PLS - DA

[catch18]

Hi,

Is it possible to use more than one set of binary response variable with partial least square discriminant analysis?

Thanks.

[PaigeMiller · Accepted solution]

Generally speaking, multiple Y can be transformed into a single Y with dummy variables.

Example: suppose you have Y1 and Y2 both binary. You can create a new Y where the new Y is level 0 if both Y1 and Y2 is low, new Y is level 1 if Y1 is high and Y2 is low, new Y is level 2 if Y1 is low and Y2 is high and new Y is level 3 if both Y1 and Y2 are high. Then you turn the new Y into three columns of dummy variables. This will handle cases where Y1 and Y2 are highly correlated.

You can also fit a model for Y1 and a different model for Y2, which is probably more appropriate when the correlation between Y1 and Y2 are low.

[catch18]

Great, thanks!

Also, considering that after dummy coding we use proc pls, is it possible to include a continuous response variable with the dummy coded Y. I'm asking because proc pls can take on several continuous response variables and based on that I'm thinking its also possible to use method=pcr and method = rrr? 

Thanks.

[PaigeMiller]

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@catch18 wrote:

Great, thanks!

Also, considering that after dummy coding we use proc pls, is it possible to include a continuous response variable with the dummy coded Y. I'm asking because proc pls can take on several continuous response variables and based on that I'm thinking its also possible to use method=pcr and method = rrr? 

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I have tried using binary responses in PROC PLS (which was designed for continuous Y) and I was not particularly happy with the results, as PLS does not hesitate to give predictions less than 0 or greater than 1. But, yes it is possible to use a continuous and binary response at the same time in PROC PLS, the PROC won't stop you, it doesn't care a bit, but you will have to vouch for the correctness and usefulness of the results. 

I generally don't see the point of PCR or RRR to replace PLS. Seems like you lose the benefits of PLS and gain the disadvantages of PCR and RRR.

By the way, I do recommend the logistic PLS algorithm at https://cedric.cnam.fr/fichiers/RC906.pdf for binary responses

[catch18]

Thanks @PaigeMiller !