords
- Exact measurement invariance
- Approximate measurement invariance
- Alignment
- Human values
- European Social Survey