# Re: st: lincom & svy commands

 From Steven Samuels To statalist@hsphsun2.harvard.edu Subject Re: st: lincom & svy commands Date Thu, 23 Oct 2008 16:01:25 -0400

Stas has provided a detailed discussion, and Maarten has already shown you the formula that -lincom- uses. If you do not understand the relationship between -lincom- (a t-test) and the regression approaches that Stas presented, consult the text for any graduate statistics course which includes regression. I will answer your second question.
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Alternative ii will be more precise in your example. Analyses with clustered data (from surveys or not) should never ignore the clustering.
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When you examine difference within the same cluster, each cluster serves "as its own control". Here is a simple example with 4 clusters. Assume that the number of observations within cluster is equal.
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Cluster	  Before-Mean	After-Mean   difference
1           5              4          1
2          10              8          2
3          15              11         4
4          20              16         4

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The differences are much less variable (range = 4) then the original observations (ranges = 15, 12).
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What are the consequences? If you apply your option i, then: n= 8, and the before-after difference is 2.75, with a SE = 4.10 and the two-sample t-test has p = .52
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If you treat the data as clustered (option ii), the before/after difference is still 2.75 with n=4 clusters, but, the se = 0.75 and the one-sample paired t-test has p= 0.03
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Now, this is just an ordinary paired t-test example utilizing the cluster means as responses. Stata's survey programs account for unequal sample-sizes within cluster and occasion. You ask for what - lincom- (or the regression equivalents) "actually" do. The equations are a bit complicated and depend on the choice of variance estimate (linearization, jackknife, bootstrap, balanced-repeated- replications). You can view generalized versions of the equations in the Stata survey manual or in any book on survey sampling. Take a look, for example, at Sharon Lohr, Sampling: Design and Analysis. Duxbury, 1999, Chapter 9. However, the logic with before/after data is the same.
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-Steve

On Oct 23, 2008, at 11:18 AM, Bell, Jacqueline S. wrote:

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```Hi

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This is a follow-on to a previous message I sent this month asking about how lincom calculates standard errors when clustering is present.
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Can anyone advise me on what lincom actually does when estimating differences in parameters from svy:mean or svy:prop?
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I have before/after data which is not paired at an individual level, but has a cluster structure. In these circumstances it is not obvious how lincom goes about estimating the before/after difference.
```The two alternatives suggested to me are:
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i) it estimates before and after separately for the whole population, then estimates the difference ii)it estimates the difference in each cluster, and then the overall difference.
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In the data there are (in most cases) before and after data for each cluster, but often quite severe imbalances in samples before/ after within cluster.
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Thanks for any help, Jacqui

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