sirt (version 1.14-0)

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:

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 also rasch.evm.pcm for assessing differential item functioning in the partial credit model.

See the difR package for a large collection of DIF detection methods.

For a download of the free DIF-Pack software (SIBTEST, ...) see http://psychometrictools.measuredprogress.org/home.

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 <- 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

## 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$female)
# summary(lrres)
# # graphical model test
# eRm::plotGOF(lrres) 
# 
# #############################################################################
# # EXAMPLE 2: Comparison with Mantel-Haenszel test
# #############################################################################
# 
# library(TAM)
# library(difR)
# 
# #*** (1) simulate data
# set.seed(776)
# N <- 1500   # number of persons per group
# I <- 12     # number of items
# mu2 <- .5   # impact (group difference)
# sd2 <- 1.3  # standard deviation group 2
# 
# # define item difficulties
# b <- seq( -1.5 , 1.5 , length=I)
# # simulate DIF effects
# bdif <- scale( stats::rnorm(I , sd = .6 ) , scale=FALSE )[,1]
# # item difficulties per group
# b1 <- b + 1/2 * bdif
# b2 <- b - 1/2 * bdif
# # simulate item responses
# dat1 <- sim.raschtype( theta = stats::rnorm(N , mean=0 , sd =1 ) , b = b1 )
# dat2 <- sim.raschtype( theta = stats::rnorm(N , mean=mu2 , sd = sd2 ) , b = b2 )
# dat <- rbind( dat1 , dat2 )
# group <- rep( c(1,2) , each=N ) # define group indicator
# 
# #*** (2) scale data 
# mod <- TAM::tam.mml( dat , group=group )
# summary(mod)
# 
# #*** (3) extract person parameter estimates
# mod_eap <- mod$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 <- dif.logistic.regression( dat=dat , score= mod_wle , group= group)
# # Model 2: assess DIF by logistic regression and EAPs
# dif2 <- 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)