mirt (version 1.35.1)

SIBTEST: Simultaneous Item Bias Test (SIBTEST)

Description

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.

Usage

SIBTEST(
  dat,
  group,
  suspect_set,
  match_set,
  focal_name = unique(group)[2],
  guess_correction = 0,
  Jmin = 5,
  na.rm = FALSE,
  LiStout1996 = FALSE,
  permute = 1000,
  pk_focal = FALSE,
  correction = TRUE,
  details = FALSE,
  plot = "none",
  ...
)

Arguments

dat

integer-based dataset to be tested, containing dichotomous or polytomous responses

group

a vector indicating group membership with the same length as the number of rows in dat

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 'anchor' 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 using unique(group)[2]

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

na.rm

logical; remove rows in dat with any missing values? If TRUE, rows with missing data will be removed, as well as the corresponding elements in the group input

LiStout1996

logical; perform the crossing test for non-compensatory bias using Li and Stout's (1996) permutation approach? Default is FALSE, which uses the Chalmers (2018) mixed degrees of freedom method

permute

number of permutations to perform when LiStout1996 = TRUE. Default is 1000

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 linear extrapolation method

details

logical; return a data.frame containing the details required to compute SIBTEST?

plot

a character input indicating the type of plot to construct. Options are 'none' (default), 'observed' for the scaled focal subtest scores against the matched subtest scores, 'weights' for the proportion weights used (i.e., the proportion of observations at each matched score), 'difference' for the difference between the scaled focal subtest scores against the matched subtest scores, and 'wdifference' for the conditional differences multiplied by each respective weight. Note that the last plot reflects the compnents used in SIBTEST, and therefore the sum of these plotted observations will equal the beta coefficient for SIBTEST

...

additional plotting arguments to be passed

Details

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 asymptotic sampling distribution version of the Crossing-SIBTEST (CSIBTEST) statistic described by Chalmers (2018) and the permutation method described by Li and Stout (1996). For convenience, the beta coefficient for CSIBTEST is always reported as an absolute value.

References

Chalmers, R. P. (2018). Improving the Crossing-SIBTEST statistic for detecting non-uniform DIF. Psychometrika, 83, 2, 376-386.

Chalmers, R., P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48(6), 1-29. 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 detection 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 detect test bias/DTF as well as item bias/DIF. Psychometrika, 58, 159-194.

Examples

# NOT RUN {
# }
# 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)

# Some plots depicting the above tests
SIBTEST(dat, group, suspect_set = 6, plot = 'observed')
SIBTEST(dat, group, suspect_set = 6, plot = 'weights')
SIBTEST(dat, group, suspect_set = 6, plot = 'wdifference')

# Include CSIBTEST with randomization method
SIBTEST(dat, group, suspect_set = 6, LiStout1996 = TRUE)

# DIF (specific anchors)
SIBTEST(dat, group, match_set = 1:5, suspect_set = 6)
SIBTEST(dat, group, match_set = 1:5, suspect_set = 6, LiStout1996=TRUE)

# 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)

# Some plots depicting the above tests
SIBTEST(dat, group, suspect_set = 11:30, plot = 'observed')
SIBTEST(dat, group, suspect_set = 11:30, plot = 'weights')
SIBTEST(dat, group, suspect_set = 11:30, plot = 'wdifference')

# 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)

# randomization method is fairly poor when smaller matched-set used
SIBTEST(dat, group, suspect_set = 30, match_set = 1:5, LiStout1996=TRUE)
SIBTEST(dat, group, suspect_set = 30, LiStout1996=TRUE)

# }