A likelihood method that approximates the behaviour of implied weighting is described. This approach provides a likelihood perspective on several aspects of implied weighting, such as guidance for the choice of concavity values, a justification to use different concavities for different numbers of taxa, and a natural basis for extended implied weighting. In this approach, the number of free parameters in the estimation depends on C, the number of characters (in contrast to the standard Mk model, which estimates 2T–3 parameters for T taxa). Depending on the characteristics of the dataset, the likelihood obtained with this approach may in some cases be similar or superior to that of the Mk model, but with fewer parameters being adjusted. Because of that tradeoff, testing against the Mk model by means of the Akaike information criterion on a set of 182 morphological datasets indicated many cases (36) in which the likelihood approximation to implied weighting is the best method, from an information‐theoretic point of view. Given that it is expected to produce (almost) the same results as this maximum‐likelihood approximation, implied weighting can therefore be seen as a valid alternative to the Mk model often used for morphological datasets, on the basis of a criterion for model fit widely advocated by likelihoodists.

中文翻译：

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可以通过 Akaike 信息准则在 Mk 模型上选择隐含权重简约的似然近似

描述了一种近似隐含加权行为的似然方法。这种方法提供了隐含权重的几个方面的可能性视角，例如选择凹度值的指导、对不同数量的分类群使用不同凹度的理由，以及扩展隐含权重的自然基础。在这种方法中，估计中的自由参数数量取决于字符数 C（与标准 Mk 模型相反，该模型估计 T 类群的 2T-3 个参数）。根据数据集的特性，使用这种方法获得的似然在某些情况下可能与 Mk 模型相似或优于 Mk 模型，但调整的参数较少。由于这种权衡，通过对一组 182 个形态数据集的 Akaike 信息标准对 Mk 模型进行测试表明，从信息理论的角度来看，在许多情况下（36），隐含权重的似然近似是最好的方法。鉴于预计会产生（几乎）与这种最大似然近似相同的结果，因此基于模型广泛拟合的标准，隐含权重可以被视为常用于形态学数据集的 Mk 模型的有效替代方案似然论者所提倡。