mipfp: An R Package for Multidimensional Array Fitting and Simulating Multivariate Bernoulli Distributions

This paper explains the mipfp package for R with the core functionality of updating an d-dimensional array with respect to given target marginal distributions, which in turn can be multi-dimensional. The implemented methods include the iterative proportional fitting procedure (IPFP), the maximum likelihood method, the minimum chi-square and least squares procedures. The package also provides an application of the IPFP to simulate data from a multivariate Bernoulli distribution. The functionalities of the package are illustrated through two practical examples: the update of a 3-dimensional contingency table to match the targets for a synthetic population and the estimation and simulation of the joint distribution of the binary attribute impaired pulmonary function as used by Qaqish, Zink, and Preisser (2012)

Mantel-Haenszel Estimators of Odds Ratios for Stratified Dependent Binomial Data

A standard approach to analyzing n binary matched pairs being usually represented in n 2 x 2 tables is to apply a subject-specifi c model; for the simplest situation it is the so-called Rasch Model. An alternative population-averaged approach is to apply a marginal model to the single 2 x 2 table formed by n subjects. For the situation of having an additional strati cation variable with K levels forming K 2 x 2 tables, standard fitting approaches, such as generalized estimating equations and maximum likelihood, or alternatively the standard Mantel-Haenszel (MH) estimator can be applied. However, while all these standard approaches are consistent under a large stratum limiting model, they are not consistent under a sparse-data limiting model. In this paper, we propose a new MH estimator along with a variance estimator that are both dually consistent; consistent under large stratum and under sparse data limiting situations. In a simulation study the properties of the proposed estimators are confi rmed and the estimator is compared with standard marginal methods, and also with subject-specifi c estimators. The simulation study also considers the case when the homogeneity assumption of the odds ratios does not hold and the asymptotic limit of the proposed MH estimator under this situation is derived. The results show that the proposed MH estimator is generally better than the standard estimator, and the same can be said about the associated Wald-type con fidence intervals