TMB让神经网络混合效应模型实现更简单，自动微分替代手动推导，提升模型复杂度和准确性。
研究人员提出使用模板模型构建器(TMB)实现神经网络混合效应模型(NMMs)的通用框架。该框架通过自动微分和拉普拉斯近似，仅需用户指定负联合对数似然和正则化项。TMB能自动积分随机效应并评估边际目标函数及其精确梯度，消除了手动推导的需求。研究通过两个数值示例展示了TMB-based NMMs的效率、灵活性和统计性能，包括单调NMMs的应用。
Implementing neural network mixed-effects models in Template Model Builder (TMB)
Neural network mixed-effects models (NMMs) have gained traction by combining the strong representation and predictive power of artificial neural networks with the capacity of mixed-effects modeling to capture complex correlation structures. However, existing estimation approaches rely heavily on manual derivations of objective functions and gradients, which inherently forces simplifying approximations and severely constrains the complexity and accuracy of NMMs. In this work, we introduce a general framework for implementing NMMs using Template Model Builder (TMB). By leveraging automatic differentiation and Laplace approximation, TMB requires users to specify only the negative joint log-likelihood and any regularization terms. The framework automatically integrates out random effects and evaluates the marginal objective function alongside its exact gradients, eliminating the need for manual derivations or ad hoc approximations. We demonstrate the efficiency, flexibility, and statistical performance of TMB-based NMMs across two numerical examples, including an application to monotonic NMMs. Reproducible code is provided to facilitate broader adoption.