Closed form GLM cumulants and GLMM tting with a SQUAR-EM-LA 2 algorithm.
Vadim Zipunnikov, James G. Booth · 2011
We nd closed form expressions for the standardized cumulants of generalized linear models. This reduces the complexity of their calculation from O(p 6 ) to O(p 2 ) operations which allows ecient construction of second-order saddlepoint approximations to the pdf of sucient statistics. We adapt the result to obtain a closed form expression for the second-order Laplace approximation for a GLMM likelihood. Using this approximation, we develop a computationally highly ecient accelerated EM procedure, SQUAR-EM-LA 2. The procedure is illustrated by tting a GLMM to a well-known data set. Extensive simulations show the phenomenal performance of the approach. Matlab software is provided for implementing the proposed algorithm.