The pure Rasch model was compared with four modifications of the model in a number of different simulations in order to ascertain the comparative efficiencies of the parameter estimations of these modifications. Because there is always noise in test score data, some individuals may have response patterns that do not fit the model and their abilities cannot be estimated accurately. The modifications used to overcome this difficulty include: the traditional correction for guessing, jackknifing, a robustified jackknife, and a method (WIM) based on an analysis of residuals. The simulation data included a guessing model with four characteristics: the need to guess, the invitation (a function of the item), the inclination (a function of the person), and glitch. The simulations were also varied by including: 3 difficulty levels, 3 test length, 2 levels of width, either 2 or 5 choice items, and 4 candidate ability levels. Both the accuracy of parameter estimation and the sampling error were combined to obtain indices of the relative efficiency of the five models. (CTM)