Generalized linear mixed-effects models (GLMMs) are widely used to analyze grouped and hierarchical data. In a GLMM, each response is assumed to follow an exponential-family distribution where the natural parameter is given by a linear function of observed covariates and a latent group-specific random effect. Since exact marginalization over the random effects is typically intractable, model parameters are estimated by maximizing an approximate marginal likelihood. In this paper, we replace the linear function with neural networks. The result is a more flexible model, the neural generalized mixed-effects model (NGMM), which captures complex relationships between covariates and responses. To fit NGMM to data, we introduce an efficient optimization procedure that maximizes the approximate marginal likelihood and is differentiable with respect to network parameters. We show that the approximation error of our objective decays at a Gaussian-tail rate in a user-chosen parameter. On synthetic data, NGMM improves over GLMMs when covariate-response relationships are nonlinear, and on real-world datasets it outperforms prior methods. Finally, we analyze a large dataset of student proficiency to demonstrate how NGMM can be extended to more complex latent-variable models.

翻译：广义线性混合效应模型（GLMM）被广泛用于分析分组与层次结构数据。在GLMM中，每个响应变量被假定服从指数族分布，其自然参数由观测协变量与潜在组别特异性随机效应的线性函数共同决定。由于对随机效应进行精确边际化通常难以实现，模型参数通过最大化近似边际似然进行估计。本文中，我们将线性函数替换为神经网络，从而得到更具灵活性的神经广义混合效应模型（NGMM），该模型能够捕捉协变量与响应间的复杂关系。为拟合NGMM，我们引入了一种高效的优化方法，该方法通过最大化近似边际似然实现，且关于网络参数可微。我们证明：在用户选择的参数下，目标函数的近似误差以高斯拖尾速率衰减。在合成数据上，当协变量-响应关系呈非线性时，NGMM相比GLMM表现出显著提升；而在真实数据集上，其性能优于既有方法。最后，我们分析了一个大规模学生能力数据集，展示如何将NGMM扩展到更复杂的潜变量模型。