st: Rbounds- interpretation of results

[Serena Masino <Serena.Masino@manchester.ac.uk>]

Hi,

I am writing to enquire regarding the interpretation of rbounds results.

When I run the rbounds test in STATA (after psmatch2), the output reports both the p-values from the Wilcoxon sign rank test and the Hodges-Lehman confidence intervals. I am unclear on whether we care only about the Gamma value where the ATT bounds in the first two columns in the table below become insignificant at the 95% level (I am only interested in the upper bound anyway) .

Or whether the Hodges-Lehman confidence interval (last two columns in the table below) has to encompass zero when the situation just described happens. 

In other words: when the upper bound estimate crosses the acceptable significance level, does this also have to correspond to a Hodges-Lehman confidence interval encompassing zero? Or do we simply care about the value of Gamma at which the upper bound p-value in column 1 is >0.05?

I ask, because, as you can see below, in my case, the Gamma at which the p val is >0.05 is around1.5. Because this is lower than 2, it should indicate the results are not too robust.

However, at that gamma value, the corresponding Hodges-Lehman confidence interval does not encompass zero. Does that mean I should not worry about hidden bias?

. rbounds delta3, gamma(1(0.1)2) alpha(.90)

Rosenbaum bounds for delta3 (N = 810 matched pairs)

Gamma       sig+      sig-        t-hat+    t-hat-          CI+       CI-

1           .000053   .000053  -3.1e-07  -3.1e-07  -3.1e-07  -3.1e-07 
1.1        .000595   3.1e-06   -3.1e-07  -3.1e-07  -3.1e-07  -3.1e-07 
1.2          .0038   1.6e-07    -3.1e-07  -3.1e-07  -3.1e-07  -3.1e-07 
1.3        .015868   7.2e-09   -3.1e-07  -3.1e-07  -3.1e-07  -3.1e-07 
1.4        .047676   3.0e-10   -3.1e-07  -3.1e-07  -3.1e-07  -3.1e-07 
1.5        .110641   1.1e-11   -3.1e-07  -3.1e-07  -3.1e-07  -3.1e-07 
1.6        .209409   4.1e-13   -3.1e-07  -3.1e-07  -3.1e-07  -3.1e-07 
1.7        .337338   1.4e-14   -3.1e-07  -3.1e-07  -3.1e-07  -3.1e-07 
1.8         .47863   4.4e-16    -3.1e-07  -3.1e-07  -3.1e-07  -3.1e-07 
1.9         .615128         0     -3.1e-07  -3.1e-07  -3.1e-07  -3.1e-07 
2            .732844         0    -3.1e-07  -3.1e-07  -3.1e-07  -3.1e-07 

* gamma  - log odds of differential assignment due to unobserved factors
sig+   - upper bound significance level
sig-   - lower bound significance level
t-hat+ - upper bound Hodges-Lehmann point estimate
t-hat- - lower bound Hodges-Lehmann point estimate
CI+    - upper bound confidence interval (a=   .9)
CI-    - lower bound confidence interval (a=   .9)

 Any help on this would be greatly appreciated.

Serena Masino




























*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/faqs/resources/statalist-faq/
*   http://www.ats.ucla.edu/stat/stata/