CONNECTIONS - INSNA

CONNECTIONS
Configurations of Homophily
as the configuration having membership in the
outcome set (Y). In the present study, the
outcome is whether or not the configuration of
homophily occurred more often than expected by
chance. Configurations whose frequency exceeds
chance are in the outcome set; those that equal or
fall below chance rates are outside of the outcome
set. Only those elements of P(X) that have
membership in the outcome set are members of Y.
The outcome is recorded for each configuration,
resulting in a truth table that serves as the basis of
analysis (i.e., Table 1).
Arriving at a QCA solution takes place through a
systematic comparison of configurations that
exhibit the outcome. If two configurations with
the outcome differ on only one condition then that
condition is considered irrelevant and can be
dropped to produce a simpler expression. For
example, given two configurations “Age and Race
Homophily” and “Age Homophily” that both
exhibit the outcome (i.e., occur more often than
expected by chance), similarity on race is
irrelevant to the outcome. Dyads existed more
often than by chance if they were similar on age,
regardless of their similarity on race. Thus, the
simpler expression “Age Homophily” is an
implicant of “Age and Race Homophily” and
“Age Homophily” because both configurations
are contained within the set “Age Homophily.”
Comparisons between implicants can also be
made and conditions that are irrelevant can be
dropped. An implicant that cannot be simplified
through comparison with another implicant is a
prime implicant. The set of prime implicants for
the configurations with the outcome will contain
as a subset only those configurations that exhibit
the outcome. Thus, the set of prime implicants for
Y provides a simplified account of the
combinations of conditions where the outcome
exists. A QCA solution contains the combinations
of conditions that are associated with the outcome.
The Quine-McCluskey algorithm provides a
systematic means of comparing configurations
and implicants to reduce a truth table and is
incorporated within the fs/QCA software used for
this research (Ragin, Drass, & Davey, 2003).
The following analysis uses QCA procedures to
simplify the configurations of homophily that
exceed the baseline and produce a solution that
identifies the basis of inbreeding tendencies.
Using fs/QCA software (Ragin et al., 2003), a
crisp set analysis was performed to determine the
types of configurations with more dyads than
expected by chance. In the QCA models that
follow, the outcome is present when the frequency
of dyads in a given configuration exceeds the
baseline. To simplify presentation, solutions are
described as leading to the outcome or not, with
solutions leading to the outcome indicating more
dyads than expected by chance.
RESULTS
The results for models predicting relations of any
type are presented in Table 2. The QCA solution
can be interpreted as follows. The first column
includes the set of solution terms from which all
solutions are drawn. In each term, characteristics
are connected by logical “and” (represented by *).
Characteristics in uppercase letters refer to
similarity on a dimension while lowercase letters
refer to dissimilarity. The columns to the right
indicate which terms are contained in the solution
for each type of relationship (designated with a
“•”). The terms for each solution are connected
by logical “or.” Thus, the first solution (column
2) indicates that more dyads than expected by
chance existed when ego and alter had similar:
sex and race and religion, or
age and race and religion, or
race and education and religion, or
age and race and education, or
age and sex and education and religion
The strong effect of race homophily is evident in
the solution. All terms in the solution term,
include similarity on race except for the final
which includes similarity on every dimension
except for race. Religion is also quite strong in
that four of the terms include similarity on
religion. However, the number of dyads with just
similarity on race and religion did not exceed
chance. It was necessary to combine similarity on
race and religion with at least one other dimension
in order to produce inbreeding homophily.
This solution can be better understood by
examining the lattice in Figure 1. Because all
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