We propose two methods to evaluate the conditional Akaike information (cAI) for nonlinear mixed-effects models with no restriction on cluster size. Method 1 is designed for continuous data and includes formulae for the derivatives of fixed and random effects estimators with respect to observations. Method 2, compatible with any type of observation, requires modeling the marginal (or prior) distribution of random effects as a multivariate normal distribution. Simulations show that Method 1 performs well with Gaussian data but struggles with skewed continuous distributions, whereas Method 2 consistently performs well across various distributions, including normal, gamma, negative binomial, and Tweedie, with flexible link functions. Based on our findings, we recommend Method 2 as a distributionally robust cAI criterion for model selection in nonlinear mixed-effects models.

翻译：本文提出了两种评估非线性混合效应模型条件赤池信息（cAI）的方法，对聚类规模无限制。方法1适用于连续数据，包含了固定效应和随机效应估计量对观测值导数的计算公式。方法2兼容任意观测类型，要求将随机效应的边际（或先验）分布建模为多元正态分布。模拟实验表明：方法1在高斯数据上表现良好，但在偏态连续分布上存在困难；而方法2在包括正态分布、伽马分布、负二项分布和Tweedie分布在内的多种分布类型下均表现稳定，且支持灵活的链接函数。基于研究结果，我们推荐将方法2作为非线性混合效应模型选择中具有分布稳健性的cAI准则。