[R] interpretation of RCS 'coefs' and 'knots'
Frank E Harrell Jr
f.harrell at vanderbilt.edu
Sat Oct 24 00:54:23 CEST 2009
Dylan Beaudette wrote:
> I have fit a series of ols() models, by group, in this manner:
> l <- ols(y ~ rcs(x, 4))
> ... where the series of 'x' values in each group is the same, however knots
> are not always identical between groups. The result is a table of 'coefs'
> derived from the ols objects, by group:
> group Intercept top top' top''
> 1 6.864 0.01 2.241 -2.65
> 2 6.836 0.047 -0.556 0.606
> 3 5.877 -0.019 0.084 -0.175
> 4 6.021 -0.003 0.121 -0.128
> 5 7.164 0.014 0.031 -0.096
> I would like to describe groups of relationships, based on the coefficients,
> however I am not sure if they are directly comparable. In addition, I would
> like to regress these coefs on another set of variables, with the aim of
> predicting a series of RCS coefficients along external gradients. In essence,
> I am hoping to use RCS coefficients to summarize y ~ rcs(x), in a way that
> can then me modeled like this: [y ~ rcs(x)] ~ z.
> Is this interpretation of RCS coefficients even possible? If not, would
> forcing knot locations make it a possibility? Or, would modeling both knots
> and RCS coefs with external variables lead to sensible predictions?
It is possible to interpret rcs coefficients. But it is not possible to
equate coefficients across fits using different know locations. My
suggestion is either to specify the same knots (e.g., rcs(x, c(2, 4, 6,
8)) across fits or to compare the fitted relationships (predictions)
rather than the coefficients.
Frank E Harrell Jr Professor and Chair School of Medicine
Department of Biostatistics Vanderbilt University
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