e-journal
The Duality of Clusters and Statistical Interactions
We contend that clusters of cases co-constitute statistical interactions
among variables. Interactions among variables imply clusters of cases within
which statistical effects differ. Regression coefficients may be productively
viewed as sums across clusters of cases, and in this sense regression coefficients
may be said to be ‘‘composed’’ of clusters of cases. We explicate a
four-step procedure that discovers interaction effects based on clusters of
cases in the data matrix, hence aiding in inductive model specification. We
illustrate with two examples. One is a reanalysis of data from a published
study of the effect of social welfare policy extensiveness on poverty rates
across 15 countries. The second uses General Social Survey data to predict
four different dimensions of ego-network homophily. We find support for
our contention that clusters of the rows of a data matrix may be exploited
to discover statistical interactions among variables that improve model fit.
Keywords: duality, interaction identification, profile similarity, statistical interactions
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