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Normal 2 Mixture Y in Generalized Regression - best transformation or distrubtion choice?

Laura_Higgins

I've see this twice this week in two different data sets: The goal is to run Generalzied Regression. The Y variable is a normal 2 mixture distribution. Any thoughts or recommendations for either transformation of the Y to an appropriate distribution, or a good choice for a distribution for modeling?

What's the overall impact of picking the wrong distribution for the Y variable in Generalized Regression on a scale from "just set the computer on fire it's so wrong and misleading" to "well, it's pretty close"?

Accepted answers

DonMcCormack

I don't think there is an appropriate transformation because it's a bimodal distribution. If the goal is to model a bivariate normal as a function of multiple inputs, I'd probably see if I could set something up using the Nonlinear platform. Not easy, particular if the user doesn't have a stat background, but doable.

Another idea worth a shot is to use a Neural Net with two nodes and linear activation functions.

The impact would depend on how far apart the two Normals are. If they're close, the results of using, say, a single normal will be OK. Further apart and you'll smell smoke.

All comments

DonMcCormack

Another idea worth a shot is to use a Neural Net with two nodes and linear activation functions.

The impact would depend on how far apart the two Normals are. If they're close, the results of using, say, a single normal will be OK. Further apart and you'll smell smoke.

Daniel_Valente

Maybe this is making this problem too simple, but could you create a categorical response with cut-points based on historical data? And then model in Gen Reg with binomial as the Distribution.

Simple example with Iris with Petal length as the "target". There is cleary a Normal 2 Mixture here, and a big gap between "low" values and "high" values, so selecting the high values and calling them Dist 1 and low values and calling them Dist 2 creates my new column and then that becomes the response I am going to model.

Just a thought if the modeling goal is to find out which predictors affect whether the response is in one distribution or the other.

Laura_Higgins

I like this idea - segmentation of the population isn't always an option but a goal. If there was more data, we could use discriminate analysis to create Mahalanobis distances, and then use those distances as Y in Generalized regression. I tried this with the Iris data and got a good prediction: I did discriminate on just the two sepal columns, used the distance metric (which is a nice lognormal distribution) as the Y in LASSO with the 2 petal measurements for Xs, and it was still a good classifier.

iris modeling.png