Abstract We study robust designs for generalized linear mixed models (GLMMs) with protections against possible departures from underlying model assumptions. Among various types of model departures, an imprecision in the assumed linear predictor or the link function has a great impact on predicting the conditional mean response function in a GLMM. We develop methods for constructing adaptive sequential designs when the fitted mean response or the link function is possibly of an incorrect parametric form. We adopt the maximum likelihood method for estimating the parameters in GLMMs and investigate both I-optimal and D-optimal design criteria for the construction of robust sequential designs. To study the empirical properties of these sequential designs, we ran a series of simulations using both logistic and Poisson mixed models. As indicated in the simulation results, the I-optimal design generally outperforms the D-optimal design for all scenarios considered. Both designs are more efficient than the conventionally used uniform design and the classical D-optimal design obtained under the assumption that the fitted models are correctly specified. The proposed designs are also illustrated in an example using actual data from a dose–response experiment.

中文翻译：

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具有可能的模型错误指定的广义线性混合模型的稳健设计

摘要 我们研究了广义线性混合模型 (GLMM) 的稳健设计，以防止可能偏离基础模型假设。在各种类型的模型偏差中，假设线性预测器或链接函数的不精确对预测 GLMM 中的条件平均响应函数有很大影响。当拟合的平均响应或链接函数可能具有不正确的参数形式时，我们开发了构建自适应序列设计的方法。我们采用最大似然法来估计 GLMM 中的参数，并研究 I 最优和 D 最优设计标准，以构建稳健的序列设计。为了研究这些顺序设计的经验特性，我们使用逻辑和泊松混合模型进行了一系列模拟。如仿真结果所示，对于所有考虑的场景，I 最优设计通常优于 D 最优设计。两种设计都比常规使用的均匀设计和在正确指定拟合模型的假设下获得的经典 D 最优设计更有效。所提出的设计还在一个示例中使用来自剂量反应实验的实际数据进行了说明。