  Traditionally, the Dirichlet-multinomial distribution has been recognized as
a key model for contingency tables generated by cluster sampling schemes. There
are, however, other possible distributions appropriate for these contingency
tables. This paper introduces new test-statistics capable to test log-linear
modeling hypotheses with no distributional specification, when the individuals
of the clusters are possibly homogeneously correlated. The estimator for the
intracluster correlation coefficient proposed in Alonso-Revenga et al. (2016),
valid for different cluster sizes, plays a crucial role in the construction of
the goodness-of-fit test-statistic.
