mirt: DRF – R documentation

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DRF

Differential Response Functioning statistics

Description

Function performs various omnibus differential item (DIF), bundle (DBF), and test (DTF) functioning procedures on an object estimated with multipleGroup(). The compensatory and non-compensatory statistics provided are described in Chalmers (2018), which generally can be interpreted as IRT generalizations of the SIBTEST and CSIBTEST statistics. These require the ACOV matrix to be computed in the fitted multiple-group model (otherwise, sets of plausible draws from the posterior are explicitly required).

Usage

DRF(
  mod,
  draws = NULL,
  focal_items = 1L:extract.mirt(mod, "nitems"),
  param_set = NULL,
  CI = 0.95,
  npts = 1000,
  quadpts = NULL,
  theta_lim = c(-6, 6),
  Theta_nodes = NULL,
  plot = FALSE,
  DIF = FALSE,
  p.adjust = "none",
  par.strip.text = list(cex = 0.7),
  par.settings = list(strip.background = list(col = "#9ECAE1"), strip.border = list(col
    = "black")),
  auto.key = list(space = "right", points = FALSE, lines = TRUE),
  ...
)

Arguments

`mod`	a multipleGroup object which estimated only 2 groups
`draws`	a number indicating how many draws to take to form a suitable multiple imputation or bootstrap estimate of the expected test scores (100 or more). If `boot = FALSE`, requires an estimated parameter information matrix. Returns a list containing the bootstrap/imputation distribution and null hypothesis test for the sDRF statistics
`focal_items`	a numeric vector indicating which items to include in the DRF tests. The default uses all of the items (note that including anchors in the focal items has no effect because they are exactly equal across groups). Selecting fewer items will result in tests of 'differential bundle functioning'
`param_set`	an N x p matrix of parameter values drawn from the posterior (e.g., using the parametric sampling approach, bootstrap, of MCMC). If supplied, then these will be used to compute the DRF measures. Can be much more efficient to pre-compute these values if DIF, DBF, or DTF are being evaluated within the same model (especially when using the bootstrap method). See `draw_parameters`
`CI`	range of confidence interval when using draws input
`npts`	number of points to use for plotting. Default is 1000
`quadpts`	number of quadrature nodes to use when constructing DRF statistics. Default is extracted from the input model object
`theta_lim`	lower and upper limits of the latent trait (theta) to be evaluated, and is used in conjunction with `quadpts` and `npts`
`Theta_nodes`	an optional matrix of Theta values to be evaluated in the draws for the sDRF statistics. 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 sDRF or uDRF statistic, for example, to determine where the difference between the test curves are large (while still accounting for sampling variability). Returns a matrix with observed variability
`plot`	logical; plot the 'sDRF' functions for the evaluated sDBF or sDTF values across the integration grid or, if `DIF = TRUE`, the selected items as a faceted plot of individual items? If plausible parameter sets were obtained/supplied then imputed confidence intervals will be included
`DIF`	logical; return a list of item-level imputation properties using the DRF statistics? These can generally be used as a DIF detection method and as a graphical display for understanding DIF within each item
`p.adjust`	string to be passed to the `p.adjust` function to adjust p-values. Adjustments are located in the `adj_pvals` element in the returned list. Only applicable when `DIF = TRUE`
`par.strip.text`	plotting argument passed to `lattice`
`par.settings`	plotting argument passed to `lattice`
`auto.key`	plotting argument passed to `lattice`
`...`	additional arguments to be passed to `lattice`

Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

References

Chalmers, R. P. (2018). Model-Based Measures for Detecting and Quantifying Response Bias. Psychometrika, 83(3), 696-732. doi: 10.1007/s11336-018-9626-9

Examples

## Not run: 

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

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

a <- matrix(1, n)
d <- matrix(rnorm(n), n)
group <- c(rep('Group_1', N), rep('Group_2', 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,
                     invariance=c('free_means', 'free_var'))
plot(mod)
plot(mod, which.items = 6:10) #DBF
plot(mod, type = 'itemscore')
plot(mod, type = 'itemscore', which.items = 10:15)

DRF(mod)
DRF(mod, focal_items = 6:10) #DBF
DRF(mod, DIF=TRUE)
DRF(mod, DIF=TRUE, focal_items = 10:15)

DRF(mod, plot = TRUE)
DRF(mod, focal_items = 6:10, plot = TRUE) #DBF
DRF(mod, DIF=TRUE, plot = TRUE)
DRF(mod, DIF=TRUE, focal_items = 10:15, plot = TRUE)

mirtCluster()
DRF(mod, draws = 500)
DRF(mod, draws = 500, plot=TRUE)

# pre-draw parameter set to save computations
param_set <- draw_parameters(mod, draws = 500)
DRF(mod, focal_items = 6, param_set=param_set) #DIF
DRF(mod, DIF=TRUE, param_set=param_set) #DIF
DRF(mod, focal_items = 6:10, param_set=param_set) #DBF
DRF(mod, param_set=param_set) #DTF

DRF(mod, focal_items = 6:10, draws=500) #DBF
DRF(mod, focal_items = 10:15, draws=500) #DBF

