dif.logistic.regression: Differential Item Functioning using Logistic Regression...
In alexanderrobitzsch/sirt: Supplementary Item Response Theory Models

dif.logistic.regression

R Documentation

Differential Item Functioning using Logistic Regression Analysis

Description

This function assesses differential item functioning using 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

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, McHorney, Stump and Perkins (2007) for further DIF effect size classifications.

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

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.

Magis, D., Beland, S., Tuerlinckx, F., & De Boeck, P. (2010). A general framework and an R package for the detection of dichotomous differential item functioning. Behavior Research Methods, 42(3), 847-862. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.3758/BRM.42.3.847")}

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(1), 92-109. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.3102/1076998606298035")}

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.

Examples

#############################################################################
# EXAMPLE 1: Mathematics data | Gender DIF
#############################################################################

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

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

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

# calculate DIF variance
dif1 <- sirt::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 <- sirt::dif.strata.variance( dif=mod1$uniformDIF, se.dif=mod1$se.uniformDIF,
              itemcluster=data.math$item$domain )
  ## $unweighted.DIFSD
  ## [1] 0.1455916

## Not run: 
#****
# Likelihood ratio test and graphical model test in eRm package
miceadds::library_install("eRm")
# estimate Rasch model
res <- eRm::RM( dat[,items] )
summary(res)
# LR-test with respect to female
lrres <- eRm::LRtest(res, splitcr=dat$female)
summary(lrres)
# graphical model test
eRm::plotGOF(lrres)

#############################################################################
# EXAMPLE 2: Comparison with Mantel-Haenszel test
#############################################################################

library(TAM)
library(difR)

#*** (1) simulate data
set.seed(776)
N <- 1500   # number of persons per group
I <- 12     # number of items
mu2 <- .5   # impact (group difference)
sd2 <- 1.3  # standard deviation group 2

# define item difficulties
b <- seq( -1.5, 1.5, length=I)
# simulate DIF effects
bdif <- scale( stats::rnorm(I, sd=.6 ), scale=FALSE )[,1]
# item difficulties per group
b1 <- b + 1/2 * bdif
b2 <- b - 1/2 * bdif
# simulate item responses
dat1 <- sirt::sim.raschtype( theta=stats::rnorm(N, mean=0, sd=1 ), b=b1 )
dat2 <- sirt::sim.raschtype( theta=stats::rnorm(N, mean=mu2, sd=sd2 ), b=b2 )
dat <- rbind( dat1, dat2 )
group <- rep( c(1,2), each=N ) # define group indicator

#*** (2) scale data
mod <- TAM::tam.mml( dat, group=group )
summary(mod)

#*** (3) extract person parameter estimates
mod_eap <- mod$person$EAP
mod_wle <- tam.wle( mod )$theta

#*********************************
# (4) techniques for assessing differential item functioning

# Model 1: assess DIF by logistic regression and WLEs
dif1 <- sirt::dif.logistic.regression( dat=dat, score=mod_wle, group=group)
# Model 2: assess DIF by logistic regression and EAPs
dif2 <- sirt::dif.logistic.regression( dat=dat, score=mod_eap, group=group)
# Model 3: assess DIF by Mantel-Haenszel statistic
dif3 <- difR::difMH(Data=dat, group=group, focal.name="1",  purify=FALSE )
print(dif3)
  ##  Mantel-Haenszel Chi-square statistic:
  ##
  ##        Stat.    P-value
  ##  I0001  14.5655   0.0001 ***
  ##  I0002 300.3225   0.0000 ***
  ##  I0003   2.7160   0.0993 .
  ##  I0004 191.6925   0.0000 ***
  ##  I0005   0.0011   0.9740
  ##  [...]
  ##  Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
  ##  Detection threshold: 3.8415 (significance level: 0.05)
  ##
  ##  Effect size (ETS Delta scale):
  ##
  ##  Effect size code:
  ##   'A': negligible effect
  ##   'B': moderate effect
  ##   'C': large effect
  ##
  ##        alphaMH deltaMH
  ##  I0001  1.3908 -0.7752 A
  ##  I0002  0.2339  3.4147 C
  ##  I0003  1.1407 -0.3093 A
  ##  I0004  2.8515 -2.4625 C
  ##  I0005  1.0050 -0.0118 A
  ##  [...]
  ##
  ##  Effect size codes: 0 'A' 1.0 'B' 1.5 'C'
  ##   (for absolute values of 'deltaMH')

# recompute DIF parameter from alphaMH
uniformDIF3 <- log(dif3$alphaMH)

# compare different DIF statistics
dfr <- data.frame( "bdif"=bdif, "LR_wle"=dif1$uniformDIF,
        "LR_eap"=dif2$uniformDIF, "MH"=uniformDIF3 )
round( dfr, 3 )
  ##       bdif LR_wle LR_eap     MH
  ##  1   0.236  0.319  0.278  0.330
  ##  2  -1.149 -1.473 -1.523 -1.453
  ##  3   0.140  0.122  0.038  0.132
  ##  4   0.957  1.048  0.938  1.048
  ##  [...]
colMeans( abs( dfr[,-1] - bdif ))
  ##      LR_wle     LR_eap         MH
  ##  0.07759187 0.19085743 0.07501708

## End(Not run)

alexanderrobitzsch/sirt documentation built on Dec. 1, 2024, 2:18 a.m.