I am having trouble extracting residuals from Major Axis and
Standardized Major Axis fits, using the smatr package. I wish to
understand the relationship between density of wood in twigs and
trunks, and how the slope of their relationship varies among sites,
among families, and with tree size. These variance-partitioning
desires push the analysis toward a mixed model framework. However, I
am not interested in predicting twig density from trunk density, nor
vice-versa. Rather, I'm interested in the slope of their allometric
relationship. This makes a Major Axis fit highly desirable. However,
slope.com() in the smatr package accepts only one grouping variable at
a time (and no continuous covariates). Therefore, I've decided to fit
the twig-trunk relationship with line.cis() and extract the residuals
for a mixed model analysis in lm().
Which brings me to the problem: residuals calculated perpendicular to
the best fit line (as are minimized in MA) are not well behaved. They
have a mean of 0, but they are biased with respect to the variable
used as X (see example below). if X and Y are positively correlated,
they have negative slope.
How then should I proceed? How can I extract unbiased residuals from a
MA or SMA fit? It may not be possible, and I may have to revert to
doing the entire analysis in a predictive lm() framework, but I'd
prefer not to have to do that.
Any advice would be appreciated!
--tim
Sample code illustrating the situation follows:
library(smatr)
par(mfrow = c(1, 3), pty = "s")
x <- 1:100 + 50 * runif(100)
y <- 1:100 + 50 * runif(100)
z <- data.frame(x = x, y = y)
plot(z)
lm_xy <- lm(z$y ~ z$x)
abline(lm_xy, col = "blue")
z$lm_resid <- z$y - (z$x * coef(lm_xy)[2]) - coef(lm_xy)[1]
ma_xy <- line.cis(y = z$y, x = z$x, method = 2)
abline(ma_xy[1,1], ma_xy[2,1], col = "red")
z$ma_resid <- (z$y - (ma_xy[2,1] * z$x) - ma_xy[1,1])/
sqrt((ma_xy[2,1])^2 + 1)
plot(z$x, z$lm_resid)
abline(lm(z$lm_resid ~ z$x), col = "blue")
plot(z$x, z$ma_resid)
abline(lm(z$ma_resid ~ z$x), col = "red")
abline(h = 0, col = "gray")
______________________
C. E. Timothy Paine
Postdoctoral Researcher
UMR Ecologie des Fôrets de Guyane - EcoFoG
Kourou, French Guiana
cetpaine@gmail.com
(+594) 594 32 92 71
Skype: cetimothypaine
968 species of rainforest trees... manuplants.org
[[alternative HTML version deleted]]
