mirt (version 0.7.0)

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 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, group.size = 150,
    mincell = 1, S_X2.tables = FALSE,
    empirical.plot = NULL, method = "EAP")

Arguments

x

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

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?

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?

group.size

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

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, ther

method

type of factor score estimation method. Can be expected a-posteriori ("EAP"), Bayes modal ("MAP"), weighted likelihood estimation ("WLE"), or maximum likelihood ("ML")

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.

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

#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]]