A0362
Title: Variable importance in generalized linear models: A unifying view using Shapley values
Authors: Christian Kleiber - Universitaet Basel (Switzerland) [presenting]
Sinan Acemoglu - University of Basel (Switzerland)
Joerg Urban - Universitaet Basel (Switzerland)
Abstract: Variable importance in regression analyses is of considerable interest in a variety of fields. There is no unique method for assessing variable importance. However, a substantial share of the available literature employs Shapley values, explicitly or implicitly, for decomposing a suitable goodness-of-fit measure, in the linear regression model, typically the classical $R^2$. Beyond linear regression, there is no generally accepted goodness-of-fit measure, just a variety of pseudo-$R^2$s. We formulate and discuss the requirements for goodness-of-fit measures that allow an interpretation of Shapley values in terms of relative and even absolute importance. We suggest employing a pseudo-$R^2$ based on the Kullback-Leibler divergence, which is of a convenient form for generalized linear models and permits to unify and extend earlier work on variable importance for linear and nonlinear models. We present several examples using data from public health and insurance.
