Examples from the help file
The examples in help irt_coef, run in full
The examples at the end of help irt_coef, on Stata’s charity data (five ordinal items on attitudes toward charitable giving). The graded response model is fit first with irt grm and then, identically, with gsem; after gsem the latent() option names the latent variable.
webuse charity, clear(Data from Zheng & Rabe-Hesketh (2007))irt grm ta1 ta2 ta3 ta4 ta5Fitting fixed-effects model:
Iteration 0: Log likelihood = -5559.6414
Iteration 1: Log likelihood = -5473.9434
Iteration 2: Log likelihood = -5467.4082
Iteration 3: Log likelihood = -5467.3926
Iteration 4: Log likelihood = -5467.3926
Fitting full model:
Iteration 0: Log likelihood = -5271.0634
Iteration 1: Log likelihood = -5162.5917
Iteration 2: Log likelihood = -5159.2947
Iteration 3: Log likelihood = -5159.2791
Iteration 4: Log likelihood = -5159.2791
Graded response model Number of obs = 945
Log likelihood = -5159.2791
------------------------------------------------------------------------------
| Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
ta1 |
Discrim | 0.908 0.096 9.495 0.000 0.720 1.095
Diff |
>=1 | -1.540 0.164 -1.861 -1.219
>=2 | 1.296 0.143 1.016 1.576
=3 | 3.305 0.325 2.668 3.942
-------------+----------------------------------------------------------------
ta2 |
Discrim | 0.943 0.097 9.752 0.000 0.754 1.133
Diff |
>=1 | -1.661 0.168 -1.990 -1.332
>=2 | 0.007 0.082 -0.154 0.168
=3 | 2.531 0.241 2.058 3.004
-------------+----------------------------------------------------------------
ta3 |
Discrim | 1.734 0.155 11.157 0.000 1.430 2.039
Diff |
>=1 | -1.080 0.084 -1.244 -0.916
>=2 | 1.017 0.080 0.860 1.173
=3 | 2.233 0.150 1.939 2.526
-------------+----------------------------------------------------------------
ta4 |
Discrim | 1.933 0.186 10.408 0.000 1.569 2.298
Diff |
>=1 | -0.345 0.058 -0.458 -0.231
>=2 | 1.466 0.098 1.273 1.659
=3 | 2.419 0.162 2.101 2.737
-------------+----------------------------------------------------------------
ta5 |
Discrim | 1.428 0.126 11.294 0.000 1.180 1.675
Diff |
>=1 | -0.855 0.083 -1.019 -0.692
>=2 | 0.681 0.075 0.534 0.827
=3 | 2.074 0.154 1.773 2.376
------------------------------------------------------------------------------irt_coef, helpy* standardized coefficients (and raw coefficient) from IRT model N=945
| Std Coef Coef Std. Err. P>|z|
-------------+-----------------------------------------------
ta1 | 0.447 0.908 0.096 0.000
ta2 | 0.461 0.943 0.097 0.000
ta3 | 0.691 1.734 0.155 0.000
ta4 | 0.729 1.933 0.186 0.000
ta5 | 0.618 1.428 0.126 0.000
Std Coef : y* standardized IRT regression coefficient
Coef : IRT raw regression coefficient
NOTE : SE and p-value based on raw regression coefficientgsem (Theta -> ta1 ta2 ta3 ta4 ta5, ologit), var(Theta@1)Fitting fixed-effects model:
Iteration 0: Log likelihood = -5467.3926
Iteration 1: Log likelihood = -5467.3926
Refining starting values:
Grid node 0: Log likelihood = -5285.1964
Fitting full model:
Iteration 0: Log likelihood = -5285.1964
Iteration 1: Log likelihood = -5168.1087
Iteration 2: Log likelihood = -5159.3229
Iteration 3: Log likelihood = -5159.2791
Iteration 4: Log likelihood = -5159.2791
Generalized structural equation model Number of obs = 945
Response: ta1 Number of obs = 885
Family: Ordinal
Link: Logit
Response: ta2 Number of obs = 912
Family: Ordinal
Link: Logit
Response: ta3 Number of obs = 929
Family: Ordinal
Link: Logit
Response: ta4 Number of obs = 934
Family: Ordinal
Link: Logit
Response: ta5 Number of obs = 923
Family: Ordinal
Link: Logit
Log likelihood = -5159.2791
( 1) [/]var(Theta) = 1
------------------------------------------------------------------------------
| Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
ta1 |
Theta | 0.908 0.096 9.495 0.000 0.720 1.095
-------------+----------------------------------------------------------------
ta2 |
Theta | 0.943 0.097 9.752 0.000 0.754 1.133
-------------+----------------------------------------------------------------
ta3 |
Theta | 1.734 0.155 11.157 0.000 1.430 2.039
-------------+----------------------------------------------------------------
ta4 |
Theta | 1.933 0.186 10.408 0.000 1.569 2.298
-------------+----------------------------------------------------------------
ta5 |
Theta | 1.428 0.126 11.294 0.000 1.180 1.675
-------------+----------------------------------------------------------------
/ta1 |
cut1 | -1.398 0.095 -1.583 -1.212
cut2 | 1.176 0.090 0.999 1.354
cut3 | 2.999 0.155 2.695 3.304
-------------+----------------------------------------------------------------
/ta2 |
cut1 | -1.567 0.099 -1.761 -1.374
cut2 | 0.006 0.078 -0.146 0.159
cut3 | 2.388 0.124 2.145 2.631
-------------+----------------------------------------------------------------
/ta3 |
cut1 | -1.873 0.136 -2.140 -1.606
cut2 | 1.763 0.133 1.501 2.024
cut3 | 3.872 0.230 3.422 4.322
-------------+----------------------------------------------------------------
/ta4 |
cut1 | -0.666 0.110 -0.882 -0.450
cut2 | 2.835 0.194 2.454 3.215
cut3 | 4.677 0.303 4.083 5.271
-------------+----------------------------------------------------------------
/ta5 |
cut1 | -1.221 0.105 -1.426 -1.016
cut2 | 0.971 0.099 0.777 1.166
cut3 | 2.961 0.161 2.645 3.277
-------------+----------------------------------------------------------------
var(Theta)| 1.000 (constrained)
------------------------------------------------------------------------------irt_coef, latent(Theta)y* standardized coefficients (and raw coefficient) from IRT model N=945
| Std Coef Coef Std. Err. P>|z|
-------------+-----------------------------------------------
ta1 | 0.447 0.908 0.096 0.000
ta2 | 0.461 0.943 0.097 0.000
ta3 | 0.691 1.734 0.155 0.000
ta4 | 0.729 1.933 0.186 0.000
ta5 | 0.618 1.428 0.126 0.000