Modeling Threshold Interaction Effects Through the Logistic Classification Trunk

Abstract

We introduce a model dealing with the identification of interaction effects in binary response data, which integrates recursive partitioning and generalized linear models. It derives from an ad-hoc specification and consequent implementation of the Simultaneous Threshold Interaction Modeling Algorithm (STIMA). The model, called Logistic Classification Trunk, allows us to obtain regression parameters by maximum likelihood through the simultaneous estimation of both main effects and threshold interaction effects. The main feature of this model is that it allows the user to evaluate a unique model and simultaneously the importance of both effects obtained by first growing a classification trunk and then by pruning it back to avoid overfitting. We investigate the choice of a suitable pruning parameter through a simulation study and compare the classification accuracy of the Logistic Classification Trunk with that of 13 alternative models/classifiers on 25 binary response datasets

The Bradly-Terry Regression Trunk approach for modelling preference data with small trees

“…Summarizing, results of the simulation study show that a value of the pruning parameter c between 0.5 and 1 is a good choice in almost all situations. These results are consistent with those reported in Dusseldorp et al (2010) for the linear regression model and in Conversano & Dusseldorp (2017) for the logistic regression model.…”

“…In this paper, this specification is aimed at estimating in an automatic and data-driven mode the main effects part of the model as well as, if present, its interaction effects part. For this purpose, we resort to the STIMA framework extended with the use of GLM in Conversano & Dusseldorp (2017), and combine the extended Bradley-Terry model including subject-specific covariates with the regression trunk methodology (Dusseldorp & Meulman, 2004). The main feature of a regression trunk is that it allows the user to evaluate in a unique model and simultaneously the importance of both main and interaction effects obtained by first growing a regression trunk and then by pruning it back to avoid overfitting.…”

“…Whereas, if one assumes that observations are independent realizations of Binomial random variables the link function corresponds to the Logit function and the effect size is computed as the relative increase in the log-likelihood R 2 observed when passing from the model which does not include the candidate interaction effect to the one that includes it. The resulting model is the logistic classification trunk (Conversano & Dusseldorp, 2017).…”

“…To overcome the drawbacks characterizing the works of Dittrich et al (2000) and Strobl et al (2011) we propose an alternative approach that fits a generalized linear model with a Poisson distribution by combining its main effects with a parsimonious number of interaction effects. Our proposal is framed within the Simultaneous Threshold Interaction Modeling Algorithm (STIMA) proposed by Dusseldorp, Conversano & Van Os (2010) and Conversano & Dusseldorp (2017) that, in the case of a numerical response, is based on the Regression Trunk Approach (Dusseldorp & Meulman, 2004). Dealing with paired comparisons, our approach combines the extended log-linear Bradley-Terry model including subject-specific covariates with the regression trunk.…”