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Hi Roy,

I think that Nate pretty much answered your question (however, to eco his remarks, I am not sure I understood you correctly). I thought I might give it a go and try to elaborate on the Siena part. I don't know if this is of general interest or if I am doing this issue justice.

If you are interested in looking at the degree centrality and betweenness of individuals, maybe you might want to control for the type of endogeneity we expect to see in tie-creation over time, such as reciprocation and transitivity. That is if you have both senders and receivers of ties in your network (and not merely an aggregate for independently observed individuals, in which case these endogeneities will go unexplained). There is limited scope for taking the dependencies between individuals into account using multilevel models as the phenomenon - measures such as geodesic distance and centrality - you want to explain is an aggregate of these ties. You could model the dyads or the ties over time using multilevel models and to take some of the dependencies into account by having ties cross-classified by the individuals pertaining to the ties ({i,j} is cross-classified by  i and j ). This would not give you what you want though, as it is a model for ties, and you might in that case be better off using a stochastic actor-oriented model (read: Siena)

A number of aggregate network measures have approximate Siena-equivalents - centralisation may be captured by e.g. in-degree popularity, connectivity by actors at distance 2, etc - and to detect trends over time you can as Nate pointed out interact these effects in siena with time-dummies. If you'd like these trends on the level of the individuals you could in principle also include dummies for the individuals (which would be a sort of fixed effect). The drawbacks of this way of couching the aggregate evolution in terms of the actor-oriented model are 3 (at least):
- very soon you would end up with rather a large number of parameters (only time-dummies might be fine though).
- the model is actor-oriented which limits the extent to which you can "model" global properties of the network (we would hesitate to assume that an actor creates a tie in order to maximise some global property of the network such as connectedness)
- it may not be straightforward at this point in time to specify arbitrary functional forms for how parameters change over time (but it would be great to have it though)

The extent to which the available Siena effects may correspond to the aggregate measures you are after, it may still be an idea to try a Siena model. Maybe changes in centrality and such may be explained by a process driven by degree - actors start out with few ties and then they create ties until they feel that they have sufficiently many? Maybe some actors become popular (have more in-ties than others)  and by the virtue of being popular they get more popular (i.e. more ties)? The way to test this is to compare the global properties predicted by the model to those of the observed graphs (using Josh Lospinoso's GOF-procedures).

Going beyond comparing networks pair-wise over time (relating to your previous analysis), it might be worth keeping in mind that some of the centrality observed at one point in time may be an artefact of centrality at previous times. Additionally, only looking at, e.g. the centrality itself it might be difficult to to say whether no change in centrality is the result of no change in the network or whether there has been a lot of change in the network. A rought and ready analysis would be to permute ties across time as well as across individuals and use these permutation distributions as null distributions. I can't say that I would be a hundred percent sure what you would reject that way.

Personally I think it is great to try different approaches to describing network evolution (there is no Siena or Ora inquisition as far as I know) but if you really want to have a valid *test* for the evolution of aggregate measures it seems hard to do this without, as you say, taking on another analysis plan. 

I am not sure if this was of any use but hope that it was a little bit helpful (and not so long and tedious).

j.


On 16 Nov 2011, at 08:55, Tom Snijders wrote:

