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Getting the Within Estimator of Cross-Level Interactions in Multilevel Models with Pooled Cross-Sections: Why Country Dummies (Sometimes) Do Not Do the Job


Giesselmann, Marco; Schmidt-Catran, Alexander W (2019). Getting the Within Estimator of Cross-Level Interactions in Multilevel Models with Pooled Cross-Sections: Why Country Dummies (Sometimes) Do Not Do the Job. Sociological Methodology, 49(1):190-219.

Abstract

Multilevel models with persons nested in countries are increasingly popular in cross-country research. Recently, social scientists have started to analyze data with a three-level structure: persons at level 1, nested in year-specific country samples at level 2, nested in countries at level 3. By using a country fixed-effects estimator, or an alternative equivalent specification in a random-effects framework, this structure is increasingly used to estimate within-country effects in order to control for unobserved heterogeneity. For the main effects of country-level characteristics, such estimators have been shown to have desirable statistical properties. However, estimators of cross-level interactions in these models are not exhibiting these attractive properties: as algebraic transformations show, they are not independent of between-country variation and thus carry country-specific heterogeneity. Monte Carlo experiments consistently reveal the standard approaches to within estimation to provide biased estimates of cross-level interactions in the presence of an unobserved correlated moderator at the country level. To obtain an unbiased within-country estimator of a cross-level interaction, effect heterogeneity must be systematically controlled. By replicating a published analysis, we demonstrate the relevance of this extended country fixed-effects estimator in research practice. The intent of this article is to provide advice for multilevel practitioners, who will be increasingly confronted with the availability of pooled cross-sectional survey data.

Abstract

Multilevel models with persons nested in countries are increasingly popular in cross-country research. Recently, social scientists have started to analyze data with a three-level structure: persons at level 1, nested in year-specific country samples at level 2, nested in countries at level 3. By using a country fixed-effects estimator, or an alternative equivalent specification in a random-effects framework, this structure is increasingly used to estimate within-country effects in order to control for unobserved heterogeneity. For the main effects of country-level characteristics, such estimators have been shown to have desirable statistical properties. However, estimators of cross-level interactions in these models are not exhibiting these attractive properties: as algebraic transformations show, they are not independent of between-country variation and thus carry country-specific heterogeneity. Monte Carlo experiments consistently reveal the standard approaches to within estimation to provide biased estimates of cross-level interactions in the presence of an unobserved correlated moderator at the country level. To obtain an unbiased within-country estimator of a cross-level interaction, effect heterogeneity must be systematically controlled. By replicating a published analysis, we demonstrate the relevance of this extended country fixed-effects estimator in research practice. The intent of this article is to provide advice for multilevel practitioners, who will be increasingly confronted with the availability of pooled cross-sectional survey data.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:06 Faculty of Arts > Institute of Sociology
Dewey Decimal Classification:300 Social sciences, sociology & anthropology
310 Statistics
Scopus Subject Areas:Social Sciences & Humanities > Sociology and Political Science
Uncontrolled Keywords:cross-level interaction, pooled cross-section, country fixed effects, fixed effects, multilevel analysis, within effect
Language:English
Date:1 August 2019
Deposited On:22 Jan 2020 08:38
Last Modified:29 Jul 2020 13:23
Publisher:Sage Publications
ISSN:0081-1750
OA Status:Closed
Publisher DOI:https://doi.org/10.1177/0081175018809150

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