Prima Marie-Caroline, Duchesne Thierry, Fortin Daniel
Département de Biologie, Université Laval, Québec, Québec, Canada.
Département de mathématiques et de statistique, Université Laval, Québec, Québec, Canada.
PLoS One. 2017 Jan 12;12(1):e0169779. doi: 10.1371/journal.pone.0169779. eCollection 2017.
Conditional logistic regression (CLR) is widely used to analyze habitat selection and movement of animals when resource availability changes over space and time. Observations used for these analyses are typically autocorrelated, which biases model-based variance estimation of CLR parameters. This bias can be corrected using generalized estimating equations (GEE), an approach that requires partitioning the data into independent clusters. Here we establish the link between clustering rules in GEE and their effectiveness to remove statistical biases in variance estimation of CLR parameters. The current lack of guidelines is such that broad variation in clustering rules can be found among studies (e.g., 14-450 clusters) with unknown consequences on the robustness of statistical inference. We simulated datasets reflecting conditions typical of field studies. Longitudinal data were generated based on several parameters of habitat selection with varying strength of autocorrelation and some individuals having more observations than others. We then evaluated how changing the number of clusters impacted the effectiveness of variance estimators. Simulations revealed that 30 clusters were sufficient to get unbiased and relatively precise estimates of variance of parameter estimates. The use of destructive sampling to increase the number of independent clusters was successful at removing statistical bias, but only when observations were temporally autocorrelated and the strength of inter-individual heterogeneity was weak. GEE also provided robust estimates of variance for different magnitudes of unbalanced datasets. Our simulations demonstrate that GEE should be estimated by assigning each individual to a cluster when at least 30 animals are followed, or by using destructive sampling for studies with fewer individuals having intermediate level of behavioural plasticity in selection and temporally autocorrelated observations. The simulations provide valuable information to build reliable habitat selection and movement models that allow for robustness of statistical inference without removing excessive amounts of ecological information.
条件逻辑回归（CLR）被广泛用于分析动物在资源可用性随空间和时间变化时的栖息地选择和移动情况。用于这些分析的观测值通常存在自相关性，这会使CLR参数基于模型的方差估计产生偏差。这种偏差可以使用广义估计方程（GEE）来校正，该方法需要将数据划分为独立的聚类。在这里，我们建立了GEE中的聚类规则与其在消除CLR参数方差估计中的统计偏差有效性之间的联系。目前缺乏指导方针，以至于在研究中可以发现聚类规则存在广泛差异（例如，14 - 450个聚类），而对统计推断的稳健性产生的后果未知。我们模拟了反映野外研究典型条件的数据集。基于栖息地选择的几个参数生成纵向数据，自相关性强度不同，并且一些个体的观测值比其他个体更多。然后，我们评估了改变聚类数量如何影响方差估计器的有效性。模拟结果表明，30个聚类足以获得无偏且相对精确的参数估计方差估计值。使用破坏性采样来增加独立聚类的数量成功地消除了统计偏差，但仅当观测值在时间上存在自相关性且个体间异质性强度较弱时才有效。GEE还为不同程度的不平衡数据集提供了稳健的方差估计。我们的模拟表明，当跟踪至少30只动物时，应通过将每个个体分配到一个聚类来估计GEE，或者对于个体较少、选择行为可塑性处于中等水平且观测值在时间上存在自相关性的研究，使用破坏性采样。这些模拟为构建可靠的栖息地选择和移动模型提供了有价值的信息，这些模型能够在不消除过多生态信息的情况下实现统计推断的稳健性。
