Testing for Measurement Invariance with Respect to an Ordinal Variable
Researchers are often interested in testing for measurement invariance with respect to an ordinal auxiliary variable such as age group, income class, or school grade. In a factor-analytic context, these tests are traditionally carried out via a likelihood ratio test statistic comparing a model where...
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Veröffentlicht in: | Psychometrika 2014-10, Vol.79 (4), p.569-584 |
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description | Researchers are often interested in testing for measurement invariance with respect to an ordinal auxiliary variable such as age group, income class, or school grade. In a factor-analytic context, these tests are traditionally carried out via a likelihood ratio test statistic comparing a model where parameters differ across groups to a model where parameters are equal across groups. This test neglects the fact that the auxiliary variable is ordinal, and it is also known to be overly sensitive at large sample sizes. In this paper, we propose test statistics that explicitly account for the ordinality of the auxiliary variable, resulting in higher power against “monotonic” violations of measurement invariance and lower power against “non-monotonic” ones. The statistics are derived from a family of tests based on stochastic processes that have recently received attention in the psychometric literature. The statistics are illustrated via an application involving real data, and their performance is studied via simulation. |
doi_str_mv | 10.1007/s11336-013-9376-7 |
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subjects | Adolescent Adult Assessment Behavioral Science and Psychology Child Ethnicity Factor Analysis Factor Analysis, Statistical High Stakes Tests Humanities Humans Hypotheses Lagrange multiplier Law Measurement Techniques Psychology Psychometrics Psychometrics - methods Quantitative psychology Random variables Research Design - statistics & numerical data Researchers Statistical Theory and Methods Statistics Statistics as Topic - methods Statistics for Social Sciences Testing and Evaluation Violations Young Adult |
title | Testing for Measurement Invariance with Respect to an Ordinal Variable |
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