Social Network Analysis
QAP Procedure
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 regression—or if the
data were a count, to use a negative
binomial, etc.)
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.
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).
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 they’ve 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.
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.
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.
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 correctly—a difficult challenge to
meet.
OLS and Network Analysis

In IR, it is common to address some of these
issues by clustering on one variable. But we
have two variables—rows and columns—that
need clustering.

In the QAP procedure for network analysis,
the standard errors are estimated using
permutations of the data set.
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 variable—and 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.
QAP (Quadratic Assignment
Procedure)

(Note that the QAP permutes the rows and
columns—but 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 / columns—but removing the relationship
between the dependent and independent variables.
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”.
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.
UCINET & QAP

And click ok.

The results?
UCINET & QAP
Unstandardized
Coefficient
Signif.
Intercept
8.920
Same Party
-.483
.275
Difference,
Ideology
-2.823
.000
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.
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”