Identifying measurement disturbance effects using Rasch item fit statistics and the Logit Residual Index

A Monte Carlo study was conducted using simulated dichotomous data to determine the effects of guessing on Rasch item fit statistics (weighted total, unweighted total, and unweighted between fit statistics) and the Logit Residual Index (LRI). The data were simulated using 100 items, 100 persons, three levels of guessing (0%, 25%, and 50%), and two item difficulty distributions (normal and uniform). The results of the study indicated that no significant differences were found between the mean Rasch item fit statistics for each distribution type as the probability of guessing the correct answer increased. The mean item scores differed significantly with uniformly distributed item difficulties, but not normally distributed item difficulties. The LRI was more sensitive to large positive item misfit values associated with the unweighted total fit statistic than to similar values associated with the weighted total fit or unweighted between fit statistics. The greatest magnitude of change in LRI values (negative) was observed when the unweighted total fit statistic had large positive values greater than 2.4. The LRI statistic was most useful in identifying the linear trend in the residuals for each item, thereby indicating differences in ability groups, i.e. differential item functioning.