Using Snijders’ approach to standardize some parametric person fit indexes with estimated ability levels: a simulation study

Several authors (Molenaar & Hoijtink, 1990; Meijer & Sijtsma, 2001) have shown that several person-fit statistics present some important limitations. One issue is that the distribution of some parametric person-fit statistics is unknown. Another important issue is that the distribution of person-fit indexes is most often derived under the true ability level. In this situation, replacing the true ability by some estimate can seriously affect the distribution of these indexes.
Snijders (2001) proposed a method to correct the mean and the variance of many parametric person-fit statistics to be approximately standard normally distributed, and derived the corrected version of the lz index. The purpose of this paper is to apply this correction to other well-known parametric indexes, and to compare them with their classical versions. The simulation results indicate that the standardized indexes have empirical type I errors close to the nominal significance level, and that the corrected indexes outperform their classical versions in this regard.