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Generalized additive models with flexible response functions

机译：具有灵活响应功能的广义添加剂模型

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摘要

Common generalized linear models depend on several assumptions: (i) the specified linear predictor, (ii) the chosen response distribution that determines the likelihood and (iii) the response function that maps the linear predictor to the conditional expectation of the response. Generalized additive models (GAM) provide a convenient way to overcome the restriction to purely linear predictors. Therefore, the covariates may be included as flexible nonlinear or spatial functions to avoid potential bias arising from misspecification. Single index models, on the other hand, utilize flexible specifications of the response function and therefore avoid the deteriorating impact of a misspecified response function. However, such single index models are usually restricted to a linear predictor and aim to compensate for potential nonlinear structures only via the estimated response function. We will show that this is insufficient in many cases and present a solution by combining a flexible approach for response function estimation using monotonic P-splines with additive predictors as in GAMs. Our approach is based on maximum likelihood estimation and also allows us to provide confidence intervals of the estimated effects. To compare our approach with existing ones, we conduct extensive simulation studies and apply our approach on two empirical examples, namely the mortality rate in SAo Paulo due to respiratory diseases based on the Poisson distribution and credit scoring of a German bank with binary responses.
机译：常见的广义线性模型取决于若干假设：（i）指定的线性预测器，（ii）确定似然和（iii）将线性预测器映射到响应的条件期望的响应函数的所选响应分布。广义添加剂模型（GAM）提供了一种克服纯线性预测器的限制的便利方式。因此，可以包括作为柔性非线性或空间函数的协变量，以避免出现误解产生的潜在偏差。另一方面，单一索引模型利用灵活的响应功能规格，从而避免了误差响应函数的影响恶化。然而，这种单一索引模型通常仅限于线性预测器，并且目的仅通过估计的响应函数来补偿潜在的非线性结构。我们将表明，许多情况下，这在许多情况下不足，并通过将灵活的方法与具有添加预测器中的单调P样条相结合，通过单调P样分组合响应函数估计来呈现解决方案。我们的方法基于最大似然估计，并且还允许我们提供估计效果的置信区间。为了将我们的方法与现有的方法进行比较，我们进行广泛的仿真研究，并在两个经验例子上应用我们的方法，即道保罗的死亡率，由于基于宠物分布和德国银行的德国银行的德国银行的呼吸疾病。

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