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SOCNET  May 2008

SOCNET May 2008

Subject:

FW: Comparison of QAP and ERGMs

From:

Garry Robins <[log in to unmask]>

Reply-To:

Garry Robins <[log in to unmask]>

Date:

Fri, 30 May 2008 09:06:30 +1000

Content-Type:

text/plain

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text/plain (201 lines)

*****  To join INSNA, visit http://www.insna.org  *****

Dear Param, David, Tom and others,
 
Pattison and Wasserman (1999) was the first paper to present models for multivariate (i.e. multiple network) ergms, permitting examination of associations between networks while controlling for structure within networks. That was in the days of Markov models and pseudolikelihood estimation, so we have moved on from that point in terms of certain very important details. But nevertheless the fundamental idea stands, that multiple networks may associate in different ways and that it is possible to construct models that examine in some detail the types of associations between networks. Lazega and Pattison (1999) and Lomi and Pattison (2006) present applications within this tradition of work.
 
QAP provides a very convenient test for whether there is an association between networks. (As noted by Tom and David, MRQAP extends this in important ways.) If this answers the research question, then QAP is fine. QAP is largely silent however about the particular form of an association.  For instance, in directed examples, one network relationship may be entailed by another (ie the different types of ties may tend to be aligned) or one network relation may tend to be reciprocated (or "exchanged") by the other. Both are forms of association between networks but it is not clear to me that a QAP test can give you the level of detail to identify these differences, if that is what you are interested in.  It is also possible that associations may occur not just at dyadic but also at triadic level - and structural balance theory is a good example if you take positive and negative ties as two different types of relations.
 
Moreover, it may be that putative associations between networks may in part be explained by structure within networks. For instance, suppose that it seems that two relations occur together in triads in a balance type way. But maybe they tend to be entrained at the dyadic level and there are also tendencies for the two networks separately to form triangles. In that case, it is quite possible that what seems to be balance type effects within multivariate triangles are explained by the across-network dyadic association and the within-network triangulation tendencies, and there is no need to postulate a specific balance process. QAP cannot give you insight into this type of detail, whereas a properly formalised ergm may.  In our recent work we have been using models for bivariate network data that use the new ergm (social circuit) specifications of Snijders et al (2006) for within-network effects, and at least dyadic entrainment and exchange for across network associations. Sometimes we use higher order triangulated network effects across networks, if they seem helpful.  We have found examples where QAP shows a positive significant association and the ergm entrainment parameter is positive and significant. That agreement is reassuring. But we have also found at least one example where the ergm entrainment and exchange parameters are significant but of opposite signs (ie working in opposite directions), so that there are very complex associations between the two networks, whereas the QAP produces a non-significant result.  These results have been presented by Yu Zhao at a couple of recent sunbelts.
 
My suggestion is that if you are not interested in this level of structural detail then a significant QAP test may be quite OK for your research purposes. If you want to determine the type of association, however, then the ergm approach might be relevant. If you do go down the ergm route, of course it is not so straightforward and there are no guarantees that you will get neatly convergent models or conveniently simple explanations. For those who want to enter these relatively uncharted waters, for bivariate network data the program XPnet on our Melnet website will permit maximum likelihood estimation for models with social circuit parameters within networks and dyadic association parameters (and some higher order triangulation parameters) between networks.
 
best
 
 
Garry
 
 
Dr Garry Robins
Associate Professor and Reader
School of Behavioural Science
University of Melbourne
Australia.
 
Telephone: 61 3 8344 4454
 
Website: http://www.psych.unimelb.edu.au/people/staff/RobinsG.html <http://www.psych.unimelb.edu.au/people/staff/RobinsG.html> 
Melnet website: http://www.sna.unimelb.edu.au/ <http://www.sna.unimelb.edu.au/> 
 

________________________________

From: Social Networks Discussion Forum on behalf of Tom Snijders
Sent: Thu 29-May-08 3:59 AM
To: [log in to unmask]
Subject: Re: Comparison of QAP and ERGMs



*****  To join INSNA, visit http://www.insna.org <http://www.insna.org/>   *****

Dear Param, David, and others,

I would like to add a bit, focusing on the fact that MRQAP and ERGM are
designed to answer different questions. These questions overlap, and for
the overlap David's remarks are very appropriate.

The MRQAP is meant to answer questions about associations between
variables on a dyadic or pairwise basis: we have two one-mode, square
matrices with entries X(i,j) and Y(i,j) (and perhaps confounders Z(i,j))
and we wish to answer the question whether there is an association
between X(i,j) and Y(i,j) on a dyadic basis; usually represented by a
linear regression model of Y(i,j) on X(i,j) (and perhaps Z(i,j)) where
the cells (i,j) of the matrix are the cases, and where the dependence
generated by the network structure is taken into account ("controlled
for"). When David writes about the cases where MRQAP might or might not
"work", I understand this as the question whether this control is adequate.

