This study compares the fit of the 3-parameter model to the Ability Removing Random Guessing (ARRG) model on data from a wide range of tests of cognitive ability in three representative samples. When the guessing parameters under the 3-parameter model are estimated individually for each item, the 3-parameter model yields the better fit to approximately 61 percent of these examinations. The ARRG model, which is designed to remove the effects of purely random guessing only, produces a better fit in 15 percent of these examinations, apparently to only those data sets which contain relatively little partial knowledge guessing behavior. The 2-parameter, free response model produces the best fit to 24 percent of these examinations. These results indicate that the 3-parameter model does make an adjustment for partial knowledge guessing. A comparison is also made between fits of the 3-parameter model with guessing parameters estimated at a constant value of one divided by the number of alternatives, and those estimated individually. Individually estimated guessing parameters are found to produce fits far superior to those estimated at a constant value. A solution to the convergence problems often obtained with the 3-parameter model is discussed. (Author/JAZ)