Comparison Of Methods For Detecting Violations Of Measurement Invariance With Continuous Construct Indicators Using Latent Variable Modeling
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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.
Measurement Invariance
Author: Rens Van De Schoot
language: en
Publisher: Frontiers Media SA
Release Date: 2015-10-05
Multi-item surveys are frequently used to study scores on latent factors, like human values, attitudes and behavior. Such studies often include a comparison, between specific groups of individuals, either at one or multiple points in time. If such latent factor means are to be meaningfully compared, the measurement structures including the latent factor and their survey items should be stable across groups and/or over time, that is ‘invariant’. Recent developments in statistics have provided new analytical tools for assessing measurement invariance (MI). The aim of this special issue is to provide a forum for a discussion of MI, covering some crucial ‘themes’: (1) ways to assess and deal with measurement non-invariance; (2) Bayesian and IRT methods employing the concept of approximate measurement invariance; and (3) new or adjusted approaches for testing MI to fit increasingly complex statistical models and specific characteristics of survey data. The special issue started with a kick-off meeting where all potential contributors shared ideas on potential papers. This expert workshop was organized at Utrecht University in The Netherlands and was funded by the Netherlands Organization for Scientific Research (NWO-VENI-451-11-008). After the kick-off meeting the authors submitted their papers, all of which were reviewed by experts in the field. The papers in the eBook are listed in alphabetical order, but in the editorial the papers are introduced thematically. Although it is impossible to cover all areas of relevant research in the field of MI, papers in this eBook provide insight on important aspects of measurement invariance. We hope that the discussions included in this special issue will stimulate further research on MI and facilitate further discussions to support the understanding of the role of MI in multi-item surveys.
Algorithms for Measurement Invariance Testing
Author: Veronica Cole
language: en
Publisher: Cambridge University Press
Release Date: 2023-12-21
Latent variable models are a powerful tool for measuring many of the phenomena in which developmental psychologists are often interested. If these phenomena are not measured equally well among all participants, this would result in biased inferences about how they unfold throughout development. In the absence of such biases, measurement invariance is achieved; if this bias is present, differential item functioning (DIF) would occur. This Element introduces the testing of measurement invariance/DIF through nonlinear factor analysis. After introducing models which are used to study these questions, the Element uses them to formulate different definitions of measurement invariance and DIF. It also focuses on different procedures for locating and quantifying these effects. The Element finally provides recommendations for researchers about how to navigate these options to make valid inferences about measurement in their own data.