R: Item fit statistics

itemfit {mirt}

R Documentation

Item fit statistics

Description

Computes item-fit statistics for a variety of unidimensional and multidimensional models. Poorly fitting items should be inspected with the empirical plots/tables for unidimensional models, otherwise itemGAM can be used to diagnose where the functional form of the IRT model was misspecified, or models can be refit using more flexible semi-parametric response models (e.g., itemtype = 'spline').

Usage

itemfit(x, fit_stats = "S_X2", which.items = 1:extract.mirt(x, "nitems"),
  group.bins = 10, group.size = NA, group.fun = mean, mincell = 1,
  mincell.X2 = 2, S_X2.tables = FALSE, empirical.plot = NULL,
  empirical.CI = 0.95, empirical.table = NULL, method = "EAP",
  Theta = NULL, impute = 0, digits = 4, par.strip.text = list(cex =
  0.7), par.settings = list(strip.background = list(col = "#9ECAE1"),
  strip.border = list(col = "black")), ...)

Arguments

`x`	a computed model object of class `SingleGroupClass`, `MultipleGroupClass`, or `DiscreteClass`
`fit_stats`	a character vector indicating which fit statistics should be computed. Supported inputs are: `'S_X2'` : Orlando and Thissen (2000, 2003) and Kang and Chen's (2007) signed chi-squared test (default) `'Zh'` : Drasgow, Levine, & Williams (1985) Zh `'X2'` : Bock's (1972) chi-squared method. The default inputs compute Yen's (1981) Q1 variant of the X2 statistic (i.e., uses a fixed `group.bins = 10`). However, Bock's group-size variable median-based method can be computed by passing `group.fun = median` and modifying the `group.size` input to the desired number of bins `'G2'` : McKinley & Mills (1985) G2 statistic (similar method to Q1, but with the likelihood-ratio test). `'infit'` : (Unidimensional Rasch model only) compute the infit and outfit statistics. Ignored if models are not from the Rasch family
`which.items`	an integer vector indicating which items to test for fit. Default tests all possible items
`group.bins`	the number of bins to use for X2 and G2. For example, setting `group.bins = 10` will will compute Yen's (1981) Q1 statistic when `'X2'` is requested
`group.size`	approximate size of each group to be used in calculating the χ^2 statistic. The default `NA` disables this command and instead uses the `group.bins` input to try and construct equally sized bins
`group.fun`	function used when `'X2'` or `'G2'` are computed. Determines the central tendancy measure within each partitioned group. E.g., setting `group.fun = median` will obtain the median of each respective ability estimate in each subgroup (this is what was used by Bock, 1972)
`mincell`	the minimum expected cell size to be used in the S-X2 computations. Tables will be collapsed across items first if polytomous, and then across scores if necessary
`mincell.X2`	the minimum expected cell size to be used in the X2 computations. Tables will be collapsed if polytomous, however if this condition can not be met then the group block will be ommited in the computations
`S_X2.tables`	logical; return the tables in a list format used to compute the S-X2 stats?
`empirical.plot`	a single numeric value or character of the item name indicating which item to plot (via `itemplot`) and overlay with the empirical θ groupings (see `empirical.CI`). Useful for plotting the expected bins based on the `'X2'` or `'G2'` method
`empirical.CI`	a numeric value indicating the width of the empirical confidence interval ranging between 0 and 1 (default of 0 plots not interval). For example, a 95 interval would be plotted when `empirical.CI = .95`. Only applicable to dichotomous items
`empirical.table`	a single numeric value or character of the item name indicating which item table of expected values should be returned. Useful for visualizing the expected bins based on the `'X2'` or `'G2'` method
`method`	type of factor score estimation method. See `fscores` for more detail
`Theta`	a matrix of factor scores for each person used for statistics that require empirical estimates. If supplied, arguments typically passed to `fscores()` will be ignored and these values will be used instead. Also required when estimating statistics with missing data via imputation
`impute`	a number indicating how many imputations to perform (passed to `imputeMissing`) when there are missing data present. Will return a data.frame object with the mean estimates of the stats and their imputed standard deviations
`digits`	number of digits to round result to. Default is 4
`par.strip.text`	plotting argument passed to `lattice`
`par.settings`	plotting argument passed to `lattice`
`...`	additional arguments to be passed to `fscores()` and `lattice`

Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

References

Bock, R. D. (1972). Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 37, 29-51.

Drasgow, F., Levine, M. V., & Williams, E. A. (1985). Appropriateness measurement with polychotomous item response models and standardized indices. British Journal of Mathematical and Statistical Psychology, 38, 67-86.

