sirt (version 0.36-30)

dif.logistic.regression: Differential Item Functioning using Logistic Regression Analysis

Description

This function estimates differential item functioning using a logistic regression analysis (Zumbo, 1999).

Usage

dif.logistic.regression(dat, group, score,quant=1.645)

Arguments

dat

Data frame with dichotomous item responses

group

Group identifier

score

Ability estimate, e.g. the WLE.

quant

Used quantile of the normal distribution for assessing statistical significance

Value

• A data frame with following variables:
• itemnr
  Numeric index of the item
• sortDIFindex
  Rank of item with respect to the uniform DIF (from negative to positive values)
• item
  Item name
• N
  Sample size per item
• R
  Value of group variable for reference group
• F
  Value of group variable for focal group
• nR
  Sample size per item in reference group
• nF
  Sample size per item in focal group
• p
  Item $p$ value
• pR
  Item $p$ value in reference group
• pF
  Item $p$ value in focal group
• pdiff
  Item $p$ value differences
• pdiff.adj
  Adjusted $p$ value difference
• uniformDIF
  Uniform DIF estimate
• se.uniformDIF
  Standard error of uniform DIF
• t.uniformDIF
  The $t$ value for uniform DIF
• sig.uniformDIF
  Significance label for uniform DIF
• DIF.ETS
  DIF classification according to the ETS classification system (see Details)
• uniform.EBDIF
  Empirical Bayes estimate of uniform DIF (Longford, Holland & Thayer, 1993) which takes degree of DIF standard error into account
• DIF.SD
  Value of the DIF standard deviation
• nonuniformDIF
  Nonuniform DIF estimate
• se.nonuniformDIF
  Standard error of nonuniform DIF
• t.nonuniformDIF
  The $t$ value for nonuniform DIF
• sig.nonuniformDIF
  Significance label for nonuniform DIF

Details

Items are classified into A (negligible DIF), B (moderate DIF) and C (large DIF) levels according to the ETS classification system (Longford, Holland & Thayer, 1993, p. 175). See also Monahan et al. (2007) for further DIF effect size classifications.

References

Longford, N. T., Holland, P. W., & Thayer, D. T. (1993). Stability of the MH D-DIF statistics across populations. In P. W. Holland & H. Wainer (Eds.). Differential Item Functioning (pp. 171-196). Hillsdale, NJ: Erlbaum. Monahan, P. O., McHorney, C. A., Stump, T. E., & Perkins, A. J. (2007). Odds ratio, delta, ETS classification, and standardization measures of DIF magnitude for binary logistic regression. Journal of Educational and Behavioral Statistics, 32, 92-109. 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 ON: Directorate of Human Resources Research and Evaluation, Department of National Defense.

See Also

For assessing DIF variance see dif.variance and dif.strata.variance See the difR package for a large collection of DIF detection methods.

Examples

#####################################
# EXAMPLE 1: Mathematics data

data( data.math )
dat <- data.math$data
items <- grep( "M" , colnames(dat))

# estimate item parameters and WLEs
mod <- rasch.mml2( dat[,items] )
wle <- wle.rasch( dat[,items] , b=mod$item$b )$theta

# assess DIF by logistic regression
mod1 <- dif.logistic.regression( dat=dat[,items] , score=wle , group=dat$female)

# calculate DIF variance
dif1 <- dif.variance( dif=mod1$uniformDIF , se.dif = mod1$se.uniformDIF )
dif1$unweighted.DIFSD
## > dif1$unweighted.DIFSD
## [1] 0.1963958

# calculate stratified DIF variance
# stratification based on domains
dif2 <- dif.strata.variance( dif=mod1$uniformDIF , se.dif = mod1$se.uniformDIF ,
        itemcluster = data.math$item$domain )
## $unweighted.DIFSD
## [1] 0.1455916

#****
# Likelihood ratio test and graphical model test in eRm package
library(eRm)
# estimate Rasch model
res <- RM( dat[,items] )
summary(res)
# LR-test with respect to female
lrres <- LRtest(res, splitcr = dat$female)
summary(lrres)
# graphical model test
plotGOF(lrres)