A Didactic Presentation of Snijders’ lz* Index of Person Fit with Emphasis on Response Model Selection and Ability Estimation
Conventional lz index has been popular and adopted in the studies of person fit. However, the index only follow the standardize normal distribution when computing by true ability. In practice, we can obtain estimated ability from collecting data, thus lz doesn’t fulfill the assumption of standardize normal distribution. As a result, pre-specific nominal level may not be achieved in such situation. Snijders’ lz had been developed to resolve the problem, however, it has not been common used nowadays. The main reason is that the procedure is not easy to follow, so that the authors tried to introduce a didactic technique on Snijders’ lz method with more concrete description. The Snijders’ lz follows standardize normal distribution when estimated ability is used on index computation if ability method meets equation 14 of the paper. As my point of view, it is really better than conventional one under the scenario of item parameters known. In the reality, item parameters and person parameter are estimated simultaneously. Thus, parameters may affected by noise of aberrant behaviors, so that Snijders’ lz would not follows the property of standardize normal distribution.