Test for balance for inverse-probability-weighted estimators
Comparison of model-adjusted covariate distributions across treatment groups
Summary statistics
Box plots
Kernel density plots
Kernel density plot comparing propensity scores across treatment groups
Treatment-effects models extract experimental-style causal effects from observational data.
In experimental data, treatment groups must be assigned randomly, meaning characteristics across groups will be approximately equal.
Treatment-effects estimators for observational data use a variety of techniques, including reweighting and matching, to achieve experimental-like balanced data results.
If the reweighting or matching is successful, the distribution of each covariate should be the same across treatment groups. In such cases, we say that the treatment model “balanced” the covariates.
We can examine whether the treatment model balanced the covariates and perform a statistical test.
Three diagnostics and one test are provided.
One diagnostic reports, for each covariate, the model-adjusted difference in means in the treatment groups and the ratio of variances.
Another diagnostic graphs the model-adjusted estimated densities of covariates; these densities can be examined visually to verify that they are approximately equal.
The third graphical diagnostic is the same as the second but uses box plots rather than probability densities.
The statistical test is an overidentification test. It tests whether the model-adjusted means of the covariates are the same between groups.
Say that we estimate the effect of smoking during pregnancy on infant birthweight using an inverse-probability-weighted (IPW) treatment-effects estimator.
We assume that treatment (smoking during pregnancy) is determined by marital status, the mother's age, attendance to prenatal care during the first quarter of pregnancy, and whether this is the mother's first pregnancy.
. teffects ipw (bweight) (mbsmoke mmarried mage prenatal1 fbaby c.mage#(c.mage
i.mmarried prenatal1))
Iteration 0: EE criterion = 9.365e-20
Iteration 1: EE criterion = 2.884e-26
Treatment-effects estimation Number of obs = 4,642
Estimator : inverse-probability weights
Outcome model : weighted mean
Treatment model: logit
| Robust | ||
| bweight | Coefficient std. err. z P>|z| [95% conf. interval] | |
| ATE | ||
| mbsmoke | ||
| (Smoker vs Nonsmoker) | -239.6875 26.43427 -9.07 0.000 -291.4977 -187.8773 | |
| POmean | ||
| mbsmoke | ||
| Nonsmoker | 3403.638 9.56792 355.73 0.000 3384.885 3422.39 | |
We find that the average treatment effect (ATE) is -240 grams.
Have we done an adequate job of balancing the covariates so that we can trust the estimated treatment effect?
We could use the overidentification test:
. tebalance overid, nolog
Overidentification test for covariate balance
H0: Covariates are balanced:
chi2(8) = 11.8612
Prob > chi2 = 0.1575
We cannot reject the null hypothesis that the covariates are balanced, and that's good.
We can look at the various diagnostics (and in real life, we probably would have used the diagnostics before using the statistical test).
tebalance summarize reports the model-adjusted difference in means and ratio of variances between the treated and untreated for each covariate:
. tebalance summarize
Covariate balance summary
Raw Weighted
Number of obs = 4,642 4,642.0 Treated obs = 864 2,329.1 Control obs = 3,778 2,312.9
Standardized differences Variance ratio Raw Weighted Raw Weighted mmarried -.5953009 .0053497 1.335944 .9953184 mage -.300179 .0410889 .8818025 1.076571 prenatal1 -.3242695 .0009807 1.496155 .9985165 fbaby -.1663271 -.0130638 .9430944 .9965406 mage# mage -.3028275 .0477465 .8274389 1.109134 mmarried# mage married -.6329701 .0197209 1.157026 1.034108 prenatal1# mage Yes -.4053969 .0182109 1.226363 1.032561
Ignore the raw columns, at least to begin, and focus on the weighted
columns. Differences in weighted means are negligible, and variance
ratios are all near one. The Raw columns show where we started, and,
before weighting, differences were large.
tebalance can show us densities or box plots so that we can examine the
entire distribution. Below we have put the graphs produced
by tebalance density and tebalance box together:
Tests and diagnostics confirm that our model balances the covariates.
To find out more about checking for balance after teffects or stteffects, see [CAUSAL] tebalance.
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