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Re: st: Nested design problem


From   Marcello Pagano <pagano@hsph.harvard.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   Re: st: Nested design problem
Date   Fri, 16 Nov 2012 07:51:02 -0500

You might want to look at the geo-spatial literature; you have a distance matrix between individuals where some of the distances may be infinite.

m.p.

On 11/16/2012 7:32 AM, Steven Raemaekers wrote:
Hello David,

Thanks for your response! You can view the connections between people as a directed graph, with arbitrary arrows between people when they have a connection.
There is not a value for each possible pair of people, a lot of connections are missing and are then considered irrelevant, but I'm only interested in the subjects which have connections to other people so this should not be a problem.

Maybe it is indeed an analysis problem because I have already collected the data and I already know my research question. Then the question becomes more how to choose a statistical model that does most justice to reality.

Regards,

Steven

On 16 nov. 2012, at 13:13, David Hoaglin wrote:

Hi, Steven.

The problem you describe is interesting.  I don't recall seeing
anything like it in the statistical literature.  I view it as an
analysis problem, rather than a design problem (you have already
collected the data).  Some of the work in sociology on networks may be
relevant.

I think it would be more appropriate to consider closeness as the
dependent variable.

Do you have a value of closeness for each of the possible pairs of
people?  If not, what is the structure of the subset of people for
whom you do have closeness?

David Hoaglin

On Thu, Nov 15, 2012 at 4:44 PM, Steven Raemaekers <s.raemaekers@sig.eu> wrote:
Hello,

I do not know where else to post this problem so I hope somebody can help me here. I have a statistical design issue which is as follows.
As an example, let's say I have a table with information on people in the following format:

Id                      IQ              Introvertness           …
person1         120             80                              …
person2         110             70                              …
person3         130             40                              …

This table contains a number of properties of certain persons, each person is a unique entry in this table. I also have a table which contains relationships between those persons:

Id1             Id2             Closeness
person1 person2 80
person1 person3 70

"Closeness" is a property of the relationship between person1 and person2. The numbers do not make sense but are just for illustration.

Now I want to test whether people that are in relationships "closer" to each other are more intelligent. I also possibly want to take into account other properties of people.
In regression terms: I want to regress the dependent variable IQ on the independent variable closeness and introvertness. How can I do this?

The problem is, persons can appear multiple time in the list so applying normal linear regression or correlation on this table produces incorrect results.
Additionally, there are two sides to the relationship, so there is a connection between the IQ of person1, the closeness of their relationship and the IQ of person2.
I believe the thing I need is called a nested hierarchical model/mixed model, but I have no idea how to design this.

My questions are therefore the following:
1) What statistical test do I need to test my hypothesis on this data?
2) What assumptions does this test make and how can I check these assumptions?
3) How should I format my data?
4) What are the commands in Stata to execute this test?

Thanks very much!

Regards,

Steven Raemaekers
PhD student
Software Improvement Group/TU Delft
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