On the other hand, ERGMs are meant to model networks Y (represented by
the same square matrix with entries Y(i,j)) as a whole, considering
dependences between different tie variables (such as how Y(i,j) depends
on Y(j,i) but also on Y(i,k) and Y(k,j) jointly for all k, relevant for
triadic closure) as well as dependencies of tie variables Y(i,j) on
other ('exogenous') variables X(i,j) and Z(i,j).

In other words, if you wish to model structural dependencies within a
network, then ERGM is an option and MRQAP is not. If you are interested
in modeling dependencies between relational variables, controlling for
network structure, then ERGM as well as MRQAP are options, and David's
considerations below are good guidelines.

Best wishes,

Tom

David Krackhardt wrote:
> ---------------------- Information from the mail header -----------------------
> Sender:       Social Networks Discussion Forum <[log in to unmask]>
> Poster:       David Krackhardt <[log in to unmask]>
> Subject:      Re: Comparison of QAP and ERGMs
> -------------------------------------------------------------------------------
>
> *****  To join INSNA, visit http://www.insna.org <http://www.insna.org/>   *****
>
> Param, good question.  And, I will add that I think there is not a
> consensus on an appropriate answer.  But, OK, I'll take a shot anyway.
>
> QAP was designed as a bivariate test (only two variables).  Generally,
> QAP is perfectly fine for almost any bivariate network problem.  ERGM or
> P* is really a multivariate procedure (if you consider all the terms
> that one usually includes in any ERGM analysis). Once you get into
> multiple independent variables, you are comparing ERGM to MRQAP
> (multiple regression quadratic assignment procedure), which is a bit
> more complicated.
>
> But, for multivariate cases, the quick and dirty answer is: If your
> dependent variable is continous or count data (like in a negative
> binomial case), MRQAP is best.  If your dependent variable is binary,
> ERGM (P*) is best. 
>
> The truth is, though, it is really not that simple.  One can perform
> ERGM models on continuous dependent data (although I don't think this is
> implemented in Statnet as of yet).  And, one can perform MRQAP on data
> that have a dichotomous dependent variable (basically,  this is
> equivalent to using a linear probability model).  The advantages and
> disadvantages of each are being actively explored as we speak, and I
> would hesitate to predict how all the constraints will play out.  To
> this day, I am still surprised by cases where I thought MRQAP would work
> (or wouldn't work) and I am led to conclude the opposite through a set
> of carefully conducted monte carlo simulations.
>
> My personal experience is that both approaches "work" (provide
> reasonably unbiased tests) in many commonly found data sets.  David
> Dekker and I presented a paper last Sunbelt in which we argued (again,
> with simulations) that the safe thing to do is simulate your own data
> conditions and test the test you want to use to make sure it is
> reasonably unbiased.  But, I will admit this is asking a lot of the
> researcher and may not be practical in many cases.
>
> Finally, I will say that given you are at the University of Washington,
> you have one of the best concentrations of ERGM resources that exists
> anywhere.  I would ask Mark Handcock or Martina Morris if I were there.
>
> -David
>
> ------------------
> David Krackhardt, Professor of Organizations, Executive Editor of JoSS
> Heinz School of Public Policy and Management, and
>       The Tepper School of Business
> Carnegie Mellon University
> Pittsburgh, PA 15213
> 412-268-4758
> website: www.andrew.cmu.edu/~krack
>     (Erdos#=2)
>
>
>
> Param Vir Singh wrote:
>> *****  To join INSNA, visit http://www.insna.org <http://www.insna.org/>   *****
>>
>> Dear Socnetters,
>> I am trying to understand when one should use QAP (Quadratic Assignment
>> Problem) or ERGM (exponential random graph models) for explaining the
>> network structure. Is there any reference which explains the advantages of
>> one over the other?
>> 
>> Thanks in Advance,
>> Param   
>> 
>>
>> --------------------------------------------
>> Param Vir Singh
>> Doctoral Candidate (PhC)
>> Information Systems
>> Michael G Foster School of Business
>> University of Washington, Seattle
>> Phone: (206)-685-6419 Fax:(206)-543-3968
>>  <http://students.washington.edu/psidhu>
>> http://students.washington.edu/psidhu
>>
>> 
>>
>> _____________________________________________________________________
>> SOCNET is a service of INSNA, the professional association for social
>> network researchers (http://www.insna.org <http://www.insna.org/> ). To unsubscribe, send
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>> UNSUBSCRIBE SOCNET in the body of the message.
>>
>>  
>
> _____________________________________________________________________
> SOCNET is a service of INSNA, the professional association for social
> network researchers (http://www.insna.org <http://www.insna.org/> ). To unsubscribe, send
> an email message to [log in to unmask] containing the line
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--
==============================================
Tom A.B. Snijders
Professor of Statistics in the Social Sciences
University of Oxford

Professor of Statistics and Methodology
Department of Sociology
University of Groningen
http://stat.gamma.rug.nl/snijders/
==============================================

_____________________________________________________________________
SOCNET is a service of INSNA, the professional association for social
network researchers (http://www.insna.org <http://www.insna.org/> ). To unsubscribe, send
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_____________________________________________________________________
SOCNET is a service of INSNA, the professional association for social
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