SIBTEST: Simultaneous Item Bias Test (SIBTEST)
In xzhaopsy/MIRT: Multidimensional Item Response Theory

Description Usage Arguments Details Author(s) References Examples

Classical test theory approach to detecting unidirectional and bidirectional (with one crossing location) DIF. This family of statistics is intended for unidimensional tests, and applies a regression-corrected matched-total score approach to quantify the response bias between two groups. Can be used for DIF, DBF, and DTF testing.

1 2	SIBTEST(dat, group, suspect_set, match_set, focal_name, guess_correction = 0, Jmin = 2, pk_focal = FALSE, correction = TRUE, details = FALSE)

`dat`	integer dataset to be tested containing dichotomous or polytomous responses
`group`	a vector indicating group membership
`suspect_set`	an integer vector indicating which items to inspect with SIBTEST. Including only one value will perform a DIF test, while including more than one will perform a simultaneous bundle test (DBF); including all non-matched items will perform DTF. If missing, a simultaneous test using all the items not listed in match_set will be used (i.e., DTF)
`match_set`	an integer vector indicating which items to use as the items which are matched (i.e., contain no DIF). These are analogous to 'achor' items in the likelihood method to locate DIF. If missing, all items other than the items found in the suspect_set will be used
`focal_name`	name of the focal group; e.g., 'focal'. If not specified then one will be selected automatically
`guess_correction`	a vector of numbers from 0 to 1 indicating how much to correct the items for guessing. It's length should be the same as ncol(dat)
`Jmin`	the minimum number of observations required when splitting the data into focal and reference groups conditioned on the matched set
`pk_focal`	logical; using the group weights from the focal group instead of the total sample? Default is FALSE as per Shealy and Stout's recommendation
`correction`	logical; apply the composite correction for the difference between focal composite scores using the true-score regression technique? Default is `TRUE`, reflecting Shealy and Stout's method
`details`	logical; return a data.frame containing the details required to compute SIBTEST?

SIBTEST is similar to the Mantel-Haenszel approach for detecting DIF but uses a regression correction based on the KR-20/coefficient alpha reliability index to correct the observed differences when the latent trait distributions are not equal. Function supports the standard SIBTEST for dichotomous and polytomous data (compensatory) and supports crossing DIF testing (i.e., non-compensatory/non-uniform) using the asymtotic sampling distribution version of the Crossing-SIBTEST (CSIBTEST) statistic described by Chalmers (accepted).

Phil Chalmers rphilip.chalmers@gmail.com

Chalmers, R. P. (accepted). Improving the Crossing-SIBTEST statistic for detecting non-uniform DIF. Psychometrika.

Chalmers, R., P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48(6), 1-29. doi: 10.18637/jss.v048.i06

Chang, H. H., Mazzeo, J. & Roussos, L. (1996). DIF for Polytomously Scored Items: An Adaptation of the SIBTEST Procedure. Journal of Educational Measurement, 33, 333-353.

Li, H.-H. & Stout, W. (1996). A new procedure for detetion of crossing DIF. Psychometrika, 61, 647-677.

Shealy, R. & Stout, W. (1993). A model-based standardization approach that separates true bias/DIF from group ability differences and ddetect test bias/DTF as well as item bias/DIF. Psychometrika, 58, 159-194.

## Not run: 

set.seed(1234)
n <- 30
N <- 500
a <- matrix(1, n)
d <- matrix(rnorm(n), n)
group <- c(rep('reference', N), rep('focal', N*2))

## -------------
# groups completely equal
dat1 <- simdata(a, d, N, itemtype = 'dich')
dat2 <- simdata(a, d, N*2, itemtype = 'dich')
dat <- rbind(dat1, dat2)

#DIF (all other items as anchors)
SIBTEST(dat, group, suspect_set = 6)

#DIF (specific anchors)
SIBTEST(dat, group, match_set = 1:5, suspect_set = 6)

# DBF (all and specific anchors, respectively)
SIBTEST(dat, group, suspect_set = 11:30)
SIBTEST(dat, group, match_set = 1:5, suspect_set = 11:30)

#DTF
SIBTEST(dat, group, suspect_set = 11:30)
SIBTEST(dat, group, match_set = 1:10) #equivalent

# different hyper pars
dat1 <- simdata(a, d, N, itemtype = 'dich')
dat2 <- simdata(a, d, N*2, itemtype = 'dich', mu = .5, sigma = matrix(1.5))
dat <- rbind(dat1, dat2)
SIBTEST(dat, group, 6:30)
SIBTEST(dat, group, 11:30)

#DIF testing with anchors 1 through 5
SIBTEST(dat, group, 6, match_set = 1:5)
SIBTEST(dat, group, 7, match_set = 1:5)
SIBTEST(dat, group, 8, match_set = 1:5)

#DIF testing with all other items as anchors
SIBTEST(dat, group, 6)
SIBTEST(dat, group, 7)
SIBTEST(dat, group, 8)

## -------------
## systematic differing slopes and intercepts (clear DTF)
dat1 <- simdata(a, d, N, itemtype = 'dich')
dat2 <- simdata(a + c(numeric(15), rnorm(n-15, 1, .25)), d + c(numeric(15), rnorm(n-15, 1, 1)),
  N*2, itemtype = 'dich')
dat <- rbind(dat1, dat2)
SIBTEST(dat, group, 6:30)
SIBTEST(dat, group, 11:30)

#DIF testing using valid anchors
SIBTEST(dat, group, suspect_set = 6, match_set = 1:5)
SIBTEST(dat, group, suspect_set = 7, match_set = 1:5)
SIBTEST(dat, group, suspect_set = 30, match_set = 1:5)


## End(Not run)