Examples from the help file
Single-level, panel, multilevel, and instrumental-variable systems
The four examples at the end of the help file, run in full. Each combines two models of one family and then calls margins on the combined system.
Ordinary single-level models
sysuse nlsw88, clear(NLSW, 1988 extract)logit union c.age i.married, vce(robust)Iteration 0: Log pseudolikelihood = -1046.6242
Iteration 1: Log pseudolikelihood = -1044.0408
Iteration 2: Log pseudolikelihood = -1044.0376
Iteration 3: Log pseudolikelihood = -1044.0376
Logistic regression Number of obs = 1,878
Wald chi2(2) = 5.22
Prob > chi2 = 0.0735
Log pseudolikelihood = -1044.0376 Pseudo R2 = 0.0025
------------------------------------------------------------------------------
| Robust
union | Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
age | 0.008 0.018 0.434 0.664 -0.027 0.042
|
married |
Married | -0.247 0.111 -2.232 0.026 -0.464 -0.030
_cons | -1.266 0.701 -1.807 0.071 -2.640 0.108
------------------------------------------------------------------------------estimates store mod1
logit union c.age i.married i.collgrad, vce(robust)Iteration 0: Log pseudolikelihood = -1046.6242
Iteration 1: Log pseudolikelihood = -1035.471
Iteration 2: Log pseudolikelihood = -1035.3994
Iteration 3: Log pseudolikelihood = -1035.3994
Logistic regression Number of obs = 1,878
Wald chi2(3) = 23.45
Prob > chi2 = 0.0000
Log pseudolikelihood = -1035.3994 Pseudo R2 = 0.0107
-------------------------------------------------------------------------------
| Robust
union | Coefficient std. err. z P>|z| [95% conf. interval]
--------------+----------------------------------------------------------------
age | 0.008 0.018 0.462 0.644 -0.027 0.043
|
married |
Married | -0.247 0.112 -2.214 0.027 -0.466 -0.028
|
collgrad |
College grad | 0.500 0.119 4.202 0.000 0.267 0.733
_cons | -1.422 0.705 -2.016 0.044 -2.804 -0.039
-------------------------------------------------------------------------------estimates store mod2
suest2 mod1 mod2Simultaneous results for mod1, mod2 Number of obs = 1,878
-------------------------------------------------------------------------------
| Robust
| Coefficient std. err. z P>|z| [95% conf. interval]
--------------+----------------------------------------------------------------
mod1_union |
age | 0.008 0.018 0.434 0.664 -0.027 0.042
|
married |
Married | -0.247 0.111 -2.232 0.026 -0.464 -0.030
_cons | -1.266 0.701 -1.807 0.071 -2.640 0.108
--------------+----------------------------------------------------------------
mod2_union |
age | 0.008 0.018 0.462 0.644 -0.027 0.043
|
married |
Married | -0.247 0.112 -2.214 0.027 -0.466 -0.028
|
collgrad |
College grad | 0.500 0.119 4.202 0.000 0.267 0.733
_cons | -1.422 0.705 -2.016 0.044 -2.804 -0.039
-------------------------------------------------------------------------------margins, dydx(age married)Average marginal effects Number of obs = 1,878
Model VCE: Robust
dy/dx wrt: age 1.married
1._predict: Pr(union), predict(model(mod1))
2._predict: Pr(union), predict(model(mod2))
------------------------------------------------------------------------------
| Delta-method
| dy/dx std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
age |
_predict |
1 | 0.001 0.003 0.434 0.664 -0.005 0.008
2 | 0.001 0.003 0.462 0.644 -0.005 0.008
-------------+----------------------------------------------------------------
0.married | (base outcome)
-------------+----------------------------------------------------------------
1.married |
_predict |
1 | -0.047 0.021 -2.196 0.028 -0.088 -0.005
2 | -0.046 0.021 -2.177 0.029 -0.088 -0.005
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.Panel models
Two fixed-effects regressions on the NLS panel, clustered on the panel identifier:
webuse nlswork, clear(National Longitudinal Survey of Young Women, 14-24 years old in 1968)xtset idcode yearPanel variable: idcode (unbalanced)
Time variable: year, 68 to 88, but with gaps
Delta: 1 unitxtreg ln_wage c.ttl_exp##i.union i.year, feFixed-effects (within) regression Number of obs = 19,238
Group variable: idcode Number of groups = 4,150
R-squared: Obs per group:
Within = 0.1437 min = 1
Between = 0.2539 avg = 4.6
Overall = 0.1908 max = 12
