Step selection functions (SSFs) are flexible models to jointly describe animals' movement and habitat preferences. Their popularity has grown rapidly and extensions have been developed to increase their utility, including various distributions to describe movement constraints, interactions to allow movements to depend on local environmental features, and random effects and latent states to account for within- and among-individual variability. Although the SSF is a relatively simple statistical model, its presentation has not been consistent in the literature, leading to confusion about model flexibility and interpretation. We believe that part of the confusion has arisen from the conflation of the SSF model with the methods used for parameter estimation. Notably, conditional logistic regression can be used to fit SSFs in exponential form, and this approach is often presented interchangeably with the actual model (the SSF itself). However, reliance on conditional logistic regression reduces model flexibility, and suggests a misleading interpretation of step selection analysis as being equivalent to a case-control study. In this review, we explicitly distinguish between model formulation and inference technique, presenting a coherent framework to fit SSFs based on numerical integration and maximum likelihood estimation. We provide an overview of common numerical integration techniques, and explain how they relate to step selection analyses. This framework unifies different model fitting techniques for SSFs, and opens the way for improved inference. In particular, it makes it straightforward to model movement with distributions outside the exponential family, and to apply different SSF formulations to a data set and compare them with AIC. By separating the model formulation from the inference technique, we hope to clarify many important concepts in step selection analysis.

翻译：步选函数（SSFs）是灵活描述动物运动与栖息地偏好的联合模型。其应用迅速扩展，衍生出增强实用性的改进，包括描述运动约束的不同分布、允许运动依赖局部环境特征的交互项，以及解释个体内和个体间差异的随机效应与潜变量。尽管SSF作为相对简单的统计模型，但其表述在文献中并不统一，导致对模型灵活性和解释的混淆。我们认为部分混淆源于SSF模型与参数估计方法的混用。具体而言，条件逻辑回归可用于拟合指数形式的SSF，该方法常与模型本身（即SSF）互换使用。然而，依赖条件逻辑回归会降低模型灵活性，并导致将步选分析等同于病例对照研究的误导性解释。在本综述中，我们明确区分模型构建与推断技术，提出基于数值积分和最大似然估计拟合SSF的连贯框架。我们概述常用数值积分技术，并阐述其与步选分析的关系。该框架统一了SSF的不同模型拟合技术，为改进推断开辟道路——尤其能轻松构建指数族之外的分布的运动模型，并对同一数据集应用不同SSF公式进行AIC比较。通过分离模型构建与推断技术，我们期望阐明步选分析中的关键概念。