Incorporating Dependence Boundaries in Simulating Associated Discrete Data

In the study of associated discrete variables, limitations on the range of the possible association measures (Pearson correlation, odds ratio, etc.) arise from the form of the joint probability function between the variables. These limitations are known as the Fréchet bounds. The bounds for cases involving associated binary variables are explored in the context of simulating datasets with a desired correlation and set of marginal probabilities. A new method for creating such datasets is compared to an existing method that uses the multivariate probit. A method for simulating associated binary variables using a desired odds ratio and known marginal probabilities is also presented. The Fréchet bounds for correlation between dependent binomial and negative binomial variables are determined as families of ranges in various cases. An example of a realistic analysis involving the Fréchet bounds in a dependent binomial setting is presented