ABSTRACT
This paper presents an IRT-based statistical test for differential item functioning (DIF). The test is developed for items conforming to the Rasch (Probabilistic models for some intelligence and attainment tests, The Danish Institute of Educational Research, Copenhagen, 1960) model but we will outline its extension to more complex IRT models. Its difference from the existing procedures is that DIF is defined in terms of the relative difficulties of pairs of items and not in terms of the difficulties of individual items. The argument is that the difficulty of an item is not identified from the observations, whereas the relative difficulties are. This leads to a test that is closely related to Lord's (Applications of item response theory to practical testing problems, Erlbaum, Hillsdale, 1980) test for item DIF albeit with a different and more correct interpretation. Illustrations with real and simulated data are provided.
Subject(s)
Data Interpretation, Statistical , Models, Statistical , Psychometrics/methods , Algorithms , Humans , Models, TheoreticalABSTRACT
The DA-T Gibbs sampler is proposed by Maris and Maris (2002) as aBayesian estimation method for a wide variety of Item Response Theory(IRT) models. The present paper provides an expository account of the DATGibbs sampler for the 2PL model. However, the scope is not limited tothe 2PL model. It is demonstrated how the DA-T Gibbs sampler for the 2PLmay be used to build, quite easily, Gibbs samplers for other IRT models.Furthermore, the paper contains a novel, intuitive derivation of the Gibbssampler and could be read for a graduate course on sampling
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Subject(s)
Humans , Logistic Models , Psychometrics/statistics & numerical dataABSTRACT
In a questionnaire study, a random sample of Dutch families was asked whether they suffered from asthma and related symptoms. From these families, a selected sample was invited to come to the hospital for further phenotyping. Families were selected if at least one family member reported a history of asthma and the twins were 18 years of age or older. Not all families that were thus selected volunteered, leaving us with a fraction of the original sample. The aim of this paper is to describe a limited dependent variable model that can be used in such situations in order to obtain estimates that are representative of the population from which the sample was originally drawn. The model is a linear (DeFries-Fulker) regression model corrected for sample selection. This correction is possible when (some of) the characteristics that determine whether subjects volunteer (or not) are known for all subjects, including those that did not volunteer. The questionnaire study is of interest by itself but serves mainly to provide a concrete illustration of our method. The present model is used to analyze the data and the results are compared to those obtained with other methods: raw (or direct) likelihood estimation, multiple imputation, and sample weighting. Throughout, Rubin's general theory of inference with missing data serves as an integrating framework.
