Penalized quasi-likelihood with spatially correlated data

This article discusses and evaluates penalized quasi-likelihood (PQL) estimation techniques for the situation where random effects are correlated, as is typical in mapping studies. This is an approximate fitting technique which uses a Laplace approximation to the integrated mixed model likelihood. It is much easier to implement than usual maximum likelihood estimation. Our results show that the PQL estimates are reasonably unbiased for analysis of mixed Poisson models when there is correlation in the random effects, except when the means are sufficiently small to yield sparse data. However, although the normal approximation to the distribution of the parameter estimates works fairly well for the parameters in the mean it does not perform as well for the variance components. In addition, when the mean mortality counts are small, the estimated standard errors of the variance components tend to become more biased than those for the mean. We illustrate our approaches by applying PQL for mapping mortality in British Columbia, Canada, over the five-year period 1985-1989. (C) 2002 Elsevier B.V. All rights reserved.