New statistics to test log-linear modeling hypothesis with no distributional specifications and clusters with homogeneous correlation

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 statistics capable of testing log-linear modeling hypotheses with distributional unspecification, when the individuals of the clusters are possibly homogeneously correlated. An estimator for the intracluster correlation coefficient, valid for different cluster sizes, plays a crucial role in the construction of the goodness-of-fit test-statistics.