QK Box 6.3

For the data from Allison and Cicchetti (1976), the two variables of interest, brain weight and body weight, will be treated as random with the focus on estimating the regression slope of the linear relationship between two random variables. The original variables were log-transformed, with both variables having strongly skewed distributions due to a small number of large-bodied (and large-brained) species.

Allison, T. & Cicchetti, D. V. (1976). Sleep in mammals: ecological and constitutional correlates. Science, 194, 732-4.

Data for this example were obtained for the first edition and are available here

Preliminaries

First, load the required packages (lmodel2)

Import allison data file (allison.csv)

allison <- read.csv("../data/allison.csv")
head(allison,10)

Transform bodywt and brainwt to log10

allison$lbodywt <- log10(allison$bodywt)
allison$lbrainwt <- log10(allison$brainwt)

Fit model 2 regression

allison2 <- lmodel2(lbrainwt~lbodywt, data=allison, range.y='interval', range.x='interval', nperm=1000)
allison2

Model II regression

Call: lmodel2(formula = lbrainwt ~ lbodywt, data = allison, range.y = "interval", range.x = "interval", nperm = 1000)

n = 62   r = 0.9595748   r-square = 0.9207837 
Parametric P-values:   2-tailed = 9.835792e-35    1-tailed = 4.917896e-35 
Angle between the two OLS regression lines = 2.294966 degrees

Permutation tests of OLS, MA, RMA slopes: 1-tailed, tail corresponding to sign
A permutation test of r is equivalent to a permutation test of the OLS slope
P-perm for SMA = NA because the SMA slope cannot be tested

Regression results

Confidence intervals

Eigenvalues: 2.912129 0.05649568 

H statistic used for computing C.I. of MA: 0.001345423