F(14, 15074) = 180.68
corr(u_i, Xb) = 0.1109 Prob > F = 0.0000
---------------------------------------------------------------------------------
ln_wage | Coefficient Std. err. t P>|t| [95% conf. interval]
----------------+----------------------------------------------------------------
ttl_exp | 0.045 0.002 27.440 0.000 0.042 0.048
1.union | 0.121 0.012 10.523 0.000 0.099 0.144
|
union#c.ttl_exp |
1 | -0.003 0.001 -2.193 0.028 -0.005 -0.000
|
year |
71 | 0.003 0.013 0.214 0.831 -0.023 0.029
72 | -0.020 0.013 -1.563 0.118 -0.046 0.005
73 | -0.042 0.014 -3.086 0.002 -0.069 -0.015
77 | -0.082 0.014 -6.024 0.000 -0.108 -0.055
78 | -0.064 0.015 -4.317 0.000 -0.092 -0.035
80 | -0.142 0.016 -9.055 0.000 -0.173 -0.111
82 | -0.180 0.017 -10.570 0.000 -0.214 -0.147
83 | -0.184 0.018 -10.129 0.000 -0.220 -0.149
85 | -0.210 0.020 -10.518 0.000 -0.249 -0.171
87 | -0.250 0.022 -11.360 0.000 -0.293 -0.207
88 | -0.262 0.024 -11.015 0.000 -0.309 -0.216
|
_cons | 1.527 0.011 141.078 0.000 1.506 1.548
----------------+----------------------------------------------------------------
sigma_u | .38034846
sigma_e | .25524001
rho | .68949663 (fraction of variance due to u_i)
---------------------------------------------------------------------------------
F test that all u_i=0: F(4149, 15074) = 8.90 Prob > F = 0.0000estimates store fe1
xtreg hours c.ttl_exp##i.union i.year, feFixed-effects (within) regression Number of obs = 19,202
Group variable: idcode Number of groups = 4,150
R-squared: Obs per group:
Within = 0.0335 min = 1
Between = 0.0601 avg = 4.6
Overall = 0.0487 max = 12
F(14, 15038) = 37.19
corr(u_i, Xb) = -0.0847 Prob > F = 0.0000
---------------------------------------------------------------------------------
hours | Coefficient Std. err. t P>|t| [95% conf. interval]
----------------+----------------------------------------------------------------
ttl_exp | 0.730 0.046 15.909 0.000 0.640 0.820
1.union | 2.054 0.322 6.378 0.000 1.423 2.685
|
union#c.ttl_exp |
1 | -0.080 0.033 -2.396 0.017 -0.146 -0.015
|
year |
71 | -1.600 0.376 -4.253 0.000 -2.338 -0.863
72 | -2.632 0.363 -7.260 0.000 -3.343 -1.921
73 | -3.607 0.381 -9.460 0.000 -4.355 -2.860
77 | -5.784 0.380 -15.237 0.000 -6.528 -5.040
78 | -6.496 0.412 -15.756 0.000 -7.304 -5.688
80 | -7.649 0.439 -17.418 0.000 -8.510 -6.788
82 | -8.631 0.478 -18.055 0.000 -9.568 -7.694
83 | -9.241 0.509 -18.144 0.000 -10.240 -8.243
85 | -9.773 0.558 -17.510 0.000 -10.868 -8.679
87 | -10.350 0.615 -16.817 0.000 -11.556 -9.144
88 | -10.692 0.667 -16.034 0.000 -11.999 -9.385
|
_cons | 38.076 0.303 125.793 0.000 37.483 38.669
----------------+----------------------------------------------------------------
sigma_u | 8.2810736
sigma_e | 7.1338816
rho | .57401081 (fraction of variance due to u_i)
---------------------------------------------------------------------------------
F test that all u_i=0: F(4149, 15038) = 4.29 Prob > F = 0.0000estimates store fe2
quietly suest2 fe1 fe2, cluster(idcode)
suest2Simultaneous fixed-effects results for fe1 fe2
(Std. err. adjusted for 4,150 clusters in idcode)
---------------------------------------------------------------------------------
| Robust
| Coefficient std. err. z P>|z| [95% conf. interval]
----------------+----------------------------------------------------------------
fe1_mean |
ttl_exp | 0.045 0.002 18.496 0.000 0.040 0.050
1.union | 0.121 0.015 8.034 0.000 0.092 0.151
|
union#c.ttl_exp |
1 | -0.003 0.002 -1.706 0.088 -0.006 0.000
|
year |
71 | 0.003 0.011 0.268 0.789 -0.018 0.024
72 | -0.020 0.012 -1.645 0.100 -0.044 0.004
73 | -0.042 0.014 -3.052 0.002 -0.069 -0.015
77 | -0.082 0.017 -4.906 0.000 -0.114 -0.049
78 | -0.064 0.018 -3.533 0.000 -0.099 -0.028
80 | -0.142 0.020 -6.979 0.000 -0.182 -0.102
82 | -0.180 0.023 -7.880 0.000 -0.225 -0.135
83 | -0.184 0.024 -7.551 0.000 -0.232 -0.136
85 | -0.210 0.028 -7.583 0.000 -0.264 -0.155
87 | -0.250 0.031 -7.941 0.000 -0.311 -0.188
88 | -0.262 0.034 -7.676 0.000 -0.329 -0.195
|
_cons | 1.527 0.012 122.911 0.000 1.502 1.551
----------------+----------------------------------------------------------------
fe2_mean |
ttl_exp | 0.730 0.074 9.866 0.000 0.585 0.875
1.union | 2.054 0.383 5.365 0.000 1.303 2.804
|
