How about Structure Coefficients?

[ericmelse]

Dear Joseph,

Not so much an issue I have but a question that actually is an option request.
I assume that you are familiar with the paper 'Tools to support interpreting multiple regression in the face of multicollinearity' published in Frontiers of Psychology by Kraha, A., Turner, H., Nimon, K., Zientek, L. R., & Henson, R. K. (2012, 3, 44).
Beside their extensive discussion of dominance analyse they also discuss the so-called Structure Coefficients: 'These are sim-
ply the Pearson correlations between Y and each predictor. When squared, they yield the proportion of variance in the effect (or, of the Y scores) that can be accounted for by the predictor alone, irrespective of collinearity with other predictors.'
Besides their use to decompose explained variance (something I am interested in), using structure coefficients is also a helpful diagnostic when (footnote 1) : Suppression is apparent when a predictor has a beta weight that is disproportionately large (thus receiving predictive credit) relative to a low or near-zero structure coefficient (thus indicating no relationship with the predicted scores).'
Furthermore, when the sum of explained variance of the structure coefficients exceeds 1 (100%) then '... two or more predictors explain some of the same part of the criterion ... suggesting [the presence of] multicollinearity...'
My thinking is that including an option to calculate and report the structure coefficients of a regression model, together with the model coefficients and their beta weight, would be a fine addition to the analytical functionality of domin.
Possibly you agree with me on this, but, if not, I am also glad to read your thoughts about the usefulness of structure coefficients.

[jluchman]

@ericmelse moved to a discussion as an 'idea'.

I am familiar with structure and commonality analysis (some of this discussion has been in the repository for the R version of domin here (jluchman/domir#9).

In short, it is something I have considered adding for some of the same reasons you mention along with commonality analysis but given the request, I can give it a bit more emphasis. I would then say there's a good chance of adding some of this to domin which would probably be a separate command packaged with the primary command.

Appreciate your thoughts here and passing this on. Might be a delay in implementing it on the development side but adding it to the list of features to add in future revisions.