dif.logistic.regression.Rd
This function assesses differential item functioning using logistic regression analysis (Zumbo, 1999).
dif.logistic.regression(dat, group, score,quant=1.645)
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 |
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.
A data frame with following variables:
Numeric index of the item
Rank of item with respect to the uniform DIF (from negative to positive values)
Item name
Sample size per item
Value of group
variable for reference group
Value of group
variable for focal group
Sample size per item in reference group
Sample size per item in focal group
Item \(p\) value
Item \(p\) value in reference group
Item \(p\) value in focal group
Item \(p\) value differences
Adjusted \(p\) value difference
Uniform DIF estimate
Standard error of uniform DIF
The \(t\) value for uniform DIF
Significance label for uniform DIF
DIF classification according to the ETS classification system (see Details)
Empirical Bayes estimate of uniform DIF (Longford, Holland & Thayer, 1993) which takes degree of DIF standard error into account
Value of the DIF standard deviation
Nonuniform DIF estimate
Standard error of nonuniform DIF
The \(t\) value for nonuniform DIF
Significance label for nonuniform DIF
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. 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. 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.
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 (Magis, Beland, Tuerlinckx, & De Boeck, 2010).
For a download of the free DIF-Pack software (SIBTEST, ...) see http://psychometrictools.measuredprogress.org/home.
############################################################################# # 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 ) ## $unweighted.DIFSD ## [1] 0.1455916 if (FALSE) { #**** # Likelihood ratio test and graphical model test in eRm package miceadds::library_install("eRm") # estimate Rasch model res <- eRm::RM( dat[,items] ) summary(res) # LR-test with respect to female lrres <- eRm::LRtest(res, splitcr=dat$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 }