PerFit (version 1.2)

U3poly: U3poly person-fit statistic

Description

Generalization of van der Flier's U3 person-fit statistic to polytomously scored items.

Usage

U3poly(matrix,Ncat)

Arguments

matrix

A data matrix of polytomous item scores: Persons as rows, items as columns, item scores are integers between 0 and (Ncat-1), no missing data.

Ncat

Number of answer options for each item.

Value

• An object of class "PerFit", which is a list with elements:
• PFscores
  A vector of length $N$ (number of respondents) with the values of the person-fit statistic.
• PFstatistic
  The name of the person-fit statistic used.

Details

Emons (2008) generalized the U3 statistic (van der Flier, 1980, 1982) to polytomous items. The idea is based on the so-called item-step difficulty, which is the probability of moving from answer category $(c)$ to answer category $(c+1)$ ($c=0,\ldots,Ncat-2$). U3poly varies from 0 (no misfit) through 1 (extreme misfit). Hence, increasingly large U3poly values provide stronger indications of answering misfit. The number of answer options, Ncat, is the same for all items. U3poly reduces to U3 when Ncat=2.

References

Emons, W. M. (2008) Nonparametric person-fit analysis of polytomous item scores. Applied Psychological Measurement, 32(3), 224--247. Karabatsos, G. (2003) Comparing the Aberrant Response Detection Performance of Thirty-Six Person-Fit Statistics. Applied Measurement In Education, 16(4), 277--298. Meijer, R. R., and Sijtsma, K. (2001) Methodology review: Evaluating person fit. Applied Psychological Measurement, 25(2), 107--135. van der Flier, H. (1980) Vergelijkbaarheid van individuele testprestaties [Comparability of individual test performance]. Lisse: The Netherlands. van der Flier, H. (1982) Deviant response patterns and comparability of test scores. Journal of Cross-Cultural Psychology, 13(3), 267--298.

See Also

U3, ZU3

Examples

# Load the physical functioning data (polytomous item scores):
data(PhysFuncData);

# Compute the U3poly scores:
U3poly(PhysFuncData,Ncat=3);