We give two prediction intervals (PI) for Generalized Linear Models that take model selection uncertainty into account. The first is a straightforward extension of asymptotic normality results and the second includes an extra optimization that improves nominal coverage for small-to--moderate samples. Both PI's are wider than would be obtained without incorporating model selection uncertyainty. We compare these two PI's with three other PI's. Two are based on bootstrapping procedures and the third is based on a PI from Bayes model averaging. We argue that for general usage either the asymptotic normality or optimized asymptotic normality PI's work best. In an Appendix we extend our results to Generalized Linear Mixed Models.

翻译：我们为广义线性模型提出了两种考虑模型选择不确定性的预测区间。第一种是渐近正态性结果的直接扩展，第二种包含额外优化，可改善小到中等样本量的名义覆盖率。这两种预测区间都比未纳入模型选择不确定性时得到的区间更宽。我们将这两种预测区间与其他三种预测区间进行比较：两种基于自助法程序，第三种基于贝叶斯模型平均法的预测区间。我们认为，对于一般用途，渐近正态性或优化渐近正态性预测区间效果最佳。在附录中，我们将结果推广到广义线性混合模型。