A comparison of the numerical properties of EI methods

Abstract

The numerical accuracy of commonly used statistical software packages has been evaluated recently by a number of authors. A primary concern among them is that different embedded numerical methods produce vastly different solutions from the same data and model. In previous work we examined the sensitivity of King's EI procedure to implementation versions, computing platforms, random number generators, and optimization options. In this chapter, we extend that work with a comparison of the numerical properties of King's EI with other solutions to the EI problem. We analyze the performance of these separate approaches to the ecological inference problem, using data perturbation and comparative reliability assessment. The data perturbation technique is used to evaluate the pseudostability of these competing techniques across identical data sets. The results that we provide illuminate the trade-offs among correctness, complexity, and numerical sensitivity. INTRODUCTION The numerical accuracy of commonly used statistical software packages has been evaluated recently by a number of concerned authors (McCullough and Vinod, 1999; McCullough 1998, 1999a, 1999b; Altman and McDonald, 2001; Altman, Gill, and McDonald, 2003). The primary concern among these authors is that different embedded numerical methods actually produce vastly different solutions from the same data and model. Clearly this is alarming.