Identifying And Minimizing Measurement Invariance Among Intersectional Groups
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Identifying and Minimizing Measurement Invariance among Intersectional Groups
Author: Rachel A. Gordon
language: en
Publisher: Cambridge University Press
Release Date: 2023-07-06
This Element demonstrates how and why the alignment method can advance measurement fairness in developmental science. It explains its application to multi-category items in an accessible way, offering sample code and demonstrating an R package that facilitates interpretation of such items' multiple thresholds. It features the implications for group mean differences when differences in the thresholds between categories are ignored because items are treated as continuous, using an example of intersectional groups defined by assigned sex and race/ethnicity. It demonstrates the interpretation of item-level partial non-invariance results and their implications for group-level differences and encourages substantive theorizing regarding measurement fairness.
Applied Statistics for the Social and Health Sciences
Covering basic univariate and bivariate statistics and regression models for nominal, ordinal, and interval outcomes, Applied Statistics for the Social and Health Sciences provides graduate students in the social and health sciences with fundamental skills to estimate, interpret, and publish quantitative research using contemporary standards. Reflecting the growing importance of "Big Data" in the social and health sciences, this thoroughly revised and streamlined new edition covers best practice in the use of statistics in social and health sciences, draws upon new literatures and empirical examples, and highlights the importance of statistical programming, including coding, reproducibility, transparency, and open science. Key features of the book include: interweaving the teaching of statistical concepts with examples from publicly available social and health science data and literature excerpts; thoroughly integrating the teaching of statistical theory with the teaching of data access, processing, and analysis in Stata; recognizing debates and critiques of the origins and uses of quantitative methods.
Comparison of Methods for Detecting Violations of Measurement Invariance with Continuous Construct Indicators Using Latent Variable Modeling
Measurement invariance (MI) refers to the fact that the measurement instrument measures the same concept in the same way in two or more groups. However, in educational and psychological testing practice, the assumption of MI is often violated due to the contamination by possible noninvariance in the measurement models. In the framework of Latent Variable Modeling (LVM), methodologists have developed different statistical methods to identify the noninvariant components. Among these methods, the free baseline method (FR) is popularly employed, but this method is limited due to the necessity of choosing a truly invariant reference indicator (RI). Two other methods, namely, the Benjamini-Hochberg method (B-H) and the alignment method (AM) are exempt from the RI setting. The B-H method applies the false discovery rate (FDR) procedure. The AM method aims to optimize the model estimates under the assumption of approximate invariance. The purpose of the present study is to address the problem of RI setting by comparing the B-H method and the AM method with the traditional free baseline method through both a simulation study and an empirical data analysis. More specifically, the simulation study is designed to investigate the performances of the three methods through varying the sample sizes and the characteristics of noninvariance embedded in the measurement models. The characteristics of noninvariance are distinguished as the location of noninvariant parameters, the degree of noninvariant parameters, and the magnitude of model noninvariance. The performances of these three methods are also compared on an empirical dataset (Openness for Problem Solving Scale in PISA 2012) that is obtained from three countries (Shanghai-China, Australia, and the United States).The simulation study finds that the wrong RI choice heavily impacts the FR method, which produces high type I error rates and low statistical power rates. Both the B-H method and the AM method perform better than the FR method in this setting. Comparatively speaking, the benefit of the B-H method is that it performs the best by achieving high powers for detecting noninvariance. The power rate increases with lowering the magnitude of model noninvariance, and with increasing sample size and degree of noninvariance. The AM method performs the best with respect to type I errors. The type I error rates estimated by the AM method are low under all simulation conditions. In the empirical study, both the B-H method and the AM method perform similarly in estimating the invariance/noninvariance patterns among the three country pairs. However, the FR method, for which the RI is the first item by default, recovers a different invariance/noninvariance pattern. The results can help the methodologists gain a better understanding of the potential advantages of the B-H method and the AM method over the traditional FR method. The study results also highlight the importance of correctly specifying the model noninvariance at the indicator level. Based on the characteristics of the noninvariant components, practitioners may consider deleting/modifying the noninvariant indicators or free the noninvariant components while building partial invariant models in order to improve the quality of cross-group comparisons.