This technical report works out details of approximate maximum likelihood estimation for aster models with random effects. Fixed and random effects are estimated by penalized log likelihood. Variance components are estimated by integrating out the random effects in the Laplace approximation of the complete data likelihood following Breslow and Clayton (1993), which can be done analytically, and maximizing the resulting approximate missing data likelihood. A further approximation treats the second derivative matrix of the cumulant function of the exponential family where it appears in the approximate missing data log likelihood as a constant (not a function of parameters). Then first and second derivatives of the approximate missing data log likelihood can be done analytically. Minus the second derivative matrix of the approximate missing data log likelihood is treated as approximate Fisher information and used to estimate standard errors.
Geyer, Charles J.; Ridley, Caroline E.; Latta, Robert G.; Etterson, Julie R.; Shaw, Ruth G..
Aster Models with Random Effects via Penalized Likelihood.
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