irt_me
Stata Command for Marginal Effects from Item Response Theory Models
(1) Introduction
irt_me is a Stata command that automates the calculation of marginal effects after Item Response Theory (IRT) models. IRT is a latent variable modeling technique for continuous latent variables and categorical items (e.g., binary, ordinal, and nominal). In IRT, the models are traditionally interpreted using the estimated coefficients (discrimination) and intercept (difficulty) parameters. Marginal effects are an alternative that quantify the relationship between the latent variable and the items in the predicted probability metric.
To read more about the background of the command and examples of its functionality see:
To read more about Item Response Theory and using marginal effects for interpretation see:
(2) Installation Instructions
To install in Stata:
net install irt_me, from("https://tdmize.github.io/data") replace
Once installed, to read the help file (also available here):
help irt_me
(3) Citation
Please cite the use of irt_me as:
Mize, Trenton D. 2024. “Stata command for marginal effects from item response theory models.” https://www.trentonmize.com/software/irt_me
(4) Examples
irt_me can be used with any latent variable model fit using Stata’s irt commands and also with models for continuous and count items fit using gsem. A mix of different item types is also allowed (e.g., a mix of binary and ordinal items). If the IRT model was fit using gsem you have to specify the name of the latent variable in the latent( ) option.
Load the data
use "https://tdmize.github.io/data/data/lvm_ah4", clear
Fit the IRT model
irt 2pl botherB bluesB keepmindB depressB tiredB dislikedB ///
sadB feltgoodBR happyBR enjoylifeBRUse irt_me to calculate marginal effects
irt_me, help
Marginal Effects of + 1.000 Increase in Latent Variable (theta) N=5113
| PrStart PrEnd ME Est. Std. Err. P>|z|
-------------+-----------------------------------------------------------
botherB | 0.240 0.574 0.334 0.013 0.000
bluesB | 0.016 0.285 0.269 0.013 0.000
keepmindB | 0.523 0.754 0.230 0.010 0.000
depressB | 0.021 0.411 0.390 0.017 0.000
tiredB | 0.586 0.748 0.161 0.009 0.000
dislikedB | 0.136 0.298 0.162 0.007 0.000
sadB | 0.192 0.768 0.576 0.020 0.000
feltgoodBR | 0.025 0.054 0.029 0.002 0.000
happyBR | 0.002 0.012 0.010 0.002 0.000
enjoylifeBR | 0.001 0.005 0.005 0.001 0.000
PrStart : Pr(y=1) at theta = -0.5
PrEnd : Pr(y=1) at theta = 0.5
ME : PrEnd - PrStart For all items, predictions are made at the default values of -0.5 (starting values) and 0.5 (ending value) for a centered +1 SD marginal effect estimate. An example interpretation:
For an average person, a one standard deviation increase in latent depression is associated with a 0.334 increase in the probability of reporting being bothered by things last week (botherB item).
An identical model as above can be fit using gsem
To fit an identical model as the irt command using gsem, you need to set the latent variable standard deviation to 1 using the var(latentvar@1) option on gsem (where latentvar is your name for your latent variable) and then specify the latentvar name when you call irt_me.
gsem (Depress -> botherB bluesB keepmindB depressB tiredB dislikedB ///
sadB feltgoodBR happyBR enjoylifeBR) ///
, logit var(Depress@1)
irt_me, latent(Depress)
Marginal Effects of + 1.000 Increase in Latent Variable (theta) N=5113
| PrStart PrEnd ME Est. Std. Err. P>|z|
-------------+-----------------------------------------------------------
botherB | 0.240 0.574 0.334 0.013 0.000
bluesB | 0.016 0.285 0.269 0.013 0.000
keepmindB | 0.523 0.754 0.230 0.010 0.000
depressB | 0.021 0.411 0.390 0.017 0.000
tiredB | 0.586 0.748 0.161 0.009 0.000
dislikedB | 0.136 0.298 0.162 0.007 0.000
sadB | 0.192 0.768 0.576 0.020 0.000
feltgoodBR | 0.025 0.054 0.029 0.002 0.000
happyBR | 0.002 0.012 0.010 0.002 0.000
enjoylifeBR | 0.001 0.005 0.005 0.001 0.000 Calculating marginal effects across the trimmed range of the latent variable
By default, irt_me calculates a centered +1 SD marginal effect (see examples above). One alternative is to estimate a marginal effect across the trimmed range of the latent variable (1st to 99th percentile) using the range option.
irt_me, range help
Marginal Effects of + 3.228 Increase in Latent Variable (theta) N=5113
| PrStart PrEnd ME Est. Std. Err. P>|z|
-------------+-----------------------------------------------------------
botherB | 0.095 0.919 0.824 0.015 0.000
bluesB | 0.001 0.978 0.976 0.006 0.000
keepmindB | 0.335 0.932 0.597 0.019 0.000
depressB | 0.001 0.992 0.990 0.003 0.000
tiredB | 0.447 0.897 0.450 0.020 0.000
dislikedB | 0.069 0.646 0.576 0.024 0.000
sadB | 0.031 0.994 0.963 0.006 0.000
feltgoodBR | 0.014 0.157 0.143 0.018 0.000
happyBR | 0.000 0.163 0.162 0.020 0.000
enjoylifeBR | 0.000 0.131 0.131 0.018 0.000
PrStart : Pr(y=1) at theta = -1.260
PrEnd : Pr(y=1) at theta = 1.968
ME : PrEnd - PrStartCustomized marginal effects
Customized marginal effects beyond the standard ones shown above can be calculated using custom starting and ending values in the start( ) and end( ) option. For example, for an ideal type of a very depressed person we could specify marginal effects from 2 to 3 SDs above the mean on the latent variable.
irt_me, start(2) end(3) help
Marginal Effects of + 1.000 Increase in Latent Variable (theta) N=5113
| PrStart PrEnd ME Est. Std. Err. P>|z|
-------------+-----------------------------------------------------------
botherB | 0.923 0.981 0.058 0.005 0.000
bluesB | 0.980 0.999 0.019 0.004 0.000
keepmindB | 0.934 0.975 0.041 0.003 0.000
depressB | 0.992 1.000 0.007 0.002 0.001
tiredB | 0.900 0.949 0.050 0.002 0.000
dislikedB | 0.653 0.835 0.182 0.003 0.000
sadB | 0.994 1.000 0.005 0.001 0.000
feltgoodBR | 0.161 0.300 0.139 0.025 0.000
happyBR | 0.171 0.579 0.407 0.050 0.000
enjoylifeBR | 0.140 0.612 0.473 0.063 0.000
PrStart : Pr(y=1) at theta = 2.000
PrEnd : Pr(y=1) at theta = 3.000
ME : PrEnd - PrStart