Recent Methods for the Study of Measurement Invariance With Many Groups Alignment and Random Effects

This article reviews and compares recently proposed factor analytic and item response theory approaches to the study of invariance across groups. Two methods are described and contrasted. The alignment method considers the groups as a fixed mode of variation, while the random-intercept, random-loadi...

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Bibliographic Details
Published inSociological methods & research Vol. 47; no. 4; pp. 637 - 664
Main Authors Muthén, Bengt, Asparouhov, Tihomir
Format Journal Article
LanguageEnglish
Published Los Angeles, CA SAGE Publications 01.11.2018
Subjects
Bayesian Statistics
Factor Analysis
Foreign Countries
Groups
Item Response Theory
Maximum Likelihood Statistics
Measurement
Statistical Analysis
factor analysis
random slopes
random intercepts
item response theory
scalar invariance
configural invariance
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Summary:This article reviews and compares recently proposed factor analytic and item response theory approaches to the study of invariance across groups. Two methods are described and contrasted. The alignment method considers the groups as a fixed mode of variation, while the random-intercept, random-loading two-level method considers the groups as a random mode of variation. Both maximum likelihood and Bayesian analyses are applied. A survey of close to 50,000 subjects in 26 countries is used as an illustration. In addition, the two methods are studied by Monte Carlo simulations. A list of considerations for choosing between the two methods is presented.
ISSN:0049-1241
1552-8294
DOI:10.1177/0049124117701488