LISTSERV mailing list manager LISTSERV 16.0

Help for SOCNET Archives


SOCNET Archives

SOCNET Archives


SOCNET@LISTS.UFL.EDU


View:

Message:

[

First

|

Previous

|

Next

|

Last

]

By Topic:

[

First

|

Previous

|

Next

|

Last

]

By Author:

[

First

|

Previous

|

Next

|

Last

]

Font:

Proportional Font

LISTSERV Archives

LISTSERV Archives

SOCNET Home

SOCNET Home

SOCNET  March 2015

SOCNET March 2015

Subject:

Re: Centrality as the Dependent Variable?

From:

Philip Leifeld <[log in to unmask]>

Reply-To:

Philip Leifeld <[log in to unmask]>

Date:

Tue, 17 Mar 2015 11:14:12 +0100

Content-Type:

text/plain

Parts/Attachments:

Parts/Attachments

text/plain (136 lines)

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

Hi Elly,

The centrality values attached to the nodes are not independent from 
each other because a high centrality value of one node may imply a high 
centrality value of an adjacent node (see measures of degree 
assortativity etc.) -- or merely because the network has a given 
centralization and increasing the centrality of one node must decrease 
the centrality of another node.

If you estimate a regression model, you should therefore specify the 
channels of influence/dependence between the nodes as covariates. For 
example, for each node you can include the cumulated and/or average 
centrality of adjacent nodes (and possibly of indirect friends with path 
length 2). Depending on the centrality measure (e.g., eigenvector 
centrality), it may also make sense to include the aggregated centrality 
scores of structurally similar nodes because being connected to the same 
important other nodes makes both nodes in a dyad similarly important. 
There may be many other ways in which a node's centrality value depends 
on other nodes' values but also potentially just on features of the 
network or the local neighborhood of a node in the network.

Regression models where the dependencies are specified like this go by 
several names:

- If you estimate linear or generalized linear models and include only 
functions of direct neighbors, this is called a "spatial autocorrelation 
model" or a "network autocorrelation model". See the work of Patrick 
Doreian, for example. There is a nice article in Social Networks on 
"Specifying the weight matrix" for these models by Roger Leenders 
(http://dx.doi.org/10.1016/S0378-8733(01)00049-1). There is an R 
implementation for the linear case in the sna package by Carter Butts 
(the lnam function).

- If you include various other dependencies and estimate a binary (= 
logit or probit) model, this was termed "autologistic actor attribute 
model" (ALAAM) by Galina Daraganova and Garry Robins in their chapter 9 
of the ERGM book ("Exponential Random Graph Models for Social Networks") 
by Dean Lusher, Johan Koskinen and Garry Robins. I think there is an 
implementation in PNet or a related program, but others may know better 
than I do. This is kind of a special case of the network autocorrelation 
model but with additional dependencies.

- If you include only basic dependencies (= functions of direct 
neighbors and their attributes), this is called "multiparametric 
spatiotemporal autoregressive model" (m-STAR) in the spatial 
econometrics literature (see an article of Jude Hays, Aya Kachi and Rob 
Franzese here: http://dx.doi.org/10.1016/j.stamet.2009.11.005).

- Finally, I have created a generalized version of all of this. I call 
it "temporal network autocorrelation model" (TNAM) because it's a 
spatial *autocorrelation model* like the one specified above (see first 
bullet point), but it also includes various kinds of dependencies (hence 
the word *"network"*, see second bullet point), and it's possible to 
estimate it with *temporal* data/repeated observations of the network 
and/or the outcome variable (see bullet point 3). More generally, you 
can plug it into any model you would like, including tobit, survival, 
linear mixed models etc. I have implemented this in the tnam function in 
my R package xergm, along with a number of dependency terms to include. 
See here (http://rpackages.ianhowson.com/rforge/xergm/man/tnam.html) and 
here (http://rpackages.ianhowson.com/rforge/xergm/man/tnam-terms.html) 
for a description. A paper will be available in a few weeks.

There are three potential caveats here:

(1) It may be difficult to specify the dependencies appropriately if the 
attributes you are explaining are centralities. It may require you to 
think hard about what is causing them and to what extent you want them 
to be explained by network/influence terms vs. covariates, but I think 
technically it should be a subproblem of the more general models 
outlined above.

(2) A cross-sectional analysis does not really allow you to infer 
causality (this is tricky enough with longitudinal data). It's 
relatively certain that some of your independent variables/model terms 
will be partially caused by the centrality of the nodes.

And (3) centrality scores are usually fairly skewed and often also bound 
between 0 and 1, so it may be inappropriate to use a linear model. But 
this is a general statistical problem, not one that is specific to 
network analysis. You may want to consult the literature on beta 
regression, Box-Cox transformations etc. TNAM should be able to deal 
with this, but you have to find out what model (e.g., GLM with a beta 
distribution) would be appropriate for your data.

