In OLS regression, I find the semipartial correlation (a.k.a. part correlation) to be a very useful indicator. When squared, it shows each predictor's unique contribution to explained variance in the outcome. If one tries several models, entering predictors in various orders, the semipartial correlation will always turn out the same by the final model. This indicator can also be a useful basis for creating Venn diagrams showing the relative importance of different predictors. Given all this, why is it cited so seldom? For example, after 6,300 questions on this site, it has never come up, nor do I see it cited in journal publications.
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Do you have some references where you've seen it used in an effective manner? I'd also like to see the Venn Diagrams you mention as well. – Andy W Nov 24 '11 at 16:41
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Elazar Pedhazur's textbook *Multiple regression in behavioral research* pays a lot of attention to it, with very thorough explanation. I can't think of any other sources, besides my own. i'll see if i can scare up a Venn diagram. – rolando2 Nov 24 '11 at 17:00
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The notion of semipartial correlation usually arises in the context when one compares the model with a predictor and the model with that predictor removed (e.g. in the context of stepwise regression). And, because squared semipartial correlation is just a standardized form of R-square decrease, texts may find it unnecessary to mention, preferring to speak about R-square change directly instead. This is because we never compare full and reduced models abstractly, we compare concrete models, where standardization is unnecessary.
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