Institute of Evolutionary Biology and Environmental Studies, University of Zurich, Zurich, Switzerland.
Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), Trondheim, Norway.
J Anim Ecol. 2020 Jan;89(1):80-92. doi: 10.1111/1365-2656.13087. Epub 2019 Sep 9.
Popular frameworks for studying habitat selection include resource-selection functions (RSFs) and step-selection functions (SSFs), estimated using logistic and conditional logistic regression, respectively. Both frameworks compare environmental covariates associated with locations animals visit with environmental covariates at a set of locations assumed available to the animals. Conceptually, slopes that vary by individual, that is, random coefficient models, could be used to accommodate inter-individual heterogeneity with either approach. While fitting such models for RSFs is possible with standard software for generalized linear mixed-effects models (GLMMs), straightforward and efficient one-step procedures for fitting SSFs with random coefficients are currently lacking. To close this gap, we take advantage of the fact that the conditional logistic regression model (i.e. the SSF) is likelihood-equivalent to a Poisson model with stratum-specific fixed intercepts. By interpreting the intercepts as a random effect with a large (fixed) variance, inference for random-slope models becomes feasible with standard Bayesian techniques, or with frequentist methods that allow one to fix the variance of a random effect. We compare this approach to other commonly applied alternatives, including models without random slopes and mixed conditional regression models fit using a two-step algorithm. Using data from mountain goats (Oreamnos americanus) and Eurasian otters (Lutra lutra), we illustrate that our models lead to valid and feasible inference. In addition, we conduct a simulation study to compare different estimation approaches for SSFs and to demonstrate the importance of including individual-specific slopes when estimating individual- and population-level habitat-selection parameters. By providing coded examples using integrated nested Laplace approximations (INLA) and Template Model Builder (TMB) for Bayesian and frequentist analysis via the R packages R-INLA and glmmTMB, we hope to make efficient estimation of RSFs and SSFs with random effects accessible to anyone in the field. SSFs with individual-specific coefficients are particularly attractive since they can provide insights into movement and habitat-selection processes at fine-spatial and temporal scales, but these models had previously been very challenging to fit.
用于研究栖息地选择的流行框架包括资源选择函数（RSF）和步长选择函数（SSF），它们分别使用逻辑回归和条件逻辑回归进行估计。这两种框架都比较了与动物访问位置相关的环境协变量与动物假定可用的一组位置的环境协变量。从概念上讲，可以使用个体斜率变化的随机系数模型（即随机系数模型）来适应两种方法的个体间异质性。虽然使用广义线性混合效应模型（GLMM）的标准软件可以为 RSF 拟合此类模型，但目前缺乏用于拟合具有随机系数的 SSF 的简单高效的一步程序。为了弥补这一差距，我们利用条件逻辑回归模型（即 SSF）与具有特定层固定截距的泊松模型具有似然等效的事实。通过将截距解释为具有较大（固定）方差的随机效应，使用标准贝叶斯技术或允许固定随机效应方差的频率方法，使随机斜率模型的推断成为可行。我们将这种方法与其他常用的替代方法进行了比较，包括没有随机斜率的模型和使用两步算法拟合的混合条件回归模型。我们使用来自山羊（Oreamnos americanus）和欧亚水獭（Lutra lutra）的数据来说明我们的模型可以得出有效且可行的推论。此外，我们进行了一项模拟研究，以比较 SSF 的不同估计方法，并演示在估计个体和种群水平的栖息地选择参数时包含个体特定斜率的重要性。通过使用集成嵌套 Laplace 逼近（INLA）和模板模型构建器（TMB）为通过 R 包 R-INLA 和 glmmTMB 进行贝叶斯和频率分析提供编码示例，我们希望使具有随机效应的 RSF 和 SSF 的有效估计能够为该领域的任何人所使用。具有个体特定系数的 SSF 特别有吸引力，因为它们可以提供有关在精细时空尺度上的运动和栖息地选择过程的见解，但这些模型以前非常难以拟合。
