Social Network Analysis

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Social Network Analysis

• QAP Procedure

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OLS and Network Analysis

• A very simple approach to Network Analysis would
  be to use OLS (or, if the data were binary, to
  use logistic regressionor if the data were a
  count, to use a negative binomial, etc.)

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OLS and Network Analysis

• The basic idea would be that you would create a
  data set that had the dyad or pair (in the
  Arizona case, pair of legislators) as the unit of
  analysis.
• The independent variables would be either
  attributes of each of one or both members of the
  pairs, or of similarities and / or matches
  between the pairs.

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OLS and Network Analysis

• For example, in the case of the Arizona
  legislature, we would have a data set that might
  include each pair of legislators, a dummy
  variable for whether they were of the same party,
  a variable that indicated how close they were in
  terms of their ideology, a variable for the
  seniority of the first cosponsor (the column
  cosponsor), and a variable for the seniority of
  the second cosponsor (the row cosponsor).

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OLS and Network Analysis

• All could reasonably be expected to influence the
  likelihood of cosponsorship. More senior
  legislators may be relatively active in
  cosponsorship (since theyve had the time to
  build up relationships), and legislators who are
  ideologically similar and who are affiliated with
  the same political party may be relatively likely
  to cosponsor with each other.

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OLS and Network Analysis

• This approach is sometimes used in International
  Relations, in order to analyze the behavior of
  dyads (or pairs) of nations.
• However, there is a problem.

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OLS and Network Analysis

• The problem is that the observations are not
  independent on each other. If A cosponsors with
  B, and B cosponsors with C, it may be relatively
  likely that A cosponsors with C.
• Moreover, the fact that there are repeating
  observations means that the errors are correlated
  with each other. Observations in individual rows
  or in individual columns tend to be highly
  correlated, which inflates or deflates standard
  errors.

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OLS and Network Analysis

• We could employ a random effects model, which
  requires modeling and estimating the covariance
  matrix. But the validity of this depends on
  whether we have estimated the model correctlya
  difficult challenge to meet.

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OLS and Network Analysis

• In IR, it is common to address some of these
  issues by clustering on one variable. But we
  have two variablesrows and columnsthat need
  clustering.
• In the QAP procedure for network analysis, the
  standard errors are estimated using permutations
  of the data set.

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QAP (Quadratic Assignment Procedure)

• Essentially, what the QAP does is to scramble
  the dependent variable data through several
  permutations. By taking the data, and
  scrambling it repeatedly, resulting in multiple
  random datasets with the dependent variableand
  then multiple analyses can be performed.
• Those datasets and analyses form an empirical
  samping distribution, and we can compare our
  coefficient with this sampling distribution of
  coefficients from all the permuted datasets.

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QAP (Quadratic Assignment Procedure)

• (Note that the QAP permutes the rows and
  columnsbut for a single node, the row and column
  remain the same, and are permuted in the same
  way, so that the rows and columns for a single
  node are not separated.)
• Essentially, you are preserving the dependence
  within rows / columnsbut removing the
  relationship between the dependent and
  independent variables.

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UCINET QAP

• UCINET will allow you to run a QAP.
• Go to Tools, to Testing Hypotheses to
  Dyadic and to Regression (QAP). Choose
  Double Dekker Semi-Partialling MRQAP.

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UCINET QAP

• Enter in the name of the file with the dependent
  (cosponsorship variable)
• Enter in the name of the two files, one with the
  sameparty information, and one with the
  diffideol information.

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UCINET QAP

• And click ok.
• The results?

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UCINET QAP
Unstandardized Coefficient Signif.
Intercept 8.920
Same Party -.483 .275
Difference, Ideology -2.823 .000
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UCINET QAP

• Once we control for the difference in ideology
  which is substantially, significantly, and
  negatively related to cosponsorship we find
  that being of the same party is not a significant
  influence on cosponsorship.

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For more information...

• QAP the Quadratic Assignment Procedure
  (William Simpson, Harvard Business School, 2001).
• Decker, Krackhardt, Snijders, Sensitivity of
  MRQAP Tests to Collinearity and Autocorrelation
  Conditions