*! version 1.01 2022.11.13
help uirt_chi2w

Title

uirt_chi2w -- Postestimation command of uirt to compute chi2W item-fit statistic

Syntax

uirt_chi2w [varlist] [,options]

varlist must include only variables that were declared in the main list of items of current uirt run.
If varlist is skipped or asterisk * is used, uirt_chi2w will either display the results that are currently stored in e(item_fit_chi2W) matrix
or it will compute chi2W item-fit statistic for all items declared in main list of items of current uirt run.
This behavior depends on whether chi2W item-fit statistics were produced by current uirt run or not.

Options

bins(#) number of ability intervals for computation of chi2W

npqmin(#) minimum expected number of observations in ability intervals (NPQ); default: npqmin(20)

npqreport report information about minimum NPQ in ability intervals

Description

uirt_chi2w is a postestimation command of uirt that computes chi2W item-fit statistic.
chi2W is a Wald-type test statistic that compares the observed and expected item mean scores over a set of ability bins.
The observed and expected scores are weighted means with weights being a posteriori density of person's ability within the bin
- likewise as in the approach used to compute observed proportions in ICC plots provided by uirt.
Properties of chi2W have been examined for dichotomous items, Type I error rate was close to nominal and it exceeded S-X2 in statistical power (Kondratek, 2022).
Behavior of chi2W in case of polytomous items, as for the time of this uirt release, has not been researched.

Options

bins(#) is used to set the number of ability intervals for computation of chi2W.
Default settings depend on the item model and number of freely estimated parameters for the item being tested.
In general, the default is either bins(3) or a minimal number of intervals allowing for 1 degree of freedom
after accounting for the number of estimated item parameters.

npqmin(#) sets a minimum for NPQ integrated over any ability interval, where:
N is the number of observations, P is the expected item mean, and Q=(max_item_score-P).
Larger NPQ values are associated with better asymptotics of chi2W.
If NPQ for a given ability bin is smaller than the value declared in npqmin(#) uirt will decrease the number of bins for that item.
Default value is npqmin(20).

npqreport adds a column to r(item_fit_chi2W)
with information about smallest observed NPQ value over the ability intervals used for computation of chi2W.

Examples

Setup

. webuse masc2

Fit an IRT model with all items being 1PLM (1PLM is a dichotomous case of PCM)

. uirt q*,pcm(*)

Compute chi2W item fit statistic for all items

. uirt_chi2w

Re-fit the model with all items being 2PLM (the default for uirt), and compute chi2W for all items under this model

. uirt q*

. uirt_chi2w

Re-fit the model asking item q6 to be 3PLM, and compute chi2W only for that item

. uirt q*,guess(q6,lr(1))

. uirt_chi2w q6

Stored results

uirt_chi2w stores the following in r():

Matrices

r(item_fit_chi2W) item-fit results for chi2W statistic

Author

Bartosz Kondratek
everythingthatcounts@gmail.com

References

Kondratek, B. (2022).
Item-Fit Statistic Based on Posterior Probabilities of Membership in Ability Groups.
Applied Psychological Measurement, 46(6), 462-478.
https://doi.org/10.1177/01466216221108061