Asymptotically Correct Standardization of Person-Fit Statistics Beyond Dichotomous Items

Sandip Sinharay ()
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Sandip Sinharay: McGraw-Hill Education CTB

Psychometrika, 2016, vol. 81, issue 4, No 5, 992-1013

Abstract: Abstract The $$l_z$$ l z statistic (Drasgow et al. in Br J Math Stat Psychol 38:67–86, 1985) is one of the most popular person-fit statistics (Armstrong et al. in Pract Assess Res Eval 12(16):1–10, 2007). Snijders (Psychometrika 66:331–342, 2001) derived the asymptotic null distribution of $$l_z$$ l z when the examinee ability parameter is estimated. He also suggested the $$l^*_z$$ l z ∗ statistic, which is the asymptotically correct standardized version of $$l_z$$ l z . However, Snijders (Psychometrika 66:331–342, 2001) only considered tests with dichotomous items. In this paper, the asymptotic null distribution of $$l_z$$ l z is derived for mixed-format tests (those that include both dichotomous and polytomous items). The asymptotically correct standardized version of $$l_z$$ l z , which can be considered as the extension of $$l^*_z$$ l z ∗ to such tests, is suggested. The Type I error rate and power of the suggested statistic are examined from several simulated datasets. The suggested statistic is computed using a real dataset. The suggested statistic appears to be a satisfactory tool for assessing person fit for mixed-format tests.

Keywords: generalized partial credit model; $$l_z$$ l z; $$l^*_z$$ l z ∗; polytomous items (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s11336-015-9465-x

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