> *****  To join INSNA, visit http://www.insna.org  *****
> 
> Dear all,
> 
> Nate is right: the Siena model has the aim to find out what determines tie formation & termination, and not in the first place to express the shape of the curves followed by network descriptives over time.
> 
> Best,
> 
> Tom
> 
> -- 
> ==============================================
> Tom A.B. Snijders
> Professor of Statistics in the Social Sciences
> Nuffield College
> University of Oxford
> 
> Professor of Statistics and Methodology
> Department of Sociology
> University of Groningen
> http://www.stats.ox.ac.uk/~snijders/
> ==============================================
> 
> 
> 
> On 15/11/2011 21:00, Nate Doogan wrote:
>> ---------------------- Information from the mail header -----------------------
>> Sender:       Social Networks Discussion Forum<[log in to unmask]>
>> Poster:       Nate Doogan<[log in to unmask]>
>> Subject:      Re: longitudinal analysis of social network data - need help
>> -------------------------------------------------------------------------------
>> 
>> --20cf307ac3ef59aaf104b1cc48a4
>> Content-Type: text/plain; charset=ISO-8859-1
>> 
>> *****  To join INSNA, visit http://www.insna.org  *****
>> 
>> Hey Roy.
>> 
>> Personally, I did not precisely understand what you were hoping to model.
>> My response is contingent upon the accuracy with which I understood your
>> post. HLM might be nice if you were studying multiple groups within which
>> dependencies were expected. But you seem to have just one. Measurements
>> within each individual would make for a nice level-one, but you can't
>> assume that the individuals themselves (level 2) are independent
>> observations--you've captured information about the social network
>> connecting them, after all.
>> 
>> I will also provide my opinion that Joe's suggestion to use a squared
>> density term in a SIENA analysis would not quite model what you expect. The
>> SIENA density effect does not model the shape of density over time. You
>> would need to make use of time-dummies to capture such an effect, I believe.
>> 
>> Nathan Doogan
>> Doctoral Student
>> The Ohio State University
>> 
>> On Tue, Nov 15, 2011 at 3:36 PM, Money, Roy<[log in to unmask]>  wrote:
>> 
>>> *****  To join INSNA, visit http://www.insna.org  *****
>>> 
>>> Thanks to Joe and David and Kathleen for your responses.
>>> I will look into ORA and Siena as an alternative to HLM.
>>> I was hoping to hear from someone about why a multilevel model was not
>>> appropriate before taking on another analysis plan.
>>> Anyone have any thoughts on that?
>>> 
>>> Roy
>>> 
>>> 
>>> 
>>> 
>>> 
>>> 
>>> Hi Roy,
>>> 
>>> I suppose you could run a SIENA model, include both the density parameter
>>> as you would normally do, and then add a square of the density parameter to
>>> test for the inverted-U shaped relationship you're expecting.
>>> 
>>> Joe
>>> Giuseppe (Joe) Labianca
>>> Gatton Endowed Associate Professor of Management
>>> Gatton College of Business&  Economics
>>> LINKS Center for Social Network Analysis
>>> University of Kentucky
>>> Lexington, KY 40506
>>> 859-257-3741 (office)
>>> 404-428-4878 (mobile)
>>> http://linkscenter.org/
>>> 
>>> 
>>> 
>>> On Mon, Nov 14, 2011 at 1:37 PM, Money, Roy<[log in to unmask]<mailto:
>>> [log in to unmask]>>  wrote:
>>> *****  To join INSNA, visit http://www.insna.org  *****
>>> 
>>> I made a simiilar post to this list last month that garnered only one
>>> response so I am trying again.
>>> 
>>> I have 8 waves (at 6 month intervals) of social network data for a
>>> interdisciplinary  research consortium of  scientists where the degree
>>> centrality measure peaks at wave 4 (18 months), and the geodesic distance
>>> bottoms out at that time point.  It does seem like 18 months represents a
>>> maximum effect time for  the aggregate network data.
>>> 
>>> Previously I used UCINET to do bootstrapped t tests for particular
>>> pair-wise time comparisons but I want to characterize the longer trajectory
>>> and the apparent change in slope at 18 months.
>>> 
>>> I also have associated survey response data for which I have used a
>>>  discontinuous level-1 HLM individual growth model to test the hypothesis
>>> that the slope changes at  time 4 (18 months).
>>> 
>>> I would like to apply a similar analysis to the individual network
>>> measures of degree centrality and geodesic distance. However I have not
>>> found in my literature searches any references to the analysis of
>>>  longitudinal social network data like I am working with.
>>> 
>>> Is a multilevel or HLM analysis an appropriate method to test for
>>> quadratic or piecewise non linear change of the individual newtwork
>>> measures ?  If not, what would be optimal ways to evaluate this apparent
>>> maxing out of the connectivity of the social network about mid way through
>>> the consortium history?
>>> 
>>> Thanks for any suggestions or references.
>>> 
>>> Roy  Money
>>> 
>>> Yale University
>>> 
>> _____________________________________________________________________
>> SOCNET is a service of INSNA, the professional association for social
>> network researchers (http://www.insna.org). To unsubscribe, send
>> an email message to [log in to unmask] containing the line
>> UNSUBSCRIBE SOCNET in the body of the message.
>> 
>> --20cf307ac3ef59aaf104b1cc48a4
>> Content-Type: text/html; charset=ISO-8859-1
>> Content-Transfer-Encoding: quoted-printable
>> 
>> *****  To join INSNA, visit http://www.insna.org  *****
>> <div>Hey Roy.</div><div><br></div>Personally, I did not precisely understan=
>> d what you were hoping to model. My response is contingent upon the accurac=
