论文标题
McFadden的$ r^2 $用于二进制和序数响应模型的修改
A Modification of McFadden's $R^2$ for Binary and Ordinal Response Models
论文作者
论文摘要
大量关于分类响应模型预测强度的摘要度量的研究都认为，似然比指数（LRI），也称为McFadden- $ r^2 $，比许多其他措施更好。我们提出了对LRI的简单修改，该修改调整了响应类别对量度的影响，并重新缩放其值，模仿了潜在的潜在度量。修改的度量适用于最大似然拟合的二进制和序数响应模型。来自仿真研究和关于野猪嗅觉感知的真实数据示例的结果表明，拟议的量度优于大多数广泛使用的二进制和序数模型的拟合优点。提出的$ r^2 $有趣的是，对于序数模型的响应类别越来越多。
A lot of studies on the summary measures of predictive strength of categorical response models consider the likelihood ratio index (LRI), also known as the McFadden-$R^2$, a better option than many other measures. We propose a simple modification of the LRI that adjusts for the effect of the number of response categories on the measure and that also rescales its values, mimicking an underlying latent measure. The modified measure is applicable to both binary and ordinal response models fitted by maximum likelihood. Results from simulation studies and a real data example on the olfactory perception of boar taint show that the proposed measure outperforms most of the widely used goodness-of-fit measures for binary and ordinal models. The proposed $R^2$ interestingly proves quite invariant to an increasing number of response categories of an ordinal model.
