The experimental design for a generalized linear model (GLM) is important but challenging since the design criterion often depends on model specification including the link function, the linear predictor, and the unknown regression coefficients. Prior to constructing locally or globally optimal designs, a pilot experiment is usually conducted to provide some insights on the model specifications. In pilot experiments, little information on the model specification of GLM is available. Surprisingly, there is very limited research on the design of pilot experiments for GLMs. In this work, we obtain some theoretical understanding of the design efficiency in pilot experiments for GLMs. Guided by the theory, we propose to adopt a low-discrepancy design with respect to some target distribution for pilot experiments. The performance of the proposed design is assessed through several numerical examples.

翻译：通用线性模型(GLM)的实验设计很重要,但具有挑战性,因为设计标准往往取决于模型规格,包括链接功能、线性预测器和未知的回归系数。在建造当地或全球最佳设计之前,通常会进行试点试验,以提供一些关于模型规格的见解。在试点实验中,关于通用线性模型示范规格的资料很少。奇怪的是,关于GLM实验设计的研究非常有限。在这项工作中,我们对GLMS实验的设计效率有一些理论理解。在理论的指导下,我们提议对试点实验的某些目标分布采用低差异设计。通过几个数字例子评估拟议设计的业绩。