Assessing person fit using l*z and the posterior predictive model checking method for dichotomous item response theory models Online publication date: Wed, 16-Sep-2015
by Sandip Sinharay
International Journal of Quantitative Research in Education (IJQRE), Vol. 2, No. 3/4, 2015
Abstract: Person-fit assessment is employed to obtain additional information regarding the answering behaviour of persons (Glas and Meijer, 2003). The lz statistic (Drasgow et al., 1985) is one of the most popular person-fit statistics. The posterior predictive model checking method (e.g., Rubin, 1984) is a popular Bayesian tool for assessing the fit of item response theory (IRT) models (e.g., Sinharay, 2005; Sinharay et al., 2006). However, the use of lz (and its modifications) combined with the PPMC method led to a conservative person-fit assessment in de la Torre and Deng (2008) and Glas and Meijer (2003). The reason of the conservativeness of this combination is provided. The use of the l*z statistic (Snijders, 2001) along with the weighted likelihood estimate (WLE; Warm, 1989) of the examinee ability and the PPMC method is suggested. The suggested approach has satisfactory power and performs as well as the best approach of de la Torre and Deng (2008). The approach is then applied to an operational dataset.
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