Empirical testing of competing theories lies at the heart of social
science research. We demonstrate that a well-known class of
statistical models, called finite mixture models, provides an
effective way of rival theory testing. In the proposed framework,
each observation is assumed to be generated either from a
statistical model implied by one of the competing theories or more
generally from a weighted combination of multiple statistical models
under consideration. Researchers can then estimate the probability
that a specific observation is consistent with each rival theory.
By modeling this probability with covariates, one can also explore
the conditions under which a particular theory applies. We discuss
a principled way to identify a list of observations that are
statistically significantly consistent with each theory, and
propose measures of the overall performance of each competing
theory. We illustrate the relative advantages of our method over
existing methods through empirical and simulation studies.