This study introduced a probabilistic model utilizing item response theory (IRT) for dealing with a variety of misconceptions. The model can be used for evaluating the transition behavior of error types, advancement of learning stages, or the stability and persistence of particular misconceptions. Moreover, it apparently can be used for relating the functional behavior of errors to other criterion measures such as creativity, anxiety, and motivation. One of several personal indices based on IRT was used to formulate the "rule space," which is a geometric representation of erroneous rules of operation. ECI4, one of the indices, which is used primarily for detecting aberrant response patterns, appeared to be effective for separating clusters of response patterns from one another. A cluster of response patterns consists of the response pattern yielded by some rule and its "slips," due to partially consistent application of the rule. Using pattern classification to separate the clusters in the rule space accounts for variability of errors in the model. (PN)