Examples from the help file
The examples in help irt_me, run in full
The examples at the end of help irt_me, on Stata’s masc1 data (five binary items from a mathematics test). The two-parameter logistic model is fit first with irt 2pl and then, identically, with gsem; after gsem the latent() option names the latent variable.
webuse masc1, clear(Data from De Boeck & Wilson (2004))irt 2pl q1 q2 q3 q4 q5Fitting fixed-effects model:
Iteration 0: Log likelihood = -2466.7785
Iteration 1: Log likelihood = -2464.4785
Iteration 2: Log likelihood = -2464.4775
Iteration 3: Log likelihood = -2464.4775
Fitting full model:
Iteration 0: Log likelihood = -2410.0168
Iteration 1: Log likelihood = -2400.2608
Iteration 2: Log likelihood = -2400.1775
Iteration 3: Log likelihood = -2400.1775
Two-parameter logistic model Number of obs = 800
Log likelihood = -2400.1775
------------------------------------------------------------------------------
| Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
q1 |
Discrim | 1.260 0.241 5.237 0.000 0.789 1.732
Diff | -0.542 0.098 -5.528 0.000 -0.735 -0.350
-------------+----------------------------------------------------------------
q2 |
Discrim | 0.739 0.145 5.082 0.000 0.454 1.024
Diff | -0.137 0.110 -1.254 0.210 -0.352 0.077
-------------+----------------------------------------------------------------
q3 |
Discrim | 0.933 0.193 4.844 0.000 0.555 1.310
Diff | -1.698 0.282 -6.031 0.000 -2.250 -1.146
-------------+----------------------------------------------------------------
q4 |
Discrim | 0.839 0.157 5.331 0.000 0.531 1.148
Diff | 0.324 0.108 2.987 0.003 0.111 0.536
-------------+----------------------------------------------------------------
q5 |
Discrim | 1.062 0.208 5.104 0.000 0.654 1.469
Diff | 1.408 0.213 6.606 0.000 0.990 1.825
------------------------------------------------------------------------------irt_me, helpMarginal Effects of + 1.000 Increase in Latent Variable (theta) N=800
| PrStart PrEnd ME Est. Std. Err. P>|z|
-------------+-----------------------------------------------------------
q1 | 0.513 0.788 0.275 0.047 0.000
q2 | 0.433 0.616 0.182 0.035 0.000
q3 | 0.754 0.886 0.132 0.022 0.000
q4 | 0.334 0.537 0.203 0.037 0.000
q5 | 0.117 0.276 0.160 0.025 0.000
PrStart : Pr(y=1) at theta = -0.500
PrEnd : Pr(y=1) at theta = 0.500
ME : PrEnd - PrStartgsem (Theta -> q1 q2 q3 q4 q5, logit), var(Theta@1)Fitting fixed-effects model:
Iteration 0: Log likelihood = -2466.7785
Iteration 1: Log likelihood = -2464.4785
Iteration 2: Log likelihood = -2464.4775
Iteration 3: Log likelihood = -2464.4775
Refining starting values:
Grid node 0: Log likelihood = -2410.0168
Fitting full model:
Iteration 0: Log likelihood = -2410.0168
Iteration 1: Log likelihood = -2400.2608
Iteration 2: Log likelihood = -2400.1775
Iteration 3: Log likelihood = -2400.1775
Generalized structural equation model Number of obs = 800
Response: q1
Family: Bernoulli
Link: Logit
Response: q2
Family: Bernoulli
Link: Logit
Response: q3
Family: Bernoulli
Link: Logit
Response: q4
Family: Bernoulli
Link: Logit
Response: q5
Family: Bernoulli
Link: Logit
Log likelihood = -2400.1775
( 1) [/]var(Theta) = 1
------------------------------------------------------------------------------
| Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
q1 |
Theta | 1.260 0.241 5.237 0.000 0.789 1.732
_cons | 0.684 0.108 6.330 0.000 0.472 0.895
-------------+----------------------------------------------------------------
q2 |
Theta | 0.739 0.145 5.082 0.000 0.454 1.024
_cons | 0.102 0.080 1.277 0.202 -0.054 0.257
-------------+----------------------------------------------------------------
q3 |
Theta | 0.933 0.193 4.844 0.000 0.555 1.310
_cons | 1.584 0.130 12.163 0.000 1.329 1.839
-------------+----------------------------------------------------------------
q4 |
Theta | 0.839 0.157 5.331 0.000 0.531 1.148
_cons | -0.272 0.083 -3.278 0.001 -0.434 -0.109
-------------+----------------------------------------------------------------
q5 |
Theta | 1.062 0.208 5.104 0.000 0.654 1.469
_cons | -1.495 0.135 -11.108 0.000 -1.758 -1.231
-------------+----------------------------------------------------------------
var(Theta)| 1.000 (constrained)
------------------------------------------------------------------------------irt_me, latent(Theta)Marginal Effects of + 1.000 Increase in Latent Variable (theta) N=800
| PrStart PrEnd ME Est. Std. Err. P>|z|
-------------+-----------------------------------------------------------
q1 | 0.513 0.788 0.275 0.047 0.000
q2 | 0.433 0.616 0.182 0.035 0.000
q3 | 0.754 0.886 0.132 0.022 0.000
q4 | 0.334 0.537 0.203 0.037 0.000
q5 | 0.117 0.276 0.160 0.025 0.000