Title: Assessing person fit using l^*_z and the posterior predictive model checking method for dichotomous item response theory models

Authors: Sandip Sinharay

Addresses: McGraw-Hill Education CTB, 20 Ryan Ranch Road, Monterey CA 93924, USA

Abstract: Person-fit assessment is employed to obtain additional information regarding the answering behaviour of persons (Glas and Meijer, 2003). The l_z 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 l_z (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.

Keywords: 3PL model; generalised partial credit model; IRT model fit; posterior predictive model checking; person fit assessment; Bayesian statistics; weighted likelihood estimate; WLE; examinee ability; behavioural statistics; psychometrics.

DOI: 10.1504/IJQRE.2015.071730

International Journal of Quantitative Research in Education, 2015 Vol.2 No.3/4, pp.265 - 284

Received: 24 Oct 2014
Accepted: 19 Feb 2015
Published online: 16 Sep 2015 *

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