PerFit (version 1.2)

Gpoly, Gnormed.poly: Number of Guttman errors for polytomous items

Description

Molenaar (1991) and Emons (2008) statistics, based on the number of Guttman errors, for polytomous items.

Usage

Gpoly(matrix,Ncat)

Gnormed.poly(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

Molenaar (1991) generalized the G person-fit statistic to polytomous items, Gpoly. The idea is based on the so-called item-step difficulty, which is the probability of moving from answer category $(c)$ to answer category $(c+1)$ ($c=0,\ldots,Ncat-2$). Just like G, Gpoly depends on the test length. Emons (2008) developed Gnormed.poly, which is a normalized version of Gpoly. Aberrant response behavior is (potentially) indicated by large values of Gpoly/Gnormed.poly (i.e., in the right tail of the sampling distribution). The number of answer options, Ncat, is the same for all items. Gpoly reduces to G, and Gnormed.poly reduces to Gnormed, 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. (1994) The number of Guttman errors as a simple and powerful person-fit statistic. Applied Psychological Measurement, 18(4), 311--314. Molenaar, I. W. (1991) A weighted Loevinger H-coefficient extending Mokken scaling to multicategory items. Kwantitatieve Methoden, 12(37), 97--117.

See Also

G, Gnormed

Examples

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

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

# Compute the Gnormed.poly scores:
Gnormed.poly(PhysFuncData,Ncat=3);