Kang, T. & Chen, Troy, T. (2007). An investigation of the performance of the generalized S-X2 item-fit index for polytomous IRT models. ACT

McKinley, R., & Mills, C. (1985). A comparison of several goodness-of-fit statistics. Applied Psychological Measurement, 9, 49-57.

Orlando, M. & Thissen, D. (2000). Likelihood-based item fit indices for dichotomous item response theory models. Applied Psychological Measurement, 24, 50-64.

Reise, S. P. (1990). A comparison of item- and person-fit methods of assessing model-data fit in IRT. Applied Psychological Measurement, 14, 127-137.

Wright B. D. & Masters, G. N. (1982). Rating scale analysis. MESA Press.

Yen, W. M. (1981). Using simulation results to choose a latent trait model. Applied Psychological Measurement, 5, 245-262.

Examples


## Not run: 

P <- function(Theta){exp(Theta^2 * 1.2 - 1) / (1 + exp(Theta^2 * 1.2 - 1))}

#make some data
set.seed(1234)
a <- matrix(rlnorm(20, meanlog=0, sdlog = .1),ncol=1)
d <- matrix(rnorm(20),ncol=1)
Theta <- matrix(rnorm(2000))
items <- rep('dich', 20)
ps <- P(Theta)
baditem <- numeric(2000)
for(i in 1:2000)
   baditem[i] <- sample(c(0,1), 1, prob = c(1-ps[i], ps[i]))
data <- cbind(simdata(a,d, 2000, items, Theta=Theta), baditem=baditem)

x <- mirt(data, 1)
raschfit <- mirt(data, 1, itemtype='Rasch')
fit <- itemfit(x)
fit

itemfit(x)
itemfit(x, 'X2') # just X2
itemfit(x, c('S_X2', 'X2')) #both S_X2 and X2
itemfit(x, group.bins=15, empirical.plot = 1) #empirical item plot with 15 points
itemfit(x, group.bins=15, empirical.plot = 21)

#empirical tables
itemfit(x, empirical.table=1)
itemfit(x, empirical.table=21)

#infit/outfit statistics. method='ML' agrees better with eRm package
itemfit(raschfit, 'infit', method = 'ML') #infit and outfit stats

#same as above, but inputting ML estimates instead
Theta <- fscores(raschfit, method = 'ML')
itemfit(raschfit, 'infit', Theta=Theta)

# fit a new more flexible model for the mis-fitting item
itemtype <- c(rep('2PL', 20), 'spline')
x2 <- mirt(data, 1, itemtype=itemtype)
itemfit(x2)
itemplot(x2, 21)
anova(x2, x)

#------------------------------------------------------------

#similar example to Kang and Chen 2007
a <- matrix(c(.8,.4,.7, .8, .4, .7, 1, 1, 1, 1))
d <- matrix(rep(c(2.0,0.0,-1,-1.5),10), ncol=4, byrow=TRUE)
dat <- simdata(a,d,2000, itemtype = rep('graded', 10))
head(dat)

mod <- mirt(dat, 1)
itemfit(mod)
itemfit(mod, 'X2') #pretty much useless given inflated Type I error rates
itemfit(mod, empirical.plot = 1)

# collapsed tables (see mincell.X2) for X2 and G2
itemfit(mod, empirical.table = 1)

mod2 <- mirt(dat, 1, 'Rasch')
itemfit(mod2, 'infit')

#massive list of tables
tables <- itemfit(mod, S_X2.tables = TRUE)

#observed and expected total score patterns for item 1 (post collapsing)
tables$O[[1]]
tables$E[[1]]

# fit stats with missing data (run in parallel using all cores)
data[sample(1:prod(dim(data)), 500)] <- NA
raschfit <- mirt(data, 1, itemtype='Rasch')

mirtCluster() # run in parallel
itemfit(raschfit, c('S_X2', 'infit'), impute = 10)

#alternative route: use only valid data, and create a model with the previous parameter estimates
data2 <- na.omit(data)
raschfit2 <- mirt(data2, 1, itemtype = 'Rasch', pars=mod2values(raschfit), TOL=NaN)
itemfit(raschfit2, 'infit')

# note that X2 and G2 do not require complete datasets
itemfit(raschfit, c('X2', 'G2'))
itemfit(raschfit, empirical.plot=1)
itemfit(raschfit, empirical.table=1)


## End(Not run)

[Package mirt version 1.21 Index]