irt_coef: Stata command for y*-standardized coefficients in IRT 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:

(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) 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