use ivbinoutdata, clearTwo-stage residual inclusion estimators
Read in binary outcome data; y outcome, x exposure, w covariate, z* instrumental variables (genotypes).
Fit the model with a single instrumental variable.
ivtsri y (x = z1)Final GMM criterion Q(b) = 1.38e-32
note: model is exactly identified.
GMM estimation
Number of parameters = 5
Number of moments = 5
Initial weight matrix: Unadjusted Number of obs = 2,500
------------------------------------------------------------------------------
| Robust
| Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
/s1xb_z1 | .9318626 .0711029 13.11 0.000 .7925034 1.071222
/a0 | 1.456817 .0466934 31.20 0.000 1.3653 1.548335
/b1 | .1433391 .0139152 10.30 0.000 .1160658 .1706123
/b2 | .0237303 .0146168 1.62 0.104 -.0049182 .0523787
/b0 | .2817003 .0268135 10.51 0.000 .2291468 .3342537
------------------------------------------------------------------------------
Instruments for equation 1: z1 _cons
Instruments for equation 2: x residuals _cons
Causal risk difference for: b1
( 1) [b1]_cons = 0
------------------------------------------------------------------------------
| Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
(1) | .1433391 .0139152 10.30 0.000 .1160658 .1706123
------------------------------------------------------------------------------
Causal risk difference for: b2
( 1) [b2]_cons = 0
------------------------------------------------------------------------------
| Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
(1) | .0237303 .0146168 1.62 0.104 -.0049182 .0523787
------------------------------------------------------------------------------Fit the model with multiple instruments.
ivtsri y (x = z1 z2 z3)Final GMM criterion Q(b) = 7.38e-33
note: model is exactly identified.
GMM estimation
Number of parameters = 7
Number of moments = 7
Initial weight matrix: Unadjusted Number of obs = 2,500
------------------------------------------------------------------------------
| Robust
| Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
/s1xb_z1 | .9945859 .0614877 16.18 0.000 .8740722 1.1151
/s1xb_z2 | .9540576 .0525572 18.15 0.000 .8510474 1.057068
/s1xb_z3 | .9554229 .0495052 19.30 0.000 .8583944 1.052451
/a0 | .0842244 .0675928 1.25 0.213 -.0482551 .2167039
/b1 | .1307856 .0067841 19.28 0.000 .1174891 .1440822
/b2 | .047557 .0084484 5.63 0.000 .0309984 .0641155
/b0 | .3046021 .0148061 20.57 0.000 .2755826 .3336216
------------------------------------------------------------------------------
Instruments for equation 1: z1 z2 z3 _cons
Instruments for equation 2: x residuals _cons
Causal risk difference for: b1
( 1) [b1]_cons = 0
------------------------------------------------------------------------------
| Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
(1) | .1307856 .0067841 19.28 0.000 .1174891 .1440822
------------------------------------------------------------------------------
Causal risk difference for: b2
( 1) [b2]_cons = 0
------------------------------------------------------------------------------
| Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
(1) | .047557 .0084484 5.63 0.000 .0309984 .0641155
------------------------------------------------------------------------------Fit the model with multiple instruments, and adjusting for w.
ivtsri y w (x = z1 z2 z3)Final GMM criterion Q(b) = 1.31e-32
note: model is exactly identified.
GMM estimation
Number of parameters = 9
Number of moments = 9
Initial weight matrix: Unadjusted Number of obs = 2,500
------------------------------------------------------------------------------
| Robust
| Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
/s1xb_z1 | .9882395 .0505573 19.55 0.000 .8891491 1.08733
/s1xb_z2 | .9152859 .0431149 21.23 0.000 .8307823 .9997895
/s1xb_z3 | .954388 .0404106 23.62 0.000 .8751847 1.033591
/s1xb_w | .9801363 .027334 35.86 0.000 .9265627 1.03371
/a0 | .0734396 .0541988 1.36 0.175 -.0327882 .1796673
/b1 | .129698 .006901 18.79 0.000 .1161722 .1432237
/b2 | .0404658 .008937 4.53 0.000 .0229495 .0579821
/s2exogxb_w | .0638726 .0103505 6.17 0.000 .0435859 .0841593
/b0 | .3041477 .0145428 20.91 0.000 .2756443 .3326511
------------------------------------------------------------------------------
Instruments for equation 1: z1 z2 z3 w _cons
Instruments for equation 2: x residuals w _cons
Causal risk difference for: b1
( 1) [b1]_cons = 0
------------------------------------------------------------------------------
| Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
(1) | .129698 .006901 18.79 0.000 .1161722 .1432237
------------------------------------------------------------------------------
Causal risk difference for: b2
( 1) [b2]_cons = 0
------------------------------------------------------------------------------
| Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
(1) | .0404658 .008937 4.53 0.000 .0229495 .0579821
------------------------------------------------------------------------------Using the log additive link function.
ivtsri y (x = z1 z2 z3), link(logadd)Final GMM criterion Q(b) = 6.65e-33
note: model is exactly identified.
