We study and compare several variants of random forests tailored to prognostic models for ordinal outcomes. Models of the conditional odds function are employed to understand the various random forest flavours. Existing random forest variants for ordinal outcomes, such as Ordinal Forests and Conditional Inference Forests, are evaluated in the presence of a non-proportional odds impact of prognostic variables. We propose two novel random forest variants in the model-based transformation forest family, only one of which explicitly assumes proportional odds. These two novel transformation forests differ in the specification of the split procedures for the underlying ordinal trees. One of these split criteria is able to detect changes in non-proportional odds situations and the other one focuses on finding proportional-odds signals. We empirically evaluate the performance of the existing and proposed methods using a simulation study and illustrate the practical aspects of the procedures by a re-analysis of the respiratory sub-item in functional rating scales of patients suffering from Amyotrophic Lateral Sclerosis (ALS).

中文翻译：

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基于模型的随机森林进行序数回归

我们研究和比较了针对序数结果的预后模型量身定制的随机森林的几种变体。使用条件赔率函数的模型来了解各种随机森林味。在存在预后变量的非比例优势影响的情况下，评估了用于序数结果的现有随机森林变量，例如序数森林和条件推理森林。我们在基于模型的转换林家族中提出了两种新颖的随机林变体，其中只有一种明确地假定成比例的优势。这两个新的转换林在针对基础序数树的拆分过程的规范方面有所不同。这些拆分标准中的一个能够检测非比例赔率情况下的变化，另一个则专注于寻找比例奇数信号。