Person Fit in the Rasch Model

Abstract

The idea of whether a person's response pattern is "believable" given his estimated ability is one of the central issues in measurement. This article traces the development of this idea from Thurstone to Rasch. It also presents the rationale behind the development of person analysis in the Rasch model. Finally, it presents data based on simulated response patterns which provide insight into the power and Type I error rates of the Rasch unweighted total and between person fit statistics under a variety of simulated measurement disturbances.

Investigating whether aberrant response behaviour in classroom maths tests is a stable characteristic of students

“…If indeed they have (or at least some of them do) then one would expect, as suggested by Smith (1986) and Lamprianou (2005), that an individual with an aberrant response pattern may exhibit such behaviour in other testing situations too. This means that aberrance may be a stable characteristic of individuals.…”

“…He attributed his findings to the fact that the test items were mainly multistep mathematical problems with partial credit awarding for partial success instead of the usual dichotomous items found in the literature and to the low status of the tests and the non-stressful administration procedure in the classroom setting. Smith (1986) and Lamprianou (2005) suggested that an individual with an aberrant response pattern may exhibit such response behaviour in other testing situations too, implying that misfit could be a stable characteristic of individuals.…”

“…Panayides (2009) found no associations with aberrance of several of the factors reported in the literature. On the other hand Smith (1986) and Lamprianou (2005) suggested that an individual with an aberrant response pattern may exhibit such response behaviour in other testing situations too, implying that misfit could be a stable characteristic of individuals. This is also implied by the various types of individuals, suggested in the literature, that exhibit aberrant response behaviour (sleepers, fumblers, plodders and guessers).…”

Assessing the fit of dichotomous item response theory models

“…Some indices-as, for example, Yen's chi-square (Yen, 1981) or Bock's chi-square (Bock, 1972)-may be applied to any of the commonly used IRT models such as the one-, two-, or three-parameter logistic models (1PL, 2PL, 3PL, respectively); others, such as the Rasch model's item fit statistic (Smith, 1988;Smith & Wright, 1987), are modelspecific indices. These fit statistics are or are based on chi-square (the Rasch model's t statistics are transfo~a tions of chi-square) and differ from one another With respect to the number intervals and the computation of the predicted score.…”

IRT model fit from different perspectives

“…In the IRT context several person fit statistics have been proposed that can be used to detect individual item score patterns that do not fit the IRT model (Levine & Rubin, 1979;Wright & Stone, 1979;Tatsuoka, 1984;Smith, 1985Smith, , 1986Klauer & Rettig, 1990;Drasgow, Levine, & McLaughlin, 1991;Glas & Dagohoy, 2007). See Meijer and Sijtsma (2001) for a review.…”