GMM estimation
Number of parameters = 7
Number of moments = 7
Initial weight matrix: Unadjusted Number of obs = 2,500
------------------------------------------------------------------------------
| Robust
| Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
/s1xb_z1 | .9945859 .0614877 16.18 0.000 .8740722 1.1151
/s1xb_z2 | .9540576 .0525572 18.15 0.000 .8510474 1.057068
/s1xb_z3 | .9554229 .0495052 19.30 0.000 .8583944 1.052451
/a0 | .0842244 .0675928 1.25 0.213 -.0482551 .2167039
/b1 | .2246119 .0145109 15.48 0.000 .1961711 .2530527
/b2 | .0995872 .016851 5.91 0.000 .0665599 .1326146
/b0 | -1.203224 .0392053 -30.69 0.000 -1.280065 -1.126383
------------------------------------------------------------------------------
Instruments for equation 1: z1 z2 z3 _cons
Instruments for equation 2: x residuals _cons
Causal risk ratio for: b1
( 1) [b1]_cons = 0
------------------------------------------------------------------------------
| exp(b) Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
(1) | 1.251837 .0181653 15.48 0.000 1.216735 1.287951
------------------------------------------------------------------------------
Causal risk ratio for: b2
( 1) [b2]_cons = 0
------------------------------------------------------------------------------
| exp(b) Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
(1) | 1.104715 .0186155 5.91 0.000 1.068825 1.14181
------------------------------------------------------------------------------Using the log multiplicative link function.
ivtsri y (x = z1 z2 z3), link(logmult)Final GMM criterion Q(b) = 6.21e-32
note: model is exactly identified.
GMM estimation
Number of parameters = 7
Number of moments = 7
Initial weight matrix: Unadjusted Number of obs = 2,500
------------------------------------------------------------------------------
| Robust
| Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
/s1xb_z1 | .9945859 .0614877 16.18 0.000 .8740722 1.1151
/s1xb_z2 | .9540576 .0525572 18.15 0.000 .8510474 1.057068
/s1xb_z3 | .9554229 .0495052 19.30 0.000 .8583944 1.052451
/a0 | .0842244 .0675928 1.25 0.213 -.0482551 .2167039
/b1 | .5193282 .0388913 13.35 0.000 .4431026 .5955538
/b2 | .1793399 .0361099 4.97 0.000 .1085658 .2501141
/b0 | -1.936359 .0941036 -20.58 0.000 -2.120799 -1.75192
------------------------------------------------------------------------------
Instruments for equation 1: z1 z2 z3 _cons
Instruments for equation 2: x residuals _cons
Causal risk ratio for: b1
( 1) [b1]_cons = 0
------------------------------------------------------------------------------
| exp(b) Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
(1) | 1.680898 .0653723 13.35 0.000 1.557532 1.814035
------------------------------------------------------------------------------
Causal risk ratio for: b2
( 1) [b2]_cons = 0
------------------------------------------------------------------------------
| exp(b) Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
(1) | 1.196427 .0432029 4.97 0.000 1.114678 1.284172
------------------------------------------------------------------------------Using the logit link function.
ivtsri y (x = z1 z2 z3), link(logit)Final GMM criterion Q(b) = 6.75e-33
note: model is exactly identified.
GMM estimation
Number of parameters = 7
Number of moments = 7
Initial weight matrix: Unadjusted Number of obs = 2,500
------------------------------------------------------------------------------
| Robust
| Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
/s1xb_z1 | .9945859 .0614877 16.18 0.000 .8740722 1.1151
/s1xb_z2 | .9540576 .0525572 18.15 0.000 .8510474 1.057068
/s1xb_z3 | .9554229 .0495052 19.30 0.000 .8583944 1.052451
/a0 | .0842244 .0675928 1.25 0.213 -.0482551 .2167039
/b1 | 1.108148 .0667702 16.60 0.000 .9772804 1.239015
/b2 | .3825741 .0664177 5.76 0.000 .2523978 .5127505
/b0 | -1.654878 .1262212 -13.11 0.000 -1.902267 -1.407489
------------------------------------------------------------------------------
Instruments for equation 1: z1 z2 z3 _cons
Instruments for equation 2: x residuals _cons
Causal odds ratio for: b1
( 1) [b1]_cons = 0
------------------------------------------------------------------------------
| exp(b) Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
(1) | 3.028743 .2022298 16.60 0.000 2.65722 3.452211
------------------------------------------------------------------------------
Causal odds ratio for: b2
( 1) [b2]_cons = 0
------------------------------------------------------------------------------
| exp(b) Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
(1) | 1.466054 .0973719 5.76 0.000 1.287108 1.669878
------------------------------------------------------------------------------Bootstrap standard errors.
bootstrap, reps(250): ivtsri y (x = z1 z2 z3), estonly(running ivtsri on estimation sample)
Bootstrap replications (250): .........10.........20.........30.........40.........50.........60.........70....
> .....80.........90.........100.........110.........120.........130.........140.........150.........160.......
> ..170.........180.........190.........200.........210.........220.........230.........240.........250 done
------------------------------------------------------------------------------
| Observed Bootstrap Normal-based
y | coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
x | .1307856 .0064668 20.22 0.000 .1181109 .1434604
residuals | .047557 .0084015 5.66 0.000 .0310903 .0640236
_cons | .3046021 .0147641 20.63 0.000 .275665 .3335392
------------------------------------------------------------------------------