A Comment on the H^T Person Fit Statistic

The non-parametric H^T fit statistic (Sijtsma, 1986) is a transposed formulation of Loevinger's H scalability coefficient for items. It is evaluated by Karabatsos (2003). He reports "Overall, the H^T statistic is best [of 36 person fit statistics] in identifying aberrant test respondents. It is also among the best in detecting each of the five different types of aberrant-responding examinees, and in detecting such examinees in each of the short, medium, and long test conditions."

H^T is defined for the rows (persons) of a complete rectangular dichotomous dataset.. Let us focus on person n in a dataset which has L items and N persons. Then, following Karabatsos (2003),

where X_ni is the scored (0,1) response of person n to item i, and P_n = S_n/L where S_n is the raw score of person n, and similarly for person m.

According to Karabatsos (2003), "the critical values H^T = .22 best identify aberrant-responding examinees." In my own informal analyses, the correlation between H^T and the Rasch Infit mean-square was about -0.9, but I was unable to identify a unique Infit mean-square value corresponding to H^T = .22. Since Sijtsma and Molenaar (2002) report 0.3 to be a critical value for coefficient H, a small simulation study may be required to determine the critical value of H^T for a specific empirical dataset.

John Michael Linacre,/p>

Karabatsos, G. (2003). Comparing the aberrant response detection performance of thirty-six person-fit statistics. Applied Measurement in Education, 16(4), 277-298.

Sijtsma, K. (1986). A coefficient of deviant response patterns. Kwantitative Methoden, 7, 131-145.

Sijtsma K,, Molenaar I.W. (2002). Introduction to Nonparametric Item Response Theory. Thousand Oaks, CA: Sage.

A Comment on the H^T Person Fit Statistic, J.M. Linacre, Rasch Measurement Transactions, 2012, 26:1, 1358

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