dlr: Logistic Regression DIF Function
In brookiem86/dDIF: MH and LR DIF Detection for Dichotomously Scored Items

Description Usage Arguments Details Value References See Also Examples

dlr identifies DIF using the logistic regression statistic method

1	dlr(idata, group, alpha = 0.05)

`idata`	a matrix or data.frame of binary scored item responses. Only includes item data
`group`	a numeric vector of values identifying group membership. The focal group should be coded as 1 while the reference group should be coded as 0. Missing values are not allowed for group.
`alpha`	identifies the alpha value used in the analyses. The default value is 0.05.

The dlr function computes logistic regression results within a DIF framework specified by Swaminathan and Rogers (1990). Three models are traditionally fitted in order to determine if an item has mixed, nonuniform, or uniformed DIF. The three models that are fitted include:

M0: logit(πg) = β0 + β1θ + β2g + β3θg

M1: logit(πg) = β0 + β1θ + β2g

M2: logit(πg) = β0 + β1θ

where πg is the probability of correctly answering an item in group g, θ is examinee’s matching criteria, and g is the group membership of the examinee.

Nonuniform DIF is assessed by comparing the M0 and M1 models. Uniform DIF is evaluated by comparing the M1 and M2 models.

The magnitude of DIF is calculated by subtracting the R^2 estimate of the compact model from the R^2 value of the augmented model. Nagelkerke R^2 estimate (Nagelkerke, 1991) is used to compute the DIF effect size. Classification indices of the magnitude of DIF are based on values suggested by Zumbo and Thomas (1997). classifications of A, B, and C represent negligible, moderate, and large DIF effect sizes.

A: deltaR^2 < or = .13 B: .13 < deltaR^2 < or = .26 C: deltaR^2 > .26

A list containing:

LRModels a list containing three data frames consisting of the results from the M0 M1 and M2 LR models

UniformDIF a data frame consisting of the uniform DIF results

NonuniformDIF a data frame consisting of the uniform DIF results

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.

Nagelkerke, N. J. D. (1991). A note on a general definition of the coefficient of determination. Biometrika, 78, 691-692.

Swaminathan, H. and Rogers, H. J. (1990). Detecting differential item functioning using logistic regression procedures. Journal of Educational Measurement, 27, 361-370.

Zumbo, B. D. (1999). A handbook on the theory and methods of differential item functioning (DIF): Logistic regression modeling as a unitary framework for binary and Likert-type (ordinal) item scores. Ottawa, Canada: Directorate of Human Resources Research and Evaluation, Department of National Defense.

Zumbo, B. D.,&Thomas, D. R. (1997). A measure of effect size for a model-based approach for studying DIF (Working paper of the Edgeworth Laboratory for Quantitative Behavioral Science). Prince George, Canada: University of Northern British Columbia.

R2N for Nagelkerke R^2

#Loading data
data(difdat)

#Testing DIF using LR approach alpha = .05
dif.lr <- dlr(difdat[, 1:21], difdat[, 1])

#Testing DIF using LR approach alpha = .01
dif.lr <- dlr(difdat[, 1:21], difdat[, 1], alpha = .01)