Guessing and the Rasch Model

Stewart questioned Beglar’s use of Rasch analysis of the Vocabulary Size Test (VST) and advocated the use of 3-parameter logistic item response theory (3PLIRT) on the basis that it models a non-zero lower asymptote for items, often called a “guessing” parameter. In support of this theory, Stewart presented fit statistics derived from Rasch analysis of random numbers displaying good data-model fit. Because data-model fit is a key assumption of the Rasch model, Stewart argued that the Rasch model was unable to identify problematic guessing. Stewart correctly observed that advice given by Beglar and Nation on the rescaling of raw scores as criterion measures of vocabulary size is problematic, but provided no empirical evidence to support his preference for 3PLIRT. Stewart’s major claims are easily testable, however, so this paper used empirical data to investigate whether Rasch analysis could identify problematic guessing and whether correction for lucky guessing affected measurement. The results showed that random guessing was easily identifiable and that correction for guessing did not change the relative positions of persons and items on the latent trait beyond the limits of measurement error.