mirt (version 1.17.1)

itemfit: Item fit statistics

Description

itemfit calculates the Zh values from Drasgow, Levine and Williams (1985), $\chi^2$ and $G^2$ values for unidimensional models, and S-X2 statistics for unidimensional and multidimensional models (Kang & Chen, 2007; Orlando & Thissen, 2000). For Rasch, partial credit, and rating scale models infit and outfit statistics are also produced. 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.

Usage

itemfit(x, which.items = 1:extract.mirt(x, "nitems"), S_X2 = TRUE,
  Zh = FALSE, X2 = FALSE, G2 = FALSE, infit = FALSE, 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

which.items

an integer vector indicating which items to test for fit. Default tests all possible items

S_X2

logical; calculate the S_X2 statistic?

Zh

logical; calculate Zh?

X2

logical; calculate the X2 statistic for unidimensional models?

G2

logical; calculate the G2 statistic for unidimensional models?

infit

logical; calculate the infit/outfit values for unidimensional Rasch models? If the models are not from the Rasch family then this will be ignored

group.bins

the number of bins to use when X2 = TRUE. For example, setting group.bins = 10 will will compute Yen's (1981) Q1 statistic

group.size

approximate size of each group to be used in calculating the $\chi^2$ 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 sub

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 $\theta$ groupings (see empirical.CI). Useful for plotting the expected bins after passing X2

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 95interval 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 plotting the expected bins after passing X2 = TRUE or G2 = TRUE

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 statisti

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 impute

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

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.

See Also

personfit, itemGAM

Examples

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, X2=TRUE)
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, method = 'ML', infit = TRUE) #infit and outfit stats

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

#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 = TRUE)
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 = TRUE)

#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, impute = 10, infit = TRUE)

#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 = TRUE)

# note that X2 and G2 do not require complete datasets
itemfit(raschfit, X2=TRUE, G2 = TRUE, S_X2=FALSE)
itemfit(raschfit, empirical.plot=1)
itemfit(raschfit, empirical.table=1)