In this paper, we extend the linear M‐quantile random intercept model (MQRE) to discrete data and use the proposed model to evaluate the effect of selected covariates on two count responses: the number of generic medical examinations and the number of specialised examinations for health districts in three regions of central Italy. The new approach represents an outlier‐robust alternative to the generalised linear mixed model with Gaussian random effects and it allows estimating the effect of the covariates at various quantiles of the conditional distribution of the target variable. Results from a simulation experiment, as well as from real data, confirm that the method proposed here presents good robustness properties and can be in certain cases more efficient than other approaches.

中文翻译：

---

离散响应的广义 M 分位数随机效应模型：对医生就诊次数的应用

在本文中，我们将线性 M 分位数随机截距模型 (MQRE) 扩展到离散数据，并使用所提出的模型来评估所选协变量对两个计数响应的影响：一般医学检查的数量和专业检查的数量意大利中部三个地区的卫生区。新方法代表了具有高斯随机效应的广义线性混合模型的异常稳健替代方案，它允许估计协变量在目标变量条件分布的各个分位数上的影响。模拟实验以及真实数据的结果证实，这里提出的方法具有良好的鲁棒性，并且在某些情况下比其他方法更有效。