Re: st: Not sure how to interpret -somersd- results

["Roger B. Newson" <r.newson@imperial.ac.uk>]

Hello Monica

Yes, we can say that 2006 child height z-scores stochastically dominate 
1996 child height z-scores, as both 95% confidence limits for Somers' D 
are above zero.

Your confidence intervals would probably be even better if you used the 
options

transf(z) tdist

for your -somersd- command, as you would then have asymmetric 95% 
confidence limits using the t-distribution, instead of symmetric 
confidence limits using the Normal distribution. These alternative 
confidence limits would be better, because Somers' D cannot really have 
a perfectly symmetric sampling distribution when a population 
association exists, and because I have found, from simulation studies, 
that the t-distribution gives confidence limits with a coverage 
probability closer to the advertized level than the Normal distribution. 
This is probably important if you have only 4 clusters.

I hope this helps. Let me know if you have any more queries.

Best wishes

Roger

Roger B Newson BSc MSc DPhil
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton Campus
Room 33, Emmanuel Kaye Building
1B Manresa Road
London SW3 6LR
UNITED KINGDOM
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Email: r.newson@imperial.ac.uk
Web page: http://www.imperial.ac.uk/nhli/r.newson/
Departmental Web page:
http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgenetics/reph/

Opinions expressed are those of the author, not of the institution.

On 02/10/2013 21:47, Jain, Monica (HarvestPlus) wrote:
> I am using -somersd- and I am unsure how to interpret the results to test stochastic dominance. I am using Stata 13 for Windows.
>
> I have a two year cross-section data on heights of children 3-5 years. I want to check if the distribution of heights z-score of children in 2006 first order stochastically dominates those in 1996. From previous threads on stochastic dominance, I saw that one could use Somers D statistic for it. I am using the following command where 2006 is year=1, haz is the height z-score:
>
>         somersd year haz, cluster(district)
>
> and I get the following result:
> Somers' D with variable: year
> Transformation: Untransformed
> Valid observations: 627
> Number of clusters: 4
>
> Symmetric 95% CI
>                                     (Std. Err. adjusted for 4 clusters in dist)
> ------------------------------------------------------------------------------
>                    |              Jackknife
>          year  |      Coef.          Std. Err.        z       P>|z|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>         haz06 |    .357832   .0434275     8.24   0.000     .2727157    .4429483
> -------------+----------------------------------------------------------------
>
> What I know is that the above result indicates that a randomly selected child in 2006 is 36% more likely to have a higher height z-score than a randomly selected child in 1996, than vice versa. But, what I do not know is how do I state this result in terms of stochastic dominance. Can I say that distribution of height z-scores in 2006 first order stochastically dominates the distribution of height z-scores in 1996? Alternatively, can I make any statement about stochastic dominance from the above result? If yes, what would it be?
>
> Monica Jain
>
>
>
> *
> *   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/
*
*   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/