Maximum likelihood for generalized linear models with nested random effects via high-order, multivariate Laplace approximation
Maximum likelihood for generalized linear models with nested random effects via high-order, multivariate Laplace approximation
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DOI：
10.2307/1390617
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发表时间：
2000-03-01
影响因子：
2.4
通讯作者：
Yosef, M
中科院分区：
文献类型：
--
作者：
Raudenbush, SW;Yang, ML;Yosef, M
Nested random effects models are often used to represent similar processes occurring in each of many clusters. Suppose that, given cluster-specific random effects b, the data y are distributed according to f(y\b, theta), while b follows a density p(b\theta). Likelihood inference requires maximization of integral f(y\b, theta)p(b\theta)db with respect to theta. Evaluation of this integral often proves difficult, making likelihood inference difficult to obtain. We propose a multivariate Taylor series approximation of the log of the integrand that can be made as accurate as desired if the integrand and all its partial derivatives with respect to b are continuous in the neighborhood of the posterior mode of b\theta, y. We then apply a Laplace approximation to the integral and maximize the approximate integrated likelihood via Fisher scoring. We develop computational formulas that implement this approach for two-level generalized linear models with canonical link and multivariate normal random effects. A comparison with approximations based on penalized quasi-likelihood, Gauss-Hermite quadrature, and adaptive Gauss-Hermite quadrature reveals that, for the hierarchical logistic regression model under the simulated conditions, the sixth-order Laplace approach is remarkably accurate and computationally fast.
