Composite likelihood usually ignores dependencies among response components, while variational approximation to likelihood ignores dependencies among parameter components. We derive a Gaussian variational approximation to the composite log-likelihood function for Poisson and Gamma regression models with crossed random effects. We show consistency and asymptotic normality of the estimates derived from this approximation and support this theory with some simulation studies. The approach is computationally much faster than a Gaussian variational approximation to the full log-likelihood function.

翻译：复合似然通常忽略响应分量间的依赖关系，而对似然进行变分近似则忽略参数分量间的依赖关系。我们推导了针对具有交叉随机效应的泊松和伽马回归模型复合对数似然函数的高斯变分近似。证明由该近似得到的估计量具有一致性和渐近正态性，并通过仿真研究支持这一理论。该方法在计算速度上远快于对完整对数似然函数进行的高斯变分近似。