irt_coef
Stata command for y*-standardized coefficients in item response theory models
(1) Introduction
irt_coef is a Stata command that calculates y*-standardized coefficients for binary and ordinal item response theory models (IRT). y*-standardized coefficients are useful for interpreting the coefficient estimates in a common scale and for comparing across items and models.
To read more about Item Response Theory and using y*-standardized coefficients for interpretation see:
My graduate course slides on Item Response Theory (pages 622 - 627 for y*-standardized coefficients)
(2) Installation Instructions
To install in Stata:
net install irt_coef, from("https://tdmize.github.io/data/irt_coef")
Once installed, to read the help file (also available here):
help irt_coef
(3) Citation
Please cite the use of irt_coef as:
Mize, Trenton D. 2024. "irt_coef: Stata command for y*-standardized coefficients in item response theory models." https://www.trentonmize.com/software/irt_coef
(4) Examples
For binary and ordinal IRT models, it is useful to rescale the coefficient in terms of a standard deviation of y*. Because we don’t know the scale of y*, putting it into a SD unit is useful for interpretation and can make comparing across models feasible. In addition, the raw binary and ordinal logit/probit coefficients are not appropriate to compare across items / models as their scale is not identified. The y* standardized coefficients can be compared across items / models as they are all on the same scale.
irt_coef command
After a binary or ordinal IRT model in Stata, use the irt_coef command to calculate y* standardized coefficients for all variables.
First, load the data:
use "https://tdmize.github.io/data/data/lvm_ah4", clear
Then, fit the model using the irt or gsem commands. E.g., Using the irt grm (graded response model) command for ordinal items:
irt grm nocontrol handle yourway overwhelm nofutureR cantchangeR ///
othersdetR interfereR lowcontrolR cantsolveR
Use irt_coef to calculate the y*-standardized coefficients. Option help adds a legend to help understand the output:
irt_coef, help
y* standardized coefficients (and raw coefficient) from IRT model N=5113
| Std Coef Coef Std. Err. P>|z|
-------------+-----------------------------------------------
nocontrol | -0.361 -0.702 0.034 0.000
handle | 0.461 0.943 0.037 0.000
yourway | 0.459 0.938 0.036 0.000
overwhelm | -0.385 -0.756 0.034 0.000
nofutureR | 0.583 1.301 0.043 0.000
cantchangeR | 0.732 1.950 0.059 0.000
othersdetR | 0.749 2.049 0.063 0.000
interfereR | 0.591 1.329 0.042 0.000
lowcontrolR | 0.795 2.376 0.070 0.000
cantsolveR | 0.815 2.551 0.082 0.000
Std Coef : y* standardized IRT regression coefficient
Coef : IRT raw regression coefficient
NOTE : SE and p-value based on raw regression coefficient
Using gsem for IRT model
An identical model to the one above can be fit using gsem. If gsem is used to fit the model the latent( ) option is required to provide the name of the latent variable for which y*-standardized coefficients should be calculated:
gsem (Mastery -> nocontrol handle yourway overwhelm nofutureR cantchangeR ///
othersdetR interfereR lowcontrolR cantsolveR, ologit) ///
, var(Mastery@1)
irt_coef, latent(Mastery)
y* standardized coefficients (and raw coefficient) from IRT model N=5113
| Std Coef Coef Std. Err. P>|z|
-------------+-----------------------------------------------
nocontrol | 0.361 0.702 0.034 0.000
handle | -0.461 -0.943 0.037 0.000
yourway | -0.459 -0.938 0.036 0.000
overwhelm | 0.385 0.756 0.034 0.000
nofutureR | -0.583 -1.301 0.043 0.000
cantchangeR | -0.732 -1.950 0.059 0.000
othersdetR | -0.749 -2.049 0.063 0.000
interfereR | -0.591 -1.329 0.042 0.000
lowcontrolR | -0.795 -2.376 0.070 0.000
cantsolveR | -0.815 -2.551 0.082 0.000