1. The effect of explanatory environmental variables on a species' distribution is often assessed using a count regression model. Poisson generalized linear models or negative binomial models are common, but the traditional approach of modelling the mean after log or square root transformation remains popular and in some cases is even advocated.
2. We propose a novel framework of linear models for count data. Similar to the traditional approach, the new models apply a transformation to count responses; however, this transformation is estimated from the data and not defined a priori. In contrast to simple least‐squares fitting and in line with Poisson or negative binomial models, the exact discrete likelihood is optimized for parameter estimation and inference. Simple interpretation of effects in the linear predictors is possible.
3. Count transformation models provide a new approach to regressing count data in a distribution‐free yet fully parametric fashion, obviating the need to a priori commit to a specific parametric family of distributions or to a specific transformation. The models are a generalization of discrete Weibull models for counts and are thus able to handle over‐ and underdispersion. We demonstrate empirically that the models are more flexible than Poisson or negative binomial models but still maintain interpretability of multiplicative effects. A re‐analysis of deer–vehicle collisions and the results of artificial simulation experiments provide evidence of the practical applicability of the model framework.
4. In ecology studies, uncertainties regarding whether and how to transform count data can be resolved in the framework of count transformation models, which were designed to simultaneously estimate an appropriate transformation and the linear effects of environmental variables by maximizing the exact count log‐likelihood. The application of data‐driven transformations allows over‐ and underdispersion to be addressed in a model‐based approach. Models in this class can be compared to Poisson or negative binomial models using the in‐ or out‐of‐sample log‐likelihood. Extensions to nonlinear additive or interaction effects, correlated observations, hurdle‐type models and other more complex situations are possible. A free software implementation is available in the cotram add‐on package to the R system for statistical computing.

中文翻译：

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计算转换模型

1. 通常使用计数回归模型评估解释性环境变量对物种分布的影响。泊松广义线性模型或负二项式模型很常见，但是对数或平方根变换后的均值建模的传统方法仍然很流行，甚至在某些情况下被提倡。
2. 我们提出了一种用于计数数据的线性模型的新颖框架。与传统方法类似，新模型应用了转换来计算响应。但是，这种转换是根据数据估算的，没有先验定义。与简单的最小二乘拟合以及与泊松或负二项式模型一致的方法相比，精确的离散似然被优化用于参数估计和推断。可以简单地解释线性预测变量中的效应。
3. 计数转换模型提供了一种新的方法来以无分布但完全参数化的方式回归计数数据，从而无需事先提交特定的参数分布族或特定的转换。这些模型是离散Weibull模型的泛化模型，因此能够处理过度分散和分散不足。我们凭经验证明，该模型比泊松或负二项式模型更灵活，但仍保持乘法效应的可解释性。对鹿与汽车碰撞的重新分析以及人工仿真实验的结果为模型框架的实际适用性提供了证据。
4. 在生态学研究中，是否可以在计数转换模型的框架内解决有关是否以及如何转换计数数据的不确定性，该模型旨在通过最大化精确的计数对数似然来同时估算适当的转换和环境变量的线性效应。数据驱动的转换的应用允许以基于模型的方法解决过度分散和分散不足的问题。可以使用样本内或样本外对数似然将此类中的模型与Poisson或负二项式模型进行比较。可能会扩展到非线性加性或相互作用效应，相关观测值，跨栏模型以及其他更复杂的情况。R的cotram附加软件包中提供了免费软件实现。 统计计算系统。