Generating Multivariate Categorical Variates Using the Iterative Proportional Fitting Algorithm

Abstract

Two recent papers have suggested methods for generating correlated binary data with fixed marginal distributions and specified degrees of pairwise association. Emrich and Piedmonte suggested a method based on the existence of a multivariate normal distribution, while Lee suggested methods based on linear programming and Archimedian copulas. In this paper, a simpler method is described using the iterative proportional fitting algorithm for generating an n-dimensional distribution of correlated categorical data with specified margins of dimension 1, 2, …, k < n. An example of generating a distribution for a generalized estimating equations (GEE) model is discussed.

Key Words:

• Correlated outcomes
• Generalized estimating equations
• Log-linear models
• Random number generation