Another Look at the Salamander Mating Data: A Modified Laplace Approximation Approach

Abstract

The salamander mating dataset of McCullagh and Nelder has drawn the attention of statisticians because of its challenging structure: the design is crossed rather than nested. The standard Laplace approximation used to evaluate marginal likelihood functions fails in this case because the dimension of the integral is the square root of the sample size. A modification has been proposed by Shun and McCullagh. This article reanalyzes the salamander data using this modified Laplace approximation and focuses on the asymptotic order and computation of the score function.

Key Words:

• Asymptotic approximation
• Exchangeable arrays
• Generalized linear mixed models
• High-dimensional integrals