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Does anybody have any suggestions about promoting the use of a regression tree over a GLM when the two models fit the data almost exactly the same?

My team's current arguments are a) a tree is easier for non-technical people to understand and b) when the two models' predictions are implemented -simplified as needed- as tables (necessary for use in actuarial software) the GLM results will be distorted more than the tree's predictions.

Any other ideas?

Background: Office politics. We want to use one of our own models instead of having our parent company's GLM forced on us without any comparison of the models, so to get our work a chance to be fairly evaluated we need to be promote our tree's advantages over a GLM.

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  • $\begingroup$ What does your response variable look like? And which GLM are you using? (Logistic regression? something else?) $\endgroup$
    – Placidia
    Commented Jun 24, 2014 at 17:11
  • $\begingroup$ Binomial, so we're using logistic. $\endgroup$
    – JenSCDC
    Commented Jun 24, 2014 at 18:24
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    $\begingroup$ You can find some arguments in the following paper. It also asks why do one or the other when you can do both? arxiv.org/pdf/1311.7326.pdf $\endgroup$
    – Momo
    Commented Jun 24, 2014 at 21:32

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Regresssion trees require far greater sample sizes than predominantly additive regression models, and make far more stringent assumptions for continuous variables (piecewise flatness with identifiable cutpoints).

Note that if you use an improper accuracy scoring rule to compare two methods (e.g., "classification" accuracy) you will get highly misleading results.

Single regression trees are not stable and do not have competitive $R^2$, hence the popularity of tree-averaging-type methods such as random forests.

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The best argument for your tree model would be that it makes better predictions. To show that, you would need training and test sets. Build a regression and a tree model from your training set, then see how well each one does on the test set. "Well" means "what proportion of items are correctly classified?".

According to Leo Breiman , both logistic regression and classification trees can produce eccentric results when the number of predictor variables is large. He developed random forests to improve the stability of RT's. You might want to look at that option as well.

If you find that logistic regression and RT's do just as well, then your best argument would be the interpretability of regression trees --- unless you are dealing with medical doctors, who find odds ratios intuitively appealing and are reluctant to consider anything else, in my experience.

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  • $\begingroup$ We're getting comparable results from the tree and the logistic regression. I've also fitted a random forest, and it gave nearly the same validation results as the other two methods. OTOH, I'm not very familiar with RFs, so my model could be sub-optimal. $\endgroup$
    – JenSCDC
    Commented Jun 24, 2014 at 20:36
  • $\begingroup$ This probably means that the model is fine, since 3 methods are giving you similar results. Can you show that your tree model runs faster by doing some benchmarking? $\endgroup$
    – Placidia
    Commented Jun 24, 2014 at 21:03
  • $\begingroup$ Speed is irrelevant- we won't be making prediction on the fly; we only do them once when we create lookup tables. $\endgroup$
    – JenSCDC
    Commented Jun 25, 2014 at 2:00
  • $\begingroup$ Are you really sure that the logistic method fits that well? Under a logistic, you have to assume that the log odds of the probability of success is a linear function of the independent variables. That's a strong assumption. Has it been fully tested? $\endgroup$
    – Placidia
    Commented Jun 25, 2014 at 2:14
  • $\begingroup$ Logistic regression and Poisson regression are industry standard methods. Our logistic model has been validated using the same data as for the tree, and the two models give nearly identical results for several measures of goodness of fit. $\endgroup$
    – JenSCDC
    Commented Jun 25, 2014 at 13:31

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