Exploring nonlinear relations: models of clinical decision making by regression with optimal scaling

In explorative regression studies, linear models are often applied without questioning the linearity of the relations between the predictor variables and the dependent variable, or linear relations are taken as an approximation. In this study, the method of regression with optimal scaling transformations is demonstrated. This method does not require predefined nonlinear functions and results in easy-to-interpret transformations that will show the form of the relations. The method is illustrated using data from a German multicenter project on the indication criteria for inpatient or day clinic psychotherapy treatment. The indication criteria to include in the regression model were selected with the Lasso, which is a tool for predictor selection that overcomes the disadvantages of stepwise regression methods. The resulting prediction model indicates that treatment status is (approximately) linearly related to some criteria and nonlinearly related to others.