Stochastic Processes for Assessing Measurement Invariance in Psychometric Models

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This project involves the application of parameter instability tests from theoretical statistics to the study of measurement invariance in psychometrics. The tests, based on Gaussian processes, have the ability to identify subgroups of both individuals and model parameters that violate measurement invariance. In contrast, existing tests of measurement invariance require the (potentially) violating subgroups and model parameters to be specified in advance. The project includes theory development, study of test performance in psychometric applications, and R software development. The work will yield a more comprehensive set of tools than currently is available for studying measurement invariance in a variety of psychometric models.Informally, measurement invariance involves the notion that a scale (or set of scales) measures everyone in the same manner. That is, if two individuals have the same "amount" of an ability of interest, a scale should assign the same score to the two individuals (save for random error). A scale violates measurement invariance if it systematically assigns different scores to the two individuals. For example, this issue is exceptionally problematic when the scales come from a college entrance exam: individuals of equal ability may systematically receive different scores. The project will apply novel statistical methods to the issue of measurement invariance, advancing theoretical knowledge and addressing standing problems on the topic. Open source software and realistic applications of the methods also will be developed, ensuring that the methods are broadly disseminated and accessible to a wide range of researchers. The project will lead to advances in applied knowledge on social science issues. Because the issue of measurement invariance involves the study of group differences, the proposed research will help ensure that psychometric scales treat diverse groups of individuals equally.