I am aware of some of the pitfalls of using banded versions of continuous variables when fitting a GLM (or other model), with a number of discussions on the subject on this forum (and a excellent list here: http://biostat.mc.vanderbilt.edu/wiki/Main/CatContinuous)

However, I’m interested to know what costs or benefits there may be in developing a model that only uses banded or binned versions of all continuous variables (with associated weighted mean bin values) and then adding the selected continuous variables later on the basis of the contribution made by their banded versions. .

I am asking as I am currently working in general insurance in the UK where a package that does just this is used extensively (it’s called Emblem and is part of a ‘pricing optimisation’ suite made by a financial services company). It does not accept any variables with more than 255 levels and so all continuous predictors have to be banded. The processed data files produced are very much smaller than their initial R or SAS counterparts and are then processed with an internal ‘R engine’.

The package allows models to be developed iteratively, adding and removing variables and interactions manually (often on the basis of expert knowledge, regulatory requirements etc.), re-fitting the model and then making a judgement on whether to keep them on the basis of graphs for each individual predictor and comparison with up to five saved ‘reference models’. Fitting times are very fast – a fraction of the time taken for the unbanded R or SAS equivalent.

All of this may be fine for a jobbing practitioner in the industry, but it got me to wondering if this approach might be appropriate for something more rigorous – what would be the pitfalls of building a model in this way and then replacing the banded versions with their original continuous values for a final evaluation for instance?

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    $\begingroup$ I'd appreciate your naming the software, so that this bizarre practice can be outed. But much depends on what the "banding" consists of. If it's replacing a continuous predictor by a set of indicator variables, I see no guarantee that it will, as it were, point in the right direction for a later continuous fit. If it's using a discretised version, where is the computational advantage? $\endgroup$ – Nick Cox Feb 16 '15 at 17:15
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    $\begingroup$ Why's fitting a model with banded predictors then fitting it again with continuous predictors quicker than just fitting it once with continuous predictors? $\endgroup$ – Scortchi Feb 16 '15 at 17:19
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    $\begingroup$ Are you in fact producing several initial models then somehow deciding between them? I think you need to be clearer about what constitutes the "model development" you're trying to speed up before anyone may be able to say anything about the costs of using binned predictors during it. I can only imagine any computational benefits when the response is discrete, in which case a table of combinations of predictor categories with frequency weights might be a good deal smaller than the original data table. $\endgroup$ – Scortchi Feb 16 '15 at 19:16
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    $\begingroup$ I've just re-written the text of the question for a little more context and I hope clarity. $\endgroup$ – AdrianD Feb 18 '15 at 14:30
  • $\begingroup$ Thanks - that's clearer (though you might also explain how the bin intervals are determined). But I'm not sure a general answer will be possible beyond stating the obvious: it'll depend how close the binned-predictor models are to their continuous-predictor counterparts, & you can probably get quite close in large data-sets. The model selection process seems too ill-defined to allow for resampling validation methods, so I assume you're using a hold-out sample for validation - why not carry out the comparison for some typical situations? $\endgroup$ – Scortchi Feb 18 '15 at 15:19

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