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Feature significance in generalized additive models

机译：广义加性模型中的特征重要性

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This paper develops inference for the significance of features such as peaks and valleys observed in additive modeling through an extension of the SiZer-type methodology of Chaudhuri and Marron (1999) and Godtliebsen et al. (2002, 2004) to the case where the outcome is discrete. We consider the problem of determining the significance of features such as peaks or valleys in observed covariate effects both for the case of additive modeling where the main predictor of interest is univariate as well as the problem of studying the significance of features such as peaks, inclines, ridges and valleys when the main predictor of interest is geographical location. We work with low rank radial spline smoothers to allow to the handling of sparse designs and large sample sizes. Reducing the problem to a Generalised Linear Mixed Model (GLMM) framework enables derivation of simulation-based critical value approximations and guards against the problem of multiple inferences over a range of predictor values. Such a reduction also allows for easy adjustment for confounders including those which have an unknown or complex effect on the outcome. A simulation study indicates that our method has satisfactory power. Finally, we illustrate our methodology on several data sets.
机译：本文通过扩展Chaudhuri和Marron（1999）的SiZer型方法以及Godtliebsen等人的方法，得出了在加性建模中观察到的特征（例如峰和谷）的重要性的推论。 （2002年，2004年）的结果是离散的。对于加法模型，在主要预测变量为单变量的情况下，我们考虑确定观察到的协变量效应中特征（例如峰或谷）的重要性的问题，以及研究特征（例如峰，斜率）的重要性的问题，山脊和山谷时，主要关注的预测指标是地理位置。我们使用低阶径向花键平滑器来处理稀疏设计和大样本量。将问题简化为广义线性混合模型（GLMM）框架可以推导基于仿真的临界值近似值，并防止在一系列预测值上进行多次推断的问题。这样的减少还可以方便地对混杂因素进行调整，包括对结果有未知或复杂影响的混杂因素。仿真研究表明我们的方法具有令人满意的功效。最后，我们在几个数据集上说明我们的方法。

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