As an alternative, you may want to consider modeling the network using 
an exponential random graph model, rather than modeling centrality 
scores, which are merely a function of the network with a huge loss of 
information. By explaining the network, you basically explain the 
structure including who is central.

Best regards

Philip

Am 17.03.2015 um 02:16 schrieb Elly Power:
> ***** To join INSNA, visit http://www.insna.org *****
> Hello all,
>
> I was hoping I could get some advice on how (or if) I could use
> centrality measures (e.g., eigenvector centrality) as the /dependent/
> variable in some analyses.
>
> I know that we usually think of centrality as an independent variable,
> but it seems reasonable that we might want to predict centrality.
> Personally, I work on religious practice, and I want to understand if
> the nature of someone's religious practice might influence his/her
> centrality.
>
> The issue, of course, is that centrality measures are not independent.
> Does anyone know of any ways to deal with this? Is there anyone who has
> tried to look at this? Any direction would be very much appreciated.
>
> Thanks in advance for all of your suggestions.
>
> - Elly Power
>
> --
> Eleanor A. Power, PhD Candidate
> Department of Anthropology
> Stanford University
> 450 Serra Mall, Bldg 50
> Stanford, CA 94305
> www.stanford.edu/~epower <http://www.stanford.edu/%7Eepower>
> _____________________________________________________________________
> 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.

_____________________________________________________________________
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.

Top of Message | Previous Page | Permalink

Advanced Options


Options

Log In

Log In

Get Password

Get Password


Search Archives

Search Archives


Subscribe or Unsubscribe

Subscribe or Unsubscribe


Archives

August 2019
July 2019
June 2019
May 2019
April 2019
March 2019
February 2019
January 2019
December 2018
November 2018
October 2018
September 2018
August 2018
July 2018
June 2018
May 2018
April 2018
March 2018
February 2018
January 2018
December 2017
November 2017
October 2017
September 2017
August 2017
July 2017
June 2017
May 2017
April 2017
March 2017
February 2017
January 2017
December 2016
November 2016
October 2016
September 2016
August 2016
July 2016
June 2016
May 2016
April 2016
March 2016
February 2016
January 2016
December 2015
November 2015
October 2015
September 2015
August 2015
July 2015
June 2015
May 2015
April 2015
March 2015
February 2015
January 2015
December 2014
November 2014
October 2014
September 2014
August 2014
July 2014
June 2014
May 2014
April 2014
March 2014
February 2014
January 2014
December 2013
November 2013
October 2013
September 2013
August 2013
July 2013
June 2013
May 2013
April 2013
March 2013
February 2013
January 2013
December 2012
November 2012
October 2012
September 2012
August 2012
July 2012
June 2012
May 2012
April 2012
March 2012
February 2012
January 2012
December 2011
November 2011
October 2011
September 2011
August 2011
July 2011
June 2011
May 2011
April 2011
March 2011
February 2011
January 2011
December 2010
November 2010
October 2010
September 2010
August 2010
July 2010
June 2010
May 2010
April 2010
March 2010
February 2010
January 2010
December 2009
November 2009
October 2009
September 2009
August 2009
July 2009
June 2009
May 2009
April 2009
March 2009
February 2009
January 2009
December 2008
November 2008
October 2008
September 2008
August 2008
July 2008, Week 62
July 2008
June 2008
May 2008
April 2008
March 2008
February 2008
January 2008
December 2007
November 2007
October 2007
September 2007
August 2007
July 2007
June 2007
May 2007
April 2007
March 2007
February 2007
January 2007
December 2006
November 2006
October 2006
September 2006
August 2006
July 2006
June 2006
May 2006
April 2006
March 2006
February 2006
January 2006
December 2005
November 2005
October 2005
September 2005
August 2005
July 2005
June 2005
May 2005
April 2005
March 2005
February 2005
January 2005
December 2004
November 2004
October 2004
September 2004
August 2004
July 2004
June 2004
May 2004
April 2004
March 2004
February 2004
January 2004
December 2003
November 2003
October 2003
September 2003
August 2003
July 2003
June 2003
May 2003
April 2003
March 2003
February 2003
January 2003
December 2002
November 2002
October 2002
September 2002
August 2002
July 2002
June 2002
May 2002
April 2002
March 2002
February 2002
January 2002
December 2001
November 2001
October 2001
September 2001
August 2001
July 2001
June 2001
May 2001

ATOM RSS1 RSS2



LISTS.UFL.EDU

CataList Email List Search Powered by the LISTSERV Email List Manager