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之间的依赖性，而似然的变分逼近则忽略参数分量之间的依赖性。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的复合对数似然函数的高斯变分逼近。我们证明了基于该逼近得到的估计量的一致性和渐近正态性，并通过一些模拟研究支持这一理论。该方法在计算上比针对完全对数似然函数的高斯变分逼近快得多。