Latent-variable mean and variance
IRT model-based test of differential item functioning
Many researchers study cognitive abilities, personality traits, attitudes, quality of life, patient satisfaction, and other attributes that cannot be measured directly. To quantify these types of latent traits, researchers develop instruments–questionnaires or tests consisting of binary, ordinal, or categorical items–to determine individuals' levels of the trait.
Item response theory (IRT) models can be used to evaluate the relationships between a latent trait and items intended to measure the trait. With IRT models, we can determine which test items are more difficult and which ones are easier. We can determine which test items provide much information about the latent trait and which ones provide only a little.
Stata's IRT suite fits IRT models and can make comparisons across groups. This means we can evaluate whether an instrument measures a latent trait in the same way for different subpopulations. For instance, we might ask the following questions:
Do students from urban and rural schools perform differently on a test intended to measure mathematical ability?
Does an instrument measuring depression perform the same today as it did five years ago?
Does one of the questions on a survey about patient satisfaction measure the trait differently for younger and older patients?
In other words, multiple-group IRT models allow us to evaluate differential item functioning (DIF).
To fit multiple-group IRT models in Stata, we simply add the group() option to the irt command.
We previously fit a two-parameter logistic (2PL) model for item1 through item10 by typing
. irt 2pl item1-item10
We now type
. irt 2pl item1-item10, group(urban)
to fit a multiple-group version of this model allowing differences for students in urban and rural schools.
We can add the group() option to any of the following irt commands and fit multiple-group models for binary, ordinal, and categorical responses.
|One-parameter logistic model
|Two-parameter logistic model
|Three-parameter logistic model
|Graded response model
|Nominal response model
|Partial credit model
|Rating scale model
|Hybrid IRT model
We can also impose constraints on these models to analyze differential item functioning (DIF).
After fitting a multiple-group model, we can easily graph the item characteristic curves, item information functions, and more.