论文标题
在协变量归一化线性条件logit模型中识别推论参数
Identification of inferential parameters in the covariate-normalized linear conditional logit model
论文作者
论文摘要
有条件的logit模型是一种使用选择数据估算客户产品功能偏好的标准工作马方法。但是，通过大规模使用这些模型，由于大价值协变量和SoftMax概率函数的组合，可能导致数值不精确和优化失败。标准的机器学习方法通过将归一化方案应用于协变量的矩阵，从而缩放所有值以在某个间隔内（例如单元单单元）来缩放所有值，从而减轻了这些问题。尽管使用模型进行预测时，这种标准化是无害的，但它具有扰动估计系数的副作用，这对于对推论感兴趣的研究人员是必不可少的。本文表明，对于指定标准和中心缩放的两种常规类别的类别，可以分析恢复数据生成数据的非缩放模型参数及其渐近分布。本文还使用缩放标准器的示例显示了分析结果的数值性能。
The conditional logit model is a standard workhorse approach to estimating customers' product feature preferences using choice data. Using these models at scale, however, can result in numerical imprecision and optimization failure due to a combination of large-valued covariates and the softmax probability function. Standard machine learning approaches alleviate these concerns by applying a normalization scheme to the matrix of covariates, scaling all values to sit within some interval (such as the unit simplex). While this type of normalization is innocuous when using models for prediction, it has the side effect of perturbing the estimated coefficients, which are necessary for researchers interested in inference. This paper shows that, for two common classes of normalizers, designated scaling and centered scaling, the data-generating non-scaled model parameters can be analytically recovered along with their asymptotic distributions. The paper also shows the numerical performance of the analytical results using an example of a scaling normalizer.
