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Article overview
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Optimal Scaling transformations to model non-linear relations in GLMs with ordered and unordered predictors | | S. J. W. Willems
; A. J. van der Kooij
; J. J. Meulman
; | | Date: |
1 Sep 2023 | | Abstract: | In Generalized Linear Models (GLMs) it is assumed that there is a linear
effect of the predictor variables on the outcome. However, this assumption is
often too strict, because in many applications predictors have a nonlinear
relation with the outcome. Optimal Scaling (OS) transformations combined with
GLMs can deal with this type of relations. Transformations of the predictors
have been integrated in GLMs before, e.g. in Generalized Additive Models.
However, the OS methodology has several benefits. For example, the levels of
categorical predictors are quantified directly, such that they can be included
in the model without defining dummy variables. This approach enhances the
interpretation and visualization of the effect of different levels on the
outcome. Furthermore, monotonicity restrictions can be applied to the OS
transformations such that the original ordering of the category values is
preserved. This improves the interpretation of the effect and may prevent
overfitting. The scaling level can be chosen for each individual predictor such
that models can include mixed scaling levels. In this way, a suitable
transformation can be found for each predictor in the model. The implementation
of OS in logistic regression is demonstrated using three datasets that contain
a binary outcome variable and a set of categorical and/or continuous predictor
variables. | | Source: | arXiv, 2309.00419 | | Services: | Forum | Review | PDF | Favorites | |
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