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Investigations of parameter invariance in IRT models : theoretical and pratical avenues for understanding a fundamental property of measurement Rupp, André Alexander

Abstract

The quest for invariance is the quest for scientific generalizability and parameter invariance is thus a fundamental property of measurement that is of interest to both theoreticians and practitioners. To investigate invariance properly, a precise mathematical definition is required, which contrasts sharply with a more conceptual and philosophical usage of this term and it is not uncommon to find that researchers think of the invariance of parameters in a measurement model as a guaranteed property of such models. This dissertation deconstructs this myth through a series of four studies that are connected by a consistent logic of inquiry for understanding what does and does not constitute parameter invariance and how a lack of parameter invariance can be assessed, quantified, and accounted for. The first study shows how the use of correlation coefficients can be insufficient to show that parameter invariance holds as such coefficients miss group-level differences in the data. The second and third studies show how biases due to a lack of invariance can be analytically derived and numerically quantified and they reveal that their practical impact is minor for many conditions. Furthermore, the work shows how the formalization of invariance provides a unique frame for discussions of model optimality, because it is shown that no single unidimensional item response theory model possesses superior optimality properties under all conditions that are considered. The fourth study illustrates how attitudinal and background variables can be used to create examinee profiles, which can be used to group examinees when investigating differential functioning of item sets for these groups using novel tools from functional data analysis. Specifically, using data from the TEVISS 1999 large-scale assessment, the study shows how observed differential performance can be accounted for using these profiles. The work in this dissertation thus combines multiple theoretical and practical perspectives to better understand this fundamental property of measurement.

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