SitemFit1: Compute the S fit statistic for 1 item

Description

Implements the Kang & Chen (2007) polytomous extension to S statistic of Orlando & Thissen (2000). Rows with missing data are ignored, but see the omit option.

Usage

SitemFit1(grp, item, free = 0, ..., method = "pearson", log = TRUE,
  qwidth = 6, qpoints = 49L, alt = FALSE, omit = 0L, .twotier = TRUE)

Arguments

grp

a list with spec, param, mean, cov, and data

item

the item of interest

free

the number of free parameters involved in estimating the item (to adjust the df)

...

Not used. Forces remaining arguments to be specified by name.

method

whether to use a pearson or rms test

log

whether to return pvalues in log units

qwidth

the positive width of the quadrature in Z units

qpoints

the number of quadrature points

alt

whether to include the item of interest in the denominator

omit

number of items to omit when calculating the observed and expected sum-score tables

.twotier

whether to enable the two-tier optimization

Details

This statistic is good at finding a small number of misfitting items among a large number of well fitting items. However, be aware that misfitting items can cause other items to misfit.

Observed tables cannot be computed when data is missing. Therefore, you can optionally omit items with the greatest number of responses missing relative to the item of interest.

Pearson is slightly more powerful than RMS in most cases I examined.

Setting alt to TRUE causes the tables to match published articles. However, the default setting of FALSE probably provides slightly more power when there are less than 10 items.

The name of the test, "S", probably stands for sum-score.

References

Kang, T. and Chen, T. T. (2007). An investigation of the performance of the generalized S-Chisq item-fit index for polytomous IRT models. ACT Research Report Series.

Orlando, M. and Thissen, D. (2000). Likelihood-Based Item-Fit Indices for Dichotomous Item Response Theory Models. Applied Psychological Measurement, 24(1), 50-64.