DIFs <- DRF(mod, draws = 500, DIF=TRUE)
print(DIFs)
DRF(mod, draws = 500, DIF=TRUE, plot=TRUE)

DIFs <- DRF(mod, draws = 500, DIF=TRUE, focal_items = 6:10)
print(DIFs)
DRF(mod, draws = 500, DIF=TRUE, focal_items = 6:10, plot = TRUE)

DRF(mod, DIF=TRUE, focal_items = 6)
DRF(mod, draws=500, DIF=TRUE, focal_items = 6)

# evaluate specific values for sDRF
Theta_nodes <- matrix(seq(-6,6,length.out = 100))

sDTF <- DRF(mod, Theta_nodes=Theta_nodes)
head(sDTF)
sDTF <- DRF(mod, Theta_nodes=Theta_nodes, draws=200)
head(sDTF)

# sDIF (isolate single item)
sDIF <- DRF(mod, Theta_nodes=Theta_nodes, focal_items=6)
head(sDIF)
sDIF <- DRF(mod, Theta_nodes=Theta_nodes, focal_items = 6, draws=200)
head(sDIF)

## -------------
## random slopes and intercepts for 15 items, and latent mean difference
##    (no systematic DTF should exist, but DIF will be present)
set.seed(1234)
dat1 <- simdata(a, d, N, itemtype = 'dich', mu=.50, sigma=matrix(1.5))
dat2 <- simdata(a + c(numeric(15), rnorm(n-15, 0, .25)),
                d + c(numeric(15), rnorm(n-15, 0, .5)), N, itemtype = 'dich')
dat <- rbind(dat1, dat2)
mod1 <- multipleGroup(dat, 1, group=group)
plot(mod1)
DRF(mod1) #does not account for group differences! Need anchors

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

#significant DIF in multiple items....
# DIF(mod2, which.par=c('a1', 'd'), items2test=16:30)
DRF(mod2)
DRF(mod2, draws=500) #non-sig DTF due to item cancellation

## -------------
## systematic differing slopes and intercepts (clear DTF)
set.seed(1234)
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,
                      invariance=c('free_means', 'free_var'))
plot(mod3) #visable DTF happening

# DIF(mod3, c('a1', 'd'), items2test=16:30)
DRF(mod3) #unsigned bias. Signed bias indicates group 2 scores generally higher on average
DRF(mod3, draws=500)
DRF(mod3, draws=500, plot=TRUE) #multiple DRF areas along Theta

# plot the DIF
DRF(mod3, draws=500, DIF=TRUE, plot=TRUE)

# evaluate specific values for sDRF
Theta_nodes <- matrix(seq(-6,6,length.out = 100))
sDTF <- DRF(mod3, Theta_nodes=Theta_nodes, draws=200)
head(sDTF)

# DIF
sDIF <- DRF(mod3, Theta_nodes=Theta_nodes, focal_items = 30, draws=200)
car::some(sDIF)

## ----------------------------------------------------------------
### multidimensional DTF

set.seed(1234)
n <- 50
N <- 1000

# only first 5 items as anchors within each dimension
model <- 'F1 = 1-25
          F2 = 26-50
          COV = F1*F2
          CONSTRAINB = (1-5, a1), (1-5, 26-30, d), (26-30, a2)'

a <- matrix(c(rep(1, 25), numeric(50), rep(1, 25)), n)
d <- matrix(rnorm(n), n)
group <- c(rep('Group_1', N), rep('Group_2', N))
Cov <- matrix(c(1, .5, .5, 1.5), 2)
Mean <- c(0, 0.5)

# groups completely equal
dat1 <- simdata(a, d, N, itemtype = 'dich', sigma = cov2cor(Cov))
dat2 <- simdata(a, d, N, itemtype = 'dich', sigma = Cov, mu = Mean)
dat <- rbind(dat1, dat2)
mod <- multipleGroup(dat, model, group=group, SE=TRUE,
                     invariance=c('free_means', 'free_var'))
coef(mod, simplify=TRUE)
plot(mod, degrees = c(45,45))
DRF(mod)

# some intercepts slightly higher in Group 2
d2 <- d
d2[c(10:15, 31:35)] <- d2[c(10:15, 31:35)] + 1
dat1 <- simdata(a, d, N, itemtype = 'dich', sigma = cov2cor(Cov))
dat2 <- simdata(a, d2, N, itemtype = 'dich', sigma = Cov, mu = Mean)
dat <- rbind(dat1, dat2)
mod <- multipleGroup(dat, model, group=group, SE=TRUE,
                     invariance=c('free_means', 'free_var'))
coef(mod, simplify=TRUE)
plot(mod, degrees = c(45,45))

DRF(mod)
DRF(mod, draws = 500)


## End(Not run)

mirt

Multidimensional Item Response Theory

v1.33.2

GPL (>= 3)

Authors

Phil Chalmers [aut, cre] (<https://orcid.org/0000-0001-5332-2810>), Joshua Pritikin [ctb], Alexander Robitzsch [ctb], Mateusz Zoltak [ctb], KwonHyun Kim [ctb], Carl F. Falk [ctb], Adam Meade [ctb], Lennart Schneider [ctb], David King [ctb], Chen-Wei Liu [ctb], Ogreden Oguzhan [ctb]

Initial release

DRF