mirt (version 1.17.1)

DIF: Differential item functioning statistics

Description

This function runs the Wald and likelihood-ratio approaches for testing differential item functioning (DIF). This is primarily a convenience wrapper to the multipleGroup function for performing standard DIF procedures. Independent models can be estimated in parallel by defining a parallel object with mirtCluster, which will help to decrease the runtime. For best results, the baseline model should contain a set of 'anchor' items and have freely estimated hyper-parameters in the focal groups.

Usage

DIF(MGmodel, which.par, scheme = "add", items2test = 1:extract.mirt(MGmodel,
  "nitems"), seq_stat = "SABIC", Wald = FALSE, p.adjust = "none",
  return_models = FALSE, max_run = Inf, plotdif = FALSE, type = "trace",
  verbose = TRUE, ...)

Arguments

MGmodel

an object returned from multipleGroup to be used as the reference model

which.par

a character vector containing the parameter names which will be inspected for DIF

scheme

type of DIF analysis to perform, either by adding or dropping constraints across groups. These can be: [object Object],[object Object],[object Object],[object Object]

items2test

a numeric vector, or character vector containing the item names, indicating which items will be tested for DIF. In models where anchor items are known, omit them from this vector. For example, if items 1 and 2 are anchors in a 10 item test, then ite

seq_stat

select a statistic to test for in the sequential schemes. Potential values are (in descending order of power) 'AIC', 'AICc', 'SABIC', and 'BIC'. If a numeric value is input that ranges between 0 and 1, t

Wald

logical; perform Wald tests for DIF instead of likelihood ratio test?

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

return_models

logical; return estimated model objects for further analysis? Default is FALSE

max_run

a number indicating the maximum number of cycles to perform in sequential searches. The default is to perform search until no further DIF is found

plotdif

logical; create item plots for items that are displaying DIF according to the seq_stat criteria? Only available for 'add' type schemes

type

the type of plot argument passed to plot(). Default is 'trace', though another good option is 'infotrace'. For ease of viewing, the facet_item argument to mirt's plot() function is set to TRUE

verbose

logical print extra information to the console?

...

additional arguments to be passed to multipleGroup and plot

Details

Generally, the precomputed baseline model should have been configured with two estimation properties: 1) a set of 'anchor' items, where the anchor items have various parameters that have been constrained to be equal across the groups, and 2) contain freely estimated latent mean and variance terms in all but one group (the so-called 'reference' group). These two properties help to fix the metric of the groups so that item parameter estimates do not contain latent distribution characteristics.

See Also

multipleGroup

Examples

#simulate data where group 2 has a smaller slopes and more extreme intercepts
set.seed(12345)
a1 <- a2 <- matrix(abs(rnorm(15,1,.3)), ncol=1)
d1 <- d2 <- matrix(rnorm(15,0,.7),ncol=1)
a2[1:2, ] <- a1[1:2, ]/3
d1[c(1,3), ] <- d2[c(1,3), ]/4
head(data.frame(a.group1 = a1, a.group2 = a2, d.group1 = d1, d.group2 = d2))
itemtype <- rep('dich', nrow(a1))
N <- 1000
dataset1 <- simdata(a1, d1, N, itemtype)
dataset2 <- simdata(a2, d2, N, itemtype, mu = .1, sigma = matrix(1.5))
dat <- rbind(dataset1, dataset2)
group <- c(rep('D1', N), rep('D2', N))

#### no anchors, all items tested for DIF by adding item constrains one item at a time.
# define a parallel cluster (optional) to help speed up internal functions
mirtCluster()

#  Information matrix with crossprod (not controlling for latent group differences)
model <- multipleGroup(dat, 1, group, SE = TRUE)

#test whether adding slopes and intercepts constraints results in DIF. Plot items showing DIF
resulta1d <- DIF(model, c('a1', 'd'), plotdif = TRUE)
resulta1d

#same as above, but using Wald tests with Benjamini & Hochberg adjustment
resulta1dWald <- DIF(model, c('a1', 'd'), Wald = TRUE, p.adjust = 'fdr')
resulta1dWald
round(resulta1dWald$adj_pvals, 4)

#test whether adding only slope constraints results in DIF for all items
resulta1 <- DIF(model, 'a1')
resulta1

#following up on resulta1d, to determine whether it's a1 or d parameter causing DIF
(a1s <- DIF(model, 'a1', items2test = 1:3))
(ds <- DIF(model, 'd', items2test = 1:3))

#### using items 4 to 15 as anchors
itemnames <- colnames(dat)
model_anchor <- multipleGroup(dat, model = 1, group = group,
  invariance = c(itemnames[4:15], 'free_means', 'free_var'))
anchor <- DIF(model_anchor, c('a1', 'd'), items2test = 1:3)
anchor

### drop down approach (freely estimating parameters accross groups) when
### specifying a highly constrained model with estimated latent parameters
model_constrained <- multipleGroup(dat, 1, group,
  invariance = c(colnames(dat), 'free_means', 'free_var'))
dropdown <- DIF(model_constrained, 'd', scheme = 'drop')
dropdown

### sequential searches using SABIC as the selection criteria
# starting from completely different models
model <- multipleGroup(dat, 1, group)
stepup <- DIF(model, c('a1', 'd'), scheme = 'add_sequential')
stepup

#step down procedure for highly constrained model
model <- multipleGroup(dat, 1, group, invariance = itemnames)
stepdown <- DIF(model, c('a1', 'd'), scheme = 'drop_sequential')
stepdown