Finite-Sample Equivalence in Statistical Models for Presence-Only Data.
Finite-Sample Equivalence in Statistical Models for Presence-Only Data.
复制标题
在统计模型中，有限样本的等效性仅在于仅存在的数据。
DOI：
10.1214/13-aoas667
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发表时间：
2013-12-01
期刊：
影响因子：
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通讯作者：
Hastie T
中科院分区：
文献类型：
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作者：
Fithian W;Hastie T
近年来，仅存在数据的统计建模在生态学文献中引起了广泛的关注，导致了各种方法的激增，包括非齐次泊松过程（IPP）模型、物种分布的最大熵（Maxent）模型和逻辑回归模型。最近的几篇文章展示了这些方法之间的密切关系。我们解释了为什么IPP强度函数在纯存在研究中比发生概率（仅根据样方大小定义）更自然地推断对象，以及为什么纯存在数据只允许估计物种发生的相对强度，而不是绝对强度。上述所有三种技术都相当于相同指数族模型下的参数密度估计（在IPP的情况下，拟合密度乘以存在记录的数量以获得拟合强度）。我们表明IPP和Maxent对这个密度给出了完全相同的估计，但在有限样本中，逻辑回归通常会产生不同的估计。当模型被错误指定时——实际上总是这样——逻辑回归和IPP在大数据集上可能有本质上不同的渐近极限。我们提出了“无限加权逻辑回归”，它完全等同于有限样本中的IPP。因此，许多已经实现的扩展逻辑回归的方法也可以使用这种技术以直接类似的方式扩展Maxent和IPP模型。
Statistical modeling of presence-only data has attracted much recent attention in the ecological literature, leading to a proliferation of methods, including the inhomogeneous Poisson process (IPP) model, maximum entropy (Maxent) modeling of species distributions and logistic regression models. Several recent articles have shown the close relationships between these methods. We explain why the IPP intensity function is a more natural object of inference in presence-only studies than occurrence probability (which is only defined with reference to quadrat size), and why presence-only data only allows estimation of relative, and not absolute intensity of species occurrence. All three of the above techniques amount to parametric density estimation under the same exponential family model (in the case of the IPP, the fitted density is multiplied by the number of presence records to obtain a fitted intensity). We show that IPP and Maxent give the exact same estimate for this density, but logistic regression in general yields a different estimate in finite samples. When the model is misspecified—as it practically always is—logistic regression and the IPP may have substantially different asymptotic limits with large data sets. We propose “infinitely weighted logistic regression,” which is exactly equivalent to the IPP in finite samples. Consequently, many already-implemented methods extending logistic regression can also extend the Maxent and IPP models in directly analogous ways using this technique.