Ponciano José Miguel, Taper Mark L
Biology Department, University of Florida, Gainesville, FL, United States.
Department of Ecology, Montana State University, Bozeman, MT, United States.
Front Ecol Evol. 2019 Nov;7. doi: 10.3389/fevo.2019.00413. Epub 2019 Nov 8.
Information criteria have had a profound impact on modern ecological science. They allow researchers to estimate which probabilistic approximating models are closest to the generating process. Unfortunately, information criterion comparison does not tell how good the best model is. In this work, we show that this shortcoming can be resolved by extending the geometric interpretation of Hirotugu Akaike's original work. Standard information criterion analysis considers only the divergences of each model from the generating process. It is ignored that there are also estimable divergence relationships amongst all of the approximating models. We then show that using both sets of divergences and an estimator of the negative self entropy, a model space can be constructed that includes an estimated location for the generating process. Thus, not only can an analyst determine which model is closest to the generating process, she/he can also determine how close to the generating process the best approximating model is. Properties of the generating process estimated from these projections are more accurate than those estimated by model averaging. We illustrate in detail our findings and our methods with two ecological examples for which we use and test two different neg-selfentropy estimators. The applications of our proposed model projection in model space extend to all areas of science where model selection through information criteria is done.
信息准则对现代生态科学产生了深远影响。它们使研究人员能够估计哪些概率近似模型最接近生成过程。不幸的是，信息准则比较并不能说明最佳模型有多好。在这项工作中，我们表明，通过扩展赤池弘次原始工作的几何解释可以解决这一缺点。标准信息准则分析仅考虑每个模型与生成过程的差异。而所有近似模型之间存在可估计的差异关系这一点却被忽略了。然后我们表明，使用这两组差异以及负自熵的估计值，可以构建一个模型空间，其中包括生成过程的估计位置。因此，分析师不仅可以确定哪个模型最接近生成过程，还可以确定最佳近似模型与生成过程的接近程度。从这些投影估计的生成过程的属性比通过模型平均估计的属性更准确。我们用两个生态实例详细说明了我们的发现和方法，在这两个实例中我们使用并测试了两种不同的负自熵估计器。我们提出的模型投影在模型空间中的应用扩展到了所有通过信息准则进行模型选择的科学领域。
