dmh: Mantel Haenszel DIF Function

In brookiem86/dDIF: MH and LR DIF Detection for Dichotomously Scored Items

Description

dmh identifies DIF using the Mantel Haenszel method

Usage

dmh(idata, group)

Arguments

idata	Matrix or data.frame of binary scored item responses. Should include only items
group	Numeric vector of values identifying group membership Missing values are not allowed for group

Details

The MH method is used to detect uniform DIF. The equation for the MH statistic was obtained from Holland and Thayer (1988). The value of 0.5 reflects Yates' correction for continuity and is included in the MH formula.

The MH statistic is computed by:

MH.Stat = [(|∑[At - ε(At)]| - 0.5)] / [ ∑ var(At)]

where

ε(At) = [nRt*nCt] / nT

and

var(At) = [nRt*nFt*nCt*nWt] / [nT^2(nT - 1)]

At: number of correct responses for the reference group Bt: number of incorrect responses for the reference group Ct: number of correct responses for the focal group Dt: number of incorrect responses for the focal group nCt: total items correct nWt: total items incorrect nRt: number of individuals in reference group nFt: number of individuals in focal group nT: Total number of responses

The common odds ratio is an indication of the degree of association (Mantel & Haenszel, 1959). Values greater than 1 indicate that on average the reference group performed better than the focal group on the item.

[∑(At*Dt)/nT] / [∑(Bt*Ct)/nT]

The common odds ratio is commonly transformed into different scales that are symmetric around 0. ETS's delta scale is a common transformation used in practice in order to better understand the magnitude of DIF (Holland & Thayer, 1985).

Delta Scale = -2.35[ln(Common Odds Ratio)]

Value

A data frame containing the MH statistic, p-values, common odds ratio, and delta scale values for each item

References

Hidalgo, M. D. and Lopez-Pina, J.A. (2004). Differential item functioning detection and effect size: a comparison between logistic regression and Mantel-Haenszel procedures. Educational and Psychological Measurement, 64, 903-915.

Holland, P. W. and Thayer, D. T. (1985). An alternative definition of the ETS delta scale of item difficulty. Research Report RR-85-43. Princeton, NJ: Educational Testing Service.

Holland, P. W. and Thayer, D. T. (1988). Differential item performance and the Mantel-Haenszel procedure. In H. Wainer and H. I. Braun (Ed.), Test validity. Hillsdale, NJ: Lawrence Erlbaum Associates.

Mantel, N. and Haenszel, W. (1959). Statistical aspects of the analysis of data from retrospective studies of disease. Journal of the National Cancer Institute, 22, 71 -748.

Examples

#Loading data
data(difdat)

# Running dmh
dmh(difdat[, 2:21], difdat[, 1])

brookiem86/dDIF documentation built on May 13, 2019, 7:50 a.m.