>> y with which I understood your post. HLM might be nice if you were studying=
>>  multiple groups within which dependencies were expected. But you seem to h=
>> ave just one. Measurements within each individual would make for a nice lev=
>> el-one, but you can&#39;t assume that the individuals themselves (level 2) =
>> are independent observations--you&#39;ve captured information about the soc=
>> ial network connecting them, after all.<div>
>> 
>> <br></div><div>I will also provide my opinion that Joe&#39;s suggestion to =
>> use a squared density term in a SIENA analysis would not quite model what y=
>> ou expect. The SIENA density effect does not model the shape of density ove=
>> r time. You would need to make use of time-dummies to capture such an effec=
>> t, I believe.</div>
>> 
>> <div><br></div><div>Nathan Doogan</div><div>Doctoral Student</div><div>The =
>> Ohio State University<br><br><div class=3D"gmail_quote">On Tue, Nov 15, 201=
>> 1 at 3:36 PM, Money, Roy<span dir=3D"ltr">&lt;<a href=3D"mailto:roy.money@=
>> yale.edu">[log in to unmask]</a>&gt;</span>  wrote:<br>
>> 
>> <blockquote class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1p=
>> x #ccc solid;padding-left:1ex;"><div class=3D"im">***** =A0To join INSNA, v=
>> isit<a href=3D"http://www.insna.org" target=3D"_blank">http://www.insna.or=
>> g</a>  =A0*****<br>
>> 
>> 
>> <br>
>> </div>Thanks to Joe and David and Kathleen for your responses.<br>
>> I will look into ORA and Siena as an alternative to HLM.<br>
>> I was hoping to hear from someone about why a multilevel model was not appr=
>> opriate before taking on another analysis plan.<br>
>> Anyone have any thoughts on that?<br>
>> <br>
>> Roy<br>
>> <br>
>> <br>
>> <br>
>> <br>
>> <br>
>> <br>
>> Hi Roy,<br>
>> <br>
>> I suppose you could run a SIENA model, include both the density parameter a=
>> s you would normally do, and then add a square of the density parameter to =
>> test for the inverted-U shaped relationship you&#39;re expecting.<br>
>> <br>
>> Joe<br>
>> Giuseppe (Joe) Labianca<br>
>> Gatton Endowed Associate Professor of Management<br>
>> Gatton College of Business&amp; Economics<br>
>> LINKS Center for Social Network Analysis<br>
>> University of Kentucky<br>
>> Lexington, KY 40506<br>
>> <a href=3D"tel:859-257-3741" value=3D"+18592573741">859-257-3741</a>=A0(off=
>> ice)<br>
>> <a href=3D"tel:404-428-4878" value=3D"+14044284878">404-428-4878</a>=A0(mob=
>> ile)<br>
>> <a href=3D"http://linkscenter.org/" target=3D"_blank">http://linkscenter.or=
>> g/</a><br>
>> <div><div class=3D"adm"><div id=3D"q_133a906d61b395d4_2" class=3D"ajR h4"><=
>> div class=3D"ajT"></div></div></div><div class=3D"h5"><br>
>> <br>
>> <br>
>> On Mon, Nov 14, 2011 at 1:37 PM, Money, Roy&lt;<a href=3D"mailto:roy.money=
>> @yale.edu">[log in to unmask]</a>&lt;mailto:<a href=3D"mailto:roy.money@yal=
>> e.edu">[log in to unmask]</a>&gt;&gt; wrote:<br>
>> ***** =A0To join INSNA, visit<a href=3D"http://www.insna.org" target=3D"_b=
>> lank">http://www.insna.org</a>  =A0*****<br>
>> <br>
>> I made a simiilar post to this list last month that garnered only one respo=
>> nse so I am trying again.<br>
>> <br>
>> I have 8 waves (at 6 month intervals) of social network data for a interdis=
>> ciplinary =A0research consortium of =A0scientists where the degree centrali=
>> ty measure peaks at wave 4 (18 months), and the geodesic distance bottoms o=
>> ut at that time point. =A0It does seem like 18 months represents a maximum =
>> effect time for =A0the aggregate network data.<br>
>> 
>> 
>> <br>
>> Previously I used UCINET to do bootstrapped t tests for particular pair-wis=
>> e time comparisons but I want to characterize the longer trajectory and the=
>>  apparent change in slope at 18 months.<br>
>> <br>
>> I also have associated survey response data for which I have used a =A0disc=
>> ontinuous level-1 HLM individual growth model to test the hypothesis that t=
>> he slope changes at =A0time 4 (18 months).<br>
>> <br>
>> I would like to apply a similar analysis to the individual network measures=
>>  of degree centrality and geodesic distance. However I have not found in my=
>>  literature searches any references to the analysis of =A0longitudinal soci=
>> al network data like I am working with.<br>
>> 
>> 
>> <br>
>> Is a multilevel or HLM analysis an appropriate method to test for quadratic=
>>  or piecewise non linear change of the individual newtwork measures ? =A0If=
>>  not, what would be optimal ways to evaluate this apparent maxing out of th=
>> e connectivity of the social network about mid way through the consortium h=
>> istory?<br>
>> 
>> 
>> <br>
>> Thanks for any suggestions or references.<br>
>> <br>
>> Roy =A0Money<br>
>> <br>
>> Yale University<br>
>> <br>
>> _____________________________________________________________________<br>
>> _____________________________________________________________________
>> SOCNET is a service of INSNA, the professional association for social
>> network researchers (http://www.insna.org). To unsubscribe, send
>> an email message to [log in to unmask] containing the line
>> UNSUBSCRIBE SOCNET in the body of the message.
>> 
>> --20cf307ac3ef59aaf104b1cc48a4--
> 
> _____________________________________________________________________
> SOCNET is a service of INSNA, the professional association for social
> network researchers (http://www.insna.org). To unsubscribe, send
> an email message to [log in to unmask] containing the line
> UNSUBSCRIBE SOCNET in the body of the message.

Social Statistics Dicipline Area
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