Abstract Hierarchical models are used to study the relationship between a response variable and a predictor in structured data. Random effects are meant to capture the structured part of variability among groups of observations. In ecology, random effects are usually incorporated into the intercept. Their application to the other parameters of the curve, especially in nonlinear curves, has been understudied. However, applying random effects to different parameters of the function is of interest, as it allows us to account for variations in the shape of the relationship over groups of observations. Our study was based on Bayesian models linking the local quantity of deadwood to the local species richness of saproxylic beetles in French forests. Our hypothesis was that it was important to account for inter-forest variations of the relationship to better fit the data. Since a sigmoidal curve seemed adapted to studying this relationship from an ecological point of view, we paid special attention to commonly used sigmoidal functions, but also included two new ones for biogeography originating from ecophysiology (one sigmoid with estimated asymptotes and one with estimated asymptotes allowing asymmetry). We applied various settings of random effects to these different mean functions. We compared, evaluated and interpreted the models and results according to several criteria (WAIC, comparison of significance of the difference in terms of LOOic, goodness-of-fit p-values and magnitude of the effect). We first found that models without random effects were systematically the worst and that the best model was not necessarily the one with random effect incorporated into the intercept, as is usually done in ecology. Secondly, we found that, in most cases, for a given mean function, the best model had several random effects, and the model with the most random effects performed nearly as well as the best models. Furthermore, the inclusion of random effects revealed statistically significant relationships between deadwood volume and species richness. Thirdly, we revealed a complementarity between the different assessment criteria, each one giving important information for the selection and interpretation of the models. In conclusion, future forest biodiversity management studies should incorporate random effects into the modeling framework so that more robust conclusions can be made about the relationships, based on complementary post-fitting analysis criteria.

中文翻译：

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随机的重要性！充分考虑非线性sigmoid分层贝叶斯模型中的随机效应揭示枯木与腐木甲虫物种丰富度之间的关系

摘要 层次模型用于研究结构化数据中响应变量和预测变量之间的关系。随机效应旨在捕捉观察组之间可变性的结构化部分。在生态学中，随机效应通常包含在截距中。他们对曲线其他参数的应用，尤其是在非线性曲线中的应用，尚未得到充分研究。然而，将随机效应应用于函数的不同参数是有意义的，因为它允许我们考虑观察组之间关系形状的变化。我们的研究基于贝叶斯模型，将当地枯木数量与法国森林中腐木甲虫的当地物种丰富度联系起来。我们的假设是，考虑森林间的关系变化以更好地拟合数据非常重要。由于 Sigmoidal 曲线似乎适合从生态的角度研究这种关系，因此我们特别关注了常用的 sigmoidal 函数，但也包括了两个源自生态生理学的生物地理学新函数（一个具有估计渐近线的 sigmoid 和一个具有估计渐近线的 sigmoid，允许不对称）。我们对这些不同的均值函数应用了各种随机效应设置。我们根据几个标准（WAIC，在 LOOic、拟合优度 p 值和效果大小方面比较差异的显着性）比较、评估和解释了模型和结果。我们首先发现没有随机效应的模型系统地最差，最好的模型不一定是将随机效应纳入截距的模型，就像生态学中通常所做的那样。其次，我们发现，在大多数情况下，对于给定的均值函数，最佳模型具有多个随机效应，而具有最多随机效应的模型的表现几乎与最佳模型一样好。此外，随机效应的加入揭示了枯木量和物种丰富度之间的统计学显着关系。第三，我们揭示了不同评估标准之间的互补性，每个标准都为模型的选择和解释提供了重要信息。综上所述，