Stata module to fit unidimensional Item Response Theory models
uirt can be used to fit a variety of unidimensional IRT models
(2PLM, 3PLM, GRM, PCM and GPCM).
It allows for multi-group modelling, DIF analysis,
and introduces extensive item-fit analysis tools.
With uirt you can also generate plausible values (PVs)
conditioned via latent regression.
If you are having trouble with fitting 3PLM to your data,
uirt will come to help, as it enables imposing priors on parameter estimation.
Alternatively, an automated explorative search for a 3PLM-fitting
subset of items is also available.
uirt was featured in the Stata Journal
(Kondratek, 2022a).
Properties of the chi2W item-fit statistic of uirt
were investigated against alternative measures
in the APM article (Kondratek, 2022b).
uirt is written mostly in Mata,
so it requires only Stata 10 to run.
It was designed to efficiently handle large datasets,
especially in the multi-group designs.
To install the latest version:
net install uirt, from(https://raw.githubusercontent.com/bkondratek/uirt/main/) replace
After installation, type:
h uirt
to see a detailed help and examples.
You can always install uirt from SSC:
ssc install uirt, replace
In general, the SSC version should be the same as the latest. But there might be a few days lag between the latest version here, and the SSC servers.
Should you want the exact uirt version
that was used the Stata Journal article:
net install st0670, from(http://www.stata-journal.com/software/sj22-2) replace
For your convenience, the SSC package is also available here and the SJ package is available here.
Load example data used in De Boeck & Wilson (2004):
webuse masc2
Run uirt on default settings
(one group, 2PLM for 0-1 items, GRM for 0-k items),
and ask to plot ICC for item q6 using the uirt_icc
postestimation command:
uirt q*
uirt_icc q6
Note that all postestimation commands of uirt can also be used
as options, by skipping the 'uirt_' part.
So, the above example is equivalent to this one-liner:
uirt q*, icc(q6)
The single-line usage will take less time to execute. Though, for the sake of readibility we will make use of the postestimation commands in the following examples.
To learn more about uirt postestimation commands type:
help uirt##postestimation
Let us continue the analysis using the estimates from previous run
as starting values. We will now ask that item q6 be 3PLM
with sub-option 'lrcrit()' turned off.
We will also customize the graph for that item a little:
uirt q*,guess(q6,lr(1)) init(prev)
uirt_icc q6, tw( xtitle(My own name for the {&theta} scale) )
The dataset is small and does not provide enough information to support
unconstrained estimation of the pseudo-guessing parameter of all items.
With uirt we can impose priors on parameters to circumvent this.
Fitting a 3PLM to all items with beta(5,18) distribution as the prior for the pseudo-guessing parameter to ensure convergence:
uirt q*, guess(*, lr(1)) priors(*, c(5,18))
Let us now fit a two-group model to this data with female as
the grouping variable; all items 2PLM.
After fitting a two-group model we can test item q1 for DIF:
uirt q*,gr(female)
uirt_dif q1
If we want to obtain ability estimates, we can ask either
for the point estimates (expected a posteriori, EAP) with their standard
errors or draw a set of plausible values. The plausible values can
(and should) be conditioned by a latent regression. uirt uses
the Stata's mixed command to run the regression part,
so any model supported by it can be used for conditioning.
Example:
uirt q* // fitting the model using defaults
uirt_theta ,eap // point estimates of ability
uirt_theta ,pv(5) pvreg(i.female) // set of 5 PVs, conditioned on female
Oh, and here are the two graphs created when running the previous examples:
gr combine DIF_q1 ICC_q6
Note that each point on the ICC graph (on the right) is the observed frequency of correct responses in a percentile group of the latent distribution. Such a fine grid essentially provides us with a nonparametric response curve for that item. By comparing it to the model-based curve (solid line) we can graphically assess the item fit.
Should you prefer to perform some statistical test of the item fit,
uirt includes the SX2 (applicable only to 0-1 items
and complete data designs) by Orlando and Thissen (2000)
and the more general chi2W by Kondratek
(2022b):
uirt q* // fitting the model with defaults
uirt_sx2 * // SX2 for all items
uirt_chi2w * // chi2W for all items
Kondratek, B. (2022). uirt: A command for unidimensional IRT modeling. The Stata Journal, 22(2), 243-268. https://doi.org/10.1177/1536867X221106368
I wish to thank Cees Glas who provided me with invaluable
consultancy on many parts of the estimation algorithms
used in uirt and Mateusz Zoltak
for very helpful hints on Mata
pointers which led to significant boost in efficiency of uirt.
Many thanks to all of my colleagues at
the Institute of Educational Research in Warsaw
for using uirt at the early stages of its development
and providing me with feedback
and encouragement to continue with this endeavor.
I am also grateful to numerous Stata users who contacted me with ideas on how to improve the software after its first release. I feel especially indebted to Eric Melse, for his support in building postestimation commands that allow for plotting information functions and expected score curves.
Last but not least, I would like to thank the anonymous
Reviewer at the Stata Journal,
who had guided me on how to rewrite uirt to make
it more user-friendly
and more aligned with Stata programming standards.
Preparation of modules of uirt related to item-fit analysis
was funded by the National Science Centre research grant
number 2015/17/N/HS6/02965.