mirt (version 1.6.1)

itemfit: Item fit statistics

Description

itemfit calculates the Zh values from Drasgow, Levine and Williams (1985), $\chi^2$ 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.

Usage

itemfit(x, Zh = TRUE, X2 = FALSE, S_X2 = TRUE, group.size = 150,
  mincell = 1, S_X2.tables = FALSE, empirical.plot = NULL,
  empirical.CI = 0, method = "EAP", Theta = NULL, impute = 0, ...)

Arguments

x

a computed model object of class ExploratoryClass, ConfirmatoryClass, MultipleGroupClass, or DiscreteClass

Zh

logical; calculate Zh and associated statistics (infit/outfit)? Disable this is you are only interested in computing the S-X2 quickly

X2

logical; calculate the X2 statistic for unidimensional models?

S_X2

logical; calculate the S_X2 statistic?

group.size

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

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

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. Only applicable when type = 'X2'. The default is NULL, therefore n

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 if empirical.CI = .95. Only applicable to dichotomous items

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. This requires a precomputed Theta input. Will return a data.frame object

...

additional arguments to be passed to fscores()

References

Drasgow, F., Levine, M. V., & Williams, E. A. (1985). Appropriateness measurement with polychotomous item response models and standardized indices. 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

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

Examples

#make some data
set.seed(1234)
a <- matrix(rlnorm(20, meanlog=0, sdlog = .1),ncol=1)
d <- matrix(rnorm(20),ncol=1)
items <- rep('dich', 20)
data <- simdata(a,d, 2000, items)

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

itemfit(x, empirical.plot = 1) #empirical item plot
itemfit(x, empirical.plot = 1, empirical.CI = .99) #empirical item plot with 99% CI's
#method='ML' agrees better with eRm package
itemfit(raschfit, method = 'ML') #infit and outfit stats
#same as above, but inputting ML estimates instead
Theta <- fscores(raschfit, method = 'ML', full.scores=TRUE, scores.only=TRUE)
itemfit(raschfit, Theta=Theta)

#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)) - 1
head(dat)

mod <- mirt(dat, 1)
itemfit(mod)

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

#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()
Theta <- fscores(raschfit, method = 'ML', full.scores=TRUE)
itemfit(raschfit, impute = 10, Theta=Theta)