Monthly seasonally adjusted temperatures above latitude 45 ∘ N were investigated from January 1973 to November 2013. The study area was divided into 69 sub-regions of similar size each in the shape of an igloo brick. The data were filtered with a second-order autoregressive process to remove autocorrelation. Two sub-regions did not have sufficient data due to substantial numbers of missing values. Factor analysis was then applied to the remaining 67 sub-regions and was used to classify regions with similar temperature changes. As a result, 63 sub-regions could be classified based on 12 factors but 4 sub-regions could not be grouped due to uniqueness. The temperatures for each group of sub-regions were found to increase dur-
Abstract. Maximum likelihood estimates in GLMM are often difficult to be obtained since the calculation involves high dimensional integrals. It is not easy to find analytical solutions for the integral so that the approximation approach is needed. In this paper, we discuss several approximation methods to solve high dimension integrals including the Laplace, Penalized Quasi likelihood (PQL) and Adaptive Gaussian Quadrature (AGQ) approximations. The performance of these methods was evaluated through simulation studies. The 'true' parameter in the simulation was set to be similar with parameter estimates obtained by analyzing a real data, particularly salamander data (McCullagh & Nelder, 1989). The simulation results showed that the Laplace approximation produced better estimates when compared to PQL and AGQ approximations in terms of their relative biases and mean square errors.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.