Premium
Extension of caution indices to mixed‐format tests
Author(s) -
Sinharay Sandip
Publication year - 2018
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/bmsp.12124
Subject(s) - polytomous rasch model , statistics , extension (predicate logic) , standardization , type i and type ii errors , mathematics , summary statistics , econometrics , computer science , item response theory , psychometrics , operating system , programming language
Tatsuoka suggested several extended caution indices and their standardized versions, and these have been used as person‐fit statistics by various researchers. However, these indices are only defined for tests with dichotomous items. This paper extends two of the popular standardized extended caution indices for use with polytomous items and mixed‐format tests. Two additional new person‐fit statistics are obtained by applying the asymptotic standardization of person‐fit statistics for mixed‐format tests. Detailed simulations are then performed to compute the Type I error rate and power of the four new person‐fit statistics. Two real data illustrations follow. The new person‐fit statistics appear to be satisfactory tools for assessing person fit for polytomous items and mixed‐format tests.