The choice of the ability estimate with asymptotically correct standardized person‐fit statistics

S nijders (2001, P sychometrika , 66 , 331) suggested a statistical adjustment to obtain the asymptotically correct standardized versions of a specific class of person‐fit statistics. His adjustment has been used to obtain the asymptotically correct standardized versions of several person‐fit statistics including the l z statistic ( D rasgow et al ., 1985, B r. J . M ath. S tat. P sychol ., 38 , 67), the infit and outfit statistics (e.g., W right & M asters, 1982, Rating scale analysis , C hicago, IL : M esa P ress), and the standardized extended caution indices ( T atsuoka, 1984, P sychometrika , 49 , 95). S nijders (2001), van K rimpen‐ S toop and M eijer (1999, A ppl. P sychol. M eas ., 23 , 327), M agis et al . (2012, J . E duc. B ehav. S tat ., 37 , 57), M agis et al . (2014, J . A ppl. M eas ., 15 , 82), and S inharay (2015b, P sychometrika , doi: 10.1007/s11336‐015‐9465‐x , 2016b, Corrections of standardized extended caution indices , Unpublished manuscript) have used the maximum likelihood estimate, the weighted likelihood estimate, and the posterior mode of the examinee ability with the adjustment of S nijders (2001). This paper broadens the applicability of the adjustment of S nijders (2001) by showing how other ability estimates such as the expected a posteriori estimate, the biweight estimate ( M islevy & B ock, 1982, E duc. P sychol. M eas ., 42 , 725), and the H uber estimate ( S chuster & Y uan, 2011, J . E duc. B ehav. S tat ., 36 , 720) can be used with the adjustment. A simulation study is performed to examine the Type I error rate and power of two asymptotically correct standardized person‐fit statistics with several ability estimates. A real data illustration follows.