Marketers increasingly face modeling situations where the number of independent variables is large and possibly approaching or exceeding the number of observations. In this setting, covariate selection and model estimation present significant challenges to usual methods of inference. These challenges are exacerbated when covariate interactions are of interest. Most extant regularization methods make no distinction between main and interaction terms in estimation. The linear VANISH model is an exception to these methods. The linear VANISH model is a regularization method for models with interaction terms that ensures proper model hierarchy by enforcing the heredity principle. We derive the generalized VANISH model for nonlinear responses, including duration, discrete choice, and count models widely used in marketing applications. In addition, we propose a VANISH model that allows to account for unobserved consumer heterogeneity via a mixture approach. In three empirical applications we demonstrate that our proposed model outperforms main effects models as well as other methods that include interaction terms.

中文翻译：

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广义线性模型的VANISH正则化

营销人员越来越多地面临建模情况，其中自变量的数量很大，并且可能接近或超过观察值的数量。在这种情况下，协变量选择和模型估计对常规推理方法提出了重大挑战。当需要对协变量进行交互时，这些挑战将会加剧。大多数现存的正则化方法在估计中没有区分主项和交互项。线性VANISH模型是这些方法的例外。线性VANISH模型是具有交互项的模型的正则化方法，通过执行遗传原理来确保适当的模型层次。我们导出了针对非线性响应的广义VANISH模型，包括持续时间，离散选择和广泛用于营销应用的计数模型。此外，我们提出了VANISH模型，该模型允许通过混合方法解决未观察到的消费者异质性问题。在三个经验应用中，我们证明了我们提出的模型优于主要效应模型以及包括交互项的其他方法。