union#c.ttl_exp |
1 | -0.080 0.036 -2.238 0.025 -0.150 -0.010
|
year |
71 | -1.600 0.322 -4.963 0.000 -2.232 -0.968
72 | -2.632 0.350 -7.514 0.000 -3.319 -1.946
73 | -3.607 0.395 -9.134 0.000 -4.382 -2.833
77 | -5.784 0.502 -11.527 0.000 -6.768 -4.801
78 | -6.496 0.542 -11.987 0.000 -7.558 -5.434
80 | -7.649 0.632 -12.098 0.000 -8.888 -6.410
82 | -8.631 0.734 -11.764 0.000 -10.069 -7.193
83 | -9.241 0.786 -11.757 0.000 -10.782 -7.701
85 | -9.773 0.893 -10.940 0.000 -11.524 -8.022
87 | -10.350 1.018 -10.168 0.000 -12.345 -8.355
88 | -10.692 1.110 -9.630 0.000 -12.868 -8.516
|
_cons | 38.076 0.334 114.034 0.000 37.421 38.730
---------------------------------------------------------------------------------margins, dydx(ttl_exp)Average marginal effects Number of obs = 19,238
Model VCE: Robust
dy/dx wrt: ttl_exp
1._predict: Linear prediction, predict(model(fe1))
2._predict: Linear prediction, predict(model(fe2))
------------------------------------------------------------------------------
| Delta-method
| dy/dx std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
ttl_exp |
_predict |
1 | 0.044 0.002 18.800 0.000 0.040 0.049
2 | 0.712 0.073 9.800 0.000 0.569 0.854
------------------------------------------------------------------------------Typing suest2 on its own redisplays the table, as with any estimation command.
Mixed models
A random-intercept logit and probit for the same outcome, with the model-specific predictions selected in margins:
webuse bangladesh, clear(Bangladesh Fertility Survey, 1989)melogit c_use urban age || district:, intpoints(5)Fitting fixed-effects model:
Iteration 0: Log likelihood = -1271.4063
Iteration 1: Log likelihood = -1269.4245
Iteration 2: Log likelihood = -1269.4236
Iteration 3: Log likelihood = -1269.4236
Refining starting values:
Grid node 0: Log likelihood = -1263.0911
Fitting full model:
Iteration 0: Log likelihood = -1263.0911 (not concave)
Iteration 1: Log likelihood = -1250.516
Iteration 2: Log likelihood = -1250.0679
Iteration 3: Log likelihood = -1250.0625
Iteration 4: Log likelihood = -1250.0625
Mixed-effects logistic regression Number of obs = 1,934
Group variable: district Number of groups = 60
Obs per group:
min = 2
avg = 32.2
max = 118
Integration method: mvaghermite Integration pts. = 5
Wald chi2(2) = 34.23
Log likelihood = -1250.0625 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
c_use | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
urban | 0.653 0.116 5.643 0.000 0.426 0.879
age | 0.009 0.005 1.669 0.095 -0.002 0.020
_cons | -0.704 0.086 -8.218 0.000 -0.871 -0.536
-------------+----------------------------------------------------------------
district |
var(_cons)| 0.195 0.068 0.098 0.386
------------------------------------------------------------------------------
LR test vs. logistic model: chibar2(01) = 38.72 Prob >= chibar2 = 0.0000estimates store me1
meprobit c_use urban age || district:, intpoints(5)Fitting fixed-effects model:
Iteration 0: Log likelihood = -1270.6112
Iteration 1: Log likelihood = -1269.3945
Iteration 2: Log likelihood = -1269.3945
Refining starting values:
Grid node 0: Log likelihood = -1281.198
Fitting full model:
Iteration 0: Log likelihood = -1281.198 (not concave)
Iteration 1: Log likelihood = -1264.2124 (not concave)
Iteration 2: Log likelihood = -1250.1961
Iteration 3: Log likelihood = -1249.8256
Iteration 4: Log likelihood = -1249.8157
Iteration 5: Log likelihood = -1249.8157
Mixed-effects probit regression Number of obs = 1,934
Group variable: district Number of groups = 60
Obs per group:
min = 2
avg = 32.2
max = 118
Integration method: mvaghermite Integration pts. = 5
Wald chi2(2) = 34.57
Log likelihood = -1249.8157 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
c_use | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
urban | 0.404 0.071 5.669 0.000 0.264 0.543
age | 0.006 0.003 1.664 0.096 -0.001 0.012
_cons | -0.435 0.052 -8.319 0.000 -0.537 -0.332
-------------+----------------------------------------------------------------
district |
var(_cons)| 0.074 0.025 0.038 0.145
------------------------------------------------------------------------------
LR test vs. probit model: chibar2(01) = 39.16 Prob >= chibar2 = 0.0000estimates store me2
suest2 me1 me2Simultaneous results for me1 me2
(Std. err. adjusted for 60 clusters in district)
--------------------------------------------------------------------------------------
| Robust
| Coefficient std. err. z P>|z| [95% conf. interval]
---------------------+----------------------------------------------------------------
me1_c_use |
urban | 0.653 0.163 4.016 0.000 0.334 0.971
age | 0.009 0.006 1.565 0.118 -0.002 0.020
_cons | -0.704 0.102 -6.875 0.000 -0.904 -0.503
---------------------+----------------------------------------------------------------
me1__ |
var(_cons[district])| 0.195 0.061 3.199 0.001 0.075 0.314
---------------------+----------------------------------------------------------------
me2_c_use |
urban | 0.404 0.100 4.057 0.000 0.209 0.599
age | 0.006 0.004 1.550 0.121 -0.001 0.013
_cons | -0.435 0.062 -7.003 0.000 -0.557 -0.313
---------------------+----------------------------------------------------------------
me2__ |
var(_cons[district])| 0.074 0.023 3.207 0.001 0.029 0.119
--------------------------------------------------------------------------------------margins, dydx(age) predict(model(me1) mu fixedonly)------------------------------------------------------------------------------
| Delta-method
| Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
me1 |
age | 0.002 0.001 1.559 0.119 -0.001 0.005
------------------------------------------------------------------------------margins, dydx(age) predict(model(me2) mu conditional(fixedonly))------------------------------------------------------------------------------
| Delta-method
| Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
me2 |
age | 0.002 0.001 1.546 0.122 -0.001 0.005
------------------------------------------------------------------------------Instrumental variables
webuse hsng2, clear(1980 Census housing data)ivregress 2sls rent pcturban (hsngval = faminc)Instrumental-variables 2SLS regression Number of obs = 50
Wald chi2(2) = 51.44
Prob > chi2 = 0.0000
R-squared = 0.2887
Root MSE = 29.517
------------------------------------------------------------------------------
rent | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
hsngval | 0.003 0.001 5.147 0.000 0.002 0.004
pcturban | -0.506 0.482 -1.052 0.293 -1.450 0.437
_cons | 113.814 20.527 5.545 0.000 73.583 154.046
------------------------------------------------------------------------------
Endogenous: hsngval
Exogenous: pcturban famincestimates store iv1
ivregress 2sls rent pcturban (hsngval = faminc i.region)Instrumental-variables 2SLS regression Number of obs = 50
Wald chi2(2) = 90.76
Prob > chi2 = 0.0000
R-squared = 0.5989
Root MSE = 22.166
------------------------------------------------------------------------------
rent | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
hsngval | 0.002 0.000 6.820 0.000 0.002 0.003
pcturban | 0.082 0.299 0.273 0.785 -0.504 0.667
_cons | 120.707 15.228 7.926 0.000 90.859 150.554
------------------------------------------------------------------------------
Endogenous: hsngval
Exogenous: pcturban faminc 2.region 3.region 4.regionestimates store iv2
suest2 iv1 iv2Simultaneous results for iv1 iv2
------------------------------------------------------------------------------
| Robust
| Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
iv1_mean |
hsngval | 0.003 0.001 4.328 0.000 0.002 0.005
pcturban | -0.506 0.543 -0.933 0.351 -1.570 0.558
_cons | 113.814 21.622 5.264 0.000 71.437 156.192
-------------+----------------------------------------------------------------
iv2_mean |
hsngval | 0.002 0.001 3.333 0.001 0.001 0.004
pcturban | 0.082 0.445 0.183 0.855 -0.790 0.953
_cons | 120.707 15.255 7.912 0.000 90.806 150.607
------------------------------------------------------------------------------margins, dydx(pcturban)------------------------------------------------------------------------------
| Delta-method
| Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
iv1 |
pcturban | -0.506 0.543 -0.933 0.351 -1.570 0.558
-------------+----------------------------------------------------------------
iv2 |
pcturban | 0.082 0.445 0.183 0.855 -0.790 0.953
------------------------------------------------------------------------------