lordif {lordif}

performs Logistic Ordinal Regression Differential Item Functioning using IRT

Description

performs iterative hybrid ordinal logistic regression/IRT DIF

Usage

lordif(resp.data, group, selection = NULL, criterion = c("Chisqr", "R2", "Beta"), 
pseudo.R2 = c("McFadden", "Nagelkerke", "CoxSnell"), alpha = 0.01, beta.change = 0.1, 
R2.change = 0.02, maxIter = 10, minCell = 5, minTheta = -4, maxTheta = 4, inc = 0.1, 
control = list(), model = "GRM", anchor = NULL, MonteCarlo = FALSE, nr = 100, 
weights = NULL, normwt = TRUE)

Arguments

resp.data

data frame or matrix containing item responses

group

a vector of group designations

selection

a vector specifying a subset of items to be analyzed or NULL for all items

criterion

criterion for flagging (i.e., "Chisqr", "R2", or "Beta")

pseudo.R2

pseudo R-squared measure (i.e., "McFadden", "Nagelkerke", or "CoxSnell")

alpha

significance level for Chi-squared criterion

beta.change

proportionate change for Beta criterion

R2.change

R-squared change for pseudo R-squared criterion

maxIter

maximum number of iterations for purification

minCell

minimum cell frequency to avoid collapsing

minTheta

minimum for theta grid

maxTheta

maximum for theta grid

inc

increment for theta grid

control

a list of control variables (refer to the mirt function in the mirt package)

model

IRT model of choice, either "GRM" or "GPCM" (default: "GRM")

anchor

a vector specifying items to be used as anchors or NULL to determine anchors through purification

MonteCarlo

TRUE to trigger Monte Carlo simulations to determine empirical thresholds

nr

number of replications for Monte Carlo simulations

weights

an optional vector (same length as nobs) of fractional case weights (refer to the lrm function in the rms package which currently generates warning messages)

normwt

set to TRUE to scale weights so they sum to nobs

Details

Performs an ordinal (common odds-ratio) logistic regression differential item functioning (DIF) analysis using IRT theta estimates as the conditioning variable. The graded response model (GRM) or the generalized partial credit model (GPCM) is used for IRT trait estimation. Items flagged for DIF are treated as unique items and group-specific item parameters are obtained. Non-DIF items serve as anchor items to the initial single-group calibration. The procedure runs iteratively until the same set of items is flagged over two consecutive iterations, unless anchor items are specified.

Value

Returns an object (list) of class "lordif" with the following components:

call

calling expression

options

options used for the run

selection

all or a subset of items analyzed

stats

matrix containing output statistics

flag

logical vector of final flags indicating whether each item is displaying DIF or not

recoded

data frame containing recoded item responses

group

vector of group designation values

ng

scalar for the number of groups

ncat

vector of the number of response categories for each item after collapsing/recoding

calib

vector of theta estimates based on the overall (non-group-specific) item parameters

calib.sparse

vector of theta estimates based on the DIF-free and group-specific item parameters

iteration

scalar for the number of iterations

ipar

data frame of the overall (non-group-specific) item parameter estimates

ipar.sparse

data frame of the group-specific item parameter estimates

stats.raw

matrix containing output statistics (the same components as stats above but based on raw scores)

meanraw

vector containing mean raw scores

flag.raw

logical vector of final DIF flags based on raw scores

DFIT

place-holder for DFIT analysis output

anchor

vector of items used as anchors

MonteCarlo

place-holder for Monte Carlo analysis output

Note

requires the mirt and rms packages

Author(s)

Seung W. Choi <[e-mail]>

References

Choi, S. W., Gibbons, L. E., Crane, P. K. (2011). lordif: An R Package for Detecting Differential Item Functioning Using Iterative Hybrid Ordinal Logistic Regression/Item Response Theory and Monte Carlo Simulations. Journal of Statistical Software, 39(8), 1-30. URL http://www.jstatsoft.org/v39/i08/.

Crane, P. K., Gibbons, L. E., Jolley, L., and van Belle, G. (2006). Differential item functioning analysis with ordinal logistic regression techniques: DIF detect and difwithpar. Medical Care, 44(11 Suppl 3), S115-S123.

See Also

rundif

Examples

  ## Not run: data(Anxiety)
  ## Not run: resp.data <- Anxiety[paste("R",1:29,sep="")]
  ## Not run: age <- Anxiety$age
  ## Not run: age.DIF <- lordif(resp.data,age,model="GPCM",anchor=c(1:5,7,8,10,12:17,19:23,25:29))
  ## Not run: print(age.DIF)