R: Compute the S fit statistic for 1 item

SitemFit1 {rpf} | R Documentation

## 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 or a character vector with the names of the 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.

[Package rpf version 0.56.1 Index]