PerFit (version 1.2)

Personal biserial statistic: Personal biserial statistic

Description

Donlon and Fischer's personal biserial statistic.

Usage

r.pbis(matrix)

Arguments

matrix

A data matrix of dichotomous item scores: Persons as rows, items as columns, item scores are either 0 or 1, no missing data.

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

Donlon and Fischer (1968) suggested to use the correlation between a respondent's score vector and the item proportion-correct scores in the sample as a measure of person fit. Low values should be indicative of misfit of the response vector with respect to the group of respondents. Response vectors (i.e., rows of matrix) that only consist of 0s or 1s need to be removed before the function can be used.

References

Donlon, T. F., and Fischer, F. E. (1968) An index of an individual's agreement with group-defined item difficulties. Educational and Psychological Measurement, 28(1), 105--113. 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.

Examples

# Load the inadequacy scale data (dichotomous item scores):
data(InadequacyData);

# Compute the r.pbis scores:
r.pbis(InadequacyData);