Differential Item Functioning (DIF) Testing with Estimation of the Latent Densities

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One important application of item response theory (IRT) is for identification of differential item functioning (DIF). DIF occurs when an item has different measurement properties for one group of people than another (e.g., men versus women), irrespective of group-mean differences on the latent variable. Typically, in IRT-based DIF testing, the latent variables are assumed to be normally distributed in the populations of people. However, this assumption may be untenable for some variables. The present research develops statistical methodology and software for IRT-based DIF testing in which the latent distribution for each group of people is estimated simultaneously with the item parameters.This research fills a gap in extant methodology and is aimed at improving the match between data and the statistical models used to assess DIF. Questionnaires measuring latent variables which are potentially nonnormally distributed are used as part of making, for example, psychological and medical diagnoses and treatment plans, and hiring or admission decisions in businesses or universities. Assessment instruments constructed based on majority-group individuals may provide misleading results for underrepresented groups. The proposed methodology could be applied in these areas to promote fair, accurate, and inclusive measurement. The research is supported by the Methodology, Measurement, and Statistics Program, the REESE Program, and a consortium of federal statistical agencies as part of a joint activity to support research on survey and statistical methodology.