tyang wrote:
The reason why I'm not interested in just the regression coefficients is because I want to use the factors (loadings) in a regression equation with an outcome measure that's not part of the response variables. And, I want to be able to use the factors (loadings) in the regression in addition to confounder variables that I want to add into the model.
I'm sorry, but apparently my understanding of PLS does not allow me to come to an understanding of what you are asking for. We are simply not communicating here. Again, you seem to me to be explaining tiny portions of the problem you are trying to solve, and I do not see the big picture, nor can I see where you have explained the big picture. What is "an outcome measure that's not part of the response variables"? Why is that a part of this discussion?
Please correct me if I'm wrong, but the ods output parameterestimates would give me the equivalent of coefficients for the group of predictor variables that bests predicts the group of response variables?
Okay, I am correcting you. The PLS parameter estimates (or regression coefficients) that are computed are for ALL predictor variables. You get one set of regression coefficients for all X variables predicting Y1, another set of regression coeffients for all X variables predicting Y2, and so on for each Y. The loadings indicate the linear combinations of the predictor variables that are "highly predictive" of linear combinations of the response variables ("highly predictive" really means maximized squared covariance between linear combination of X and linear combination of Y, after accounting for the effects of previous dimensions...)
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