Multiple Regression on distance Matrices
Multiple regression on distance matrices (MRM) using permutation tests of significance for regression coefficients and R-squared.
MRM(formula = formula(data), data, nperm = 1000, method = "linear", mrank = FALSE)
formula |
formula describing the test to be conducted. |
data |
an optional dataframe containing the variables in the model as columns of dissimilarities. By default the variables are taken from the current environment. |
nperm |
number of permutations to use. If set to 0, the permutation test will be omitted. |
mrank |
if this is set to FALSE (the default option), Pearson correlations will be used. If set to TRUE, the Spearman correlation (correlation ranked distances) will be used. |
method |
if "linear", the default, uses multiple regression analysis. If "logistic", performs logistic regression with appropriate permutation testing. Note that this may be substantially slower. |
Performs multiple regression on distance matrices following the methods outlined in Legendre et al. 1994. Specificaly, the permutation test uses a pseudo-t test to assess significance, rather than using the regression coefficients directly.
coef |
A matrix with regression coefficients and associated p-values from the permutation test (using the pseudo-t of Legendre et al. 1994). |
r.squared |
Regression R-squared and associated p-value from the permutation test (linear only). |
F.test |
F-statistic and p-value for overall F-test for lack of fit (linear only). |
dev |
Residual deviance, degrees of freedom, and associated p-value (logistic only). |
Sarah Goslee
Lichstein, J. 2007. Multiple regression on distance matrices: A multivariate spatial analysis tool. Plant Ecology 188: 117-131.
Legendre, P.; Lapointe, F. and Casgrain, P. 1994. Modeling brain evolution from behavior: A permutational regression approach. Evolution 48: 1487-1499.
data(graze) # Abundance of this grass is related to forest cover but not location MRM(dist(LOAR10) ~ dist(sitelocation) + dist(forestpct), data=graze, nperm=10) # Abundance of this legume is related to location but not forest cover MRM(dist(TRRE3) ~ dist(sitelocation) + dist(forestpct), data=graze, nperm=10) # Compare to presence/absence of grass LOAR10 using logistic regression LOAR10.presence <- ifelse(graze$LOAR10 > 0, 1, 0) MRM(dist(LOