The score test for the two‐sample occupancy model
The score test for the two‐sample occupancy model
复制标题
双样本占用模型的得分检验
DOI：
10.1111/anzs.12288
复制
发表时间：
2020
影响因子：
1.1
通讯作者：
Byron J. T. Morgan
中科院分区：
文献类型：
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作者：
N. Karavarsamis;G. Guillera‐Arroita;Richard Huggins;Byron J. T. Morgan
由观测信息得到的分数检验统计量很容易用数值计算。它在零假设下的大样本分布是众所周知的，并且等价于基于期望信息的得分检验、似然比检验和Wald检验。然而，几位作者指出，在另一种假设下，这不再成立，特别是来自观察信息的分数统计可能采用负值。我们将分数测试的选集扩展到研究物种发生时对生态学感兴趣的问题。这是两个独立样本在不完全检测下的两个零膨胀二项随机变量的比较。在该设置中对与分数测试相关联的特征值的分析有助于理解为什么在分数测试中使用观察到的信息矩阵可能是有问题的。我们通过模拟和理论分析相结合的方法证明，随着被比较的总体变得更加不同，根据观察到的信息计算的得分检验的威力会降低。特别是，基于观察信息的分数测试不一致。最后，我们提出了一个改进的规则，当使用观察到的信息为负或大于通常的卡方截止值来计算得分统计量时，该规则拒绝零假设。在我们设置的模拟中，这具有与Wald和似然比测试相当的能力，并且一致性在很大程度上得到了恢复。我们的新测试很容易使用，而且可以进行推理。根据期刊说明，本文的补充材料可在网上获得。
The score test statistic from the observed information is easy to compute numerically. Its large sample distribution under the null hypothesis is well known and is equivalent to that of the score test based on the expected information, the likelihood‐ratio test and the Wald test. However, several authors have noted that under the alternative hypothesis this no longer holds and in particular the score statistic from the observed information can take negative values. We extend the anthology on the score test to a problem of interest in ecology when studying species occurrence. This is the comparison of two zero‐inflated binomial random variables from two independent samples under imperfect detection. An analysis of eigenvalues associated with the score test in this setting assists in understanding why using the observed information matrix in the score test can be problematic. We demonstrate through a combination of simulations and theoretical analysis that the power of the score test calculated under the observed information decreases as the populations being compared become more dissimilar. In particular, the score test based on the observed information is inconsistent. Finally, we propose a modified rule that rejects the null hypothesis when the score statistic is computed using the observed information is negative or is larger than the usual chi‐square cut‐off. In simulations in our setting this has power that is comparable to the Wald and likelihood ratio tests and consistency is largely restored. Our new test is easy to use and inference is possible. Supplementary material for this article is available online as per journal instructions.