mirt (version 1.6.1)

DTF: Differential test functioning

Description

THIS FUNCTION IS CURRENTLY EXPERIMENTAL.

Usage

DTF(mod, MI = NULL, CI = 0.95, npts = 1000, theta_lim = c(-6, 6),
  Theta_nodes = NULL, plot = FALSE, auto.key = TRUE, ...)

Arguments

mod

a multipleGroup object which estimated only 2 groups

MI

a number indicating how many draws to take to form a suitable multiple imputation for the expected test scores (100 or more). Requires an estimated parameter information matrix. Returns a list containing the bootstrap distribution and null hypothesis test

CI

range of confidence interval when using MI input

npts

number of points to use in the integration. Default is 1000

theta_lim

lower and upper limits of the latent trait (theta) to be evaluated, and is used in conjunction with npts

Theta_nodes

an optional matrix of Theta values to be evaluated in the MI draws for the sDTF statistic. However, these values are not averaged across, and instead give the bootstrap confidence intervals at the respective Theta nodes. Useful when following up a large u

plot

logical; plot the test score functions with imputed confidence envelopes?

auto.key

logical; automatically generate key in lattice plot?

...

additional arguments to be passed to lattice

Details

Function performs various omnibus differential test functioning procedures on an object estimated with multipleGroup(). If the latent means/covariances are suspected to differ then the input object should contain a set of 'anchor' items to ensure that only differential test features are being detected rather than group differences. Returns signed (average area above and below) and unsigned (total area) statistics, with descriptives such as the percent average bias between group total scores for each statistic.

See Also

multipleGroup, DIF

Examples

set.seed(1234)
n <- 30
N <- 500

# only first 5 items as anchors
model <- mirt.model('F = 1-30
                    CONSTRAINB = (1-5, a1), (1-5, d)')

a <- matrix(1, n)
d <- matrix(rnorm(n), n)
group <- c(rep('G1', N), rep('G2', N))

## -------------
# groups completely equal
dat1 <- simdata(a, d, N, itemtype = 'dich')
dat2 <- simdata(a, d, N, itemtype = 'dich')
dat <- rbind(dat1, dat2)
mod <- multipleGroup(dat, model, group=group, SE=TRUE, SE.type='crossprod',
                     invariance=c('free_means', 'free_var'))
plot(mod, type = 'score')

DTF(mod)
mirtCluster()
DTF(mod, MI = 1000) #95% C.I. for sDTI containing 0. uDTF is very small

## -------------
## random slopes and intercepts for 15 items, and latent mean difference
##    (no systematic DTF should exist, but DIF will be present)
dat1 <- simdata(a, d, N, itemtype = 'dich', mu=.50, sigma=matrix(1.5))
dat2 <- simdata(a + c(numeric(15), sign(rnorm(n-15))*runif(n-15, .25, .5)),
                d + c(numeric(15), sign(rnorm(n-15))*runif(n-15, .5, 1)), N, itemtype = 'dich')
dat <- rbind(dat1, dat2)
mod1 <- multipleGroup(dat, 1, group=group)
plot(mod1, type = 'score') #does not account for group differences! Need anchors

mod2 <- multipleGroup(dat, model, group=group, SE=TRUE, SE.type = 'crossprod',
                      invariance=c('free_means', 'free_var'))
plot(mod2, type = 'score')

#significant DIF in multiple items....
DIF(mod2, which.par=c('a1', 'd'), items2test=16:30)
DTF(mod2)
DTF(mod2, MI=1000)

## -------------
## systematic differing slopes and intercepts (clear DTF)
dat1 <- simdata(a, d, N, itemtype = 'dich', mu=.50, sigma=matrix(1.5))
dat2 <- simdata(a + c(numeric(15), rnorm(n-15, 1, .25)), d + c(numeric(15), rnorm(n-15, 1, .5)),
                N, itemtype = 'dich')
dat <- rbind(dat1, dat2)
mod3 <- multipleGroup(dat, model, group=group, SE=TRUE, SE.type='crossprod',
                      invariance=c('free_means', 'free_var'))
plot(mod3, type = 'score') #visable DTF happening

DIF(mod3, c('a1', 'd'), items2test=16:30)
DTF(mod3) #unsigned bias. Signed bias indicates group 2 scores generally lower
DTF(mod3, MI=1000)
DTF(mod3, MI=1000, plot=TRUE)