## Abstract

Recursive partitioning algorithms separate a feature space into a set of disjoint rectangles.

Then, usually, a constant in every partition is fitted. While this is a simple and

intuitive approach, it may still lack interpretability as to how a specific relationship between dependent and

independent variables may look. Or it may be that a certain model is assumed or of

interest and there is a number of candidate variables that may non-linearily give rise to

different model parameter values.

We present an approach that combines generalized linear models with recursive partitioning

that offers enhanced interpretability of classical trees as well as providing an

explorative way to assess a candidate variable's influence on a parametric model.

This method conducts recursive partitioning of a the generalized linear model by

(1) fitting the model to the data set, (2) testing for parameter instability over a set of

partitioning variables, (3) splitting the data set with respect to the variable associated with

the highest instability. The outcome is a tree where each terminal node is associated with a generalized linear model.

We will show the methods versatility and suitability to gain additional insight

into the relationship of dependent and independent variables by two examples, modelling

voting behaviour and a failure model for debt amortization.

Then, usually, a constant in every partition is fitted. While this is a simple and

intuitive approach, it may still lack interpretability as to how a specific relationship between dependent and

independent variables may look. Or it may be that a certain model is assumed or of

interest and there is a number of candidate variables that may non-linearily give rise to

different model parameter values.

We present an approach that combines generalized linear models with recursive partitioning

that offers enhanced interpretability of classical trees as well as providing an

explorative way to assess a candidate variable's influence on a parametric model.

This method conducts recursive partitioning of a the generalized linear model by

(1) fitting the model to the data set, (2) testing for parameter instability over a set of

partitioning variables, (3) splitting the data set with respect to the variable associated with

the highest instability. The outcome is a tree where each terminal node is associated with a generalized linear model.

We will show the methods versatility and suitability to gain additional insight

into the relationship of dependent and independent variables by two examples, modelling

voting behaviour and a failure model for debt amortization.

Original language | English |
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Publication status | Published - 1 Nov 2011 |

### Publication series

Name | Research Report Series / Department of Statistics and Mathematics |
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No. | 109 |

## WU Working Paper Series

- Research Report Series / Department of Statistics and Mathematics