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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.
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
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> 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 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
> website: www.andrew.cmu.edu/~krack
> Param Vir Singh wrote:
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>> 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 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
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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
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