[R] Estimating variance components of groups of covariates within regression model

From: awade <awade_at_warnercnr.colostate.edu>
Date: Thu, 27 Mar 2008 20:13:19 -0600

I am interested in estimating the variance components from different groups of variables in a linear regression.

For example, I want to model dependent variable “Y” based on six covariates as follows: (these are land use types measured at three scales for each Y, "Local", "Riparian", and "Catchment" - these are not nested as there is a unique area for each Y - and Y is a measure of stream health)

L_W =c(-0.3,-0.3,-0.3,4.55,3.2,-0.3,-0.3,-0.3,8.55,-0.3)
R_A = c(-1.4,-1.06,-1.43,-1.72,-0.78,-1.72,-1.72,-1.72,-0.74,-1.32)
R_W = c(-0.77,0.62,0.1,-0.77,2.85,-0.77,-0.77,-0.77,2.27,-0.45)
C_U = c(-0.19,-0.2,1.88,2.41,0.11,2.33,2.38,2.5,0.2,1.99)
C_F = c(2.86,3.11,-0.72,-0.9,2.09,-0.92,-0.85,-1.2,1.57,-0.52)
Y = c(1.4,2.75,1.4,1.94,2.11,2.44,1.94,1,2.11,1.4)

model = lm(Y ~ L_F + L_W + R_A + R_W + C_U + C_F)

I want to identify how much of the variance is attributable to L, R, and C - three groups each having two covariates in the model.

While I find several examples that apply lmer, aov, or CorVarr functions to estimate variance components,
I don't see how to apply these to my design. I both don't see how to block my data so that I can run aov, nor do I see how to do so from within the linear regression model, as other examples (that I find) are purely repeat measures or specifically nested.
A side question is, if eventually the answer relies on correct blocking, how do I handle the issue if group "L" has 2 covariates, but group "R" has 3, as blocking with gl() won't allow this?

Thanks for any and all suggestions. I'm happy to be pointed to some examples that fit my model - I may be searching the wrong keywords. Thanks again,
Alisa Wade
Department of Geosciences
Colorado State University

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