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In Generalized Linear Models (GLMs) it is assumed that there is a lineareffect of the predictor variables on the outcome. However, this assumption isoften too strict, because in many applications predictors have a nonlinearrelation with the outcome. Optimal Scaling (OS) transformations combined withGLMs can deal with this type of relations. Transformations of the predictorshave been integrated in GLMs before, e.g. in Generalized Additive Models.However, the OS methodology has several benefits. For example, the levels ofcategorical predictors are quantified directly, such that they can be includedin the model without defining dummy variables. This approach enhances theinterpretation and visualization of the effect of different levels on theoutcome. Furthermore, monotonicity restrictions can be applied to the OStransformations such that the original ordering of the category values ispreserved. This improves the interpretation of the effect and may preventoverfitting. The scaling level can be chosen for each individual predictor suchthat models can include mixed scaling levels. In this way, a suitabletransformation can be found for each predictor in the model. The implementationof OS in logistic regression is demonstrated using three datasets that containa binary outcome variable and a set of categorical and/or continuous predictorvariables.

Optimal Scaling transformations to model non-linear relations in GLMs with ordered and unordered predictors