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Biometrika 1993 80(4):791-795; doi:10.1093/biomet/80.4.791
© 1993 by Biometrika Trust
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Laplace's approximation for nonlinear mixed models

RUSS WOLFINGER

SAS Institute Inc. SAS Campus Drive, Cary, North Carolina 27513, U. S. A.

An approximation to Laplace's method for integrals is applied to marginal distributions of data arising from models in which both fixed and random effects enter nonlinearly. The approach provides alternative derivations of some recent algorithms for fitting such models, and it has direct ties with Gaussian restricted maximum likelihood and the accompanying mixed model equations.

Key Words: First-order method • Generalized linear models • Modified profile likelihood • Random effects • Restricted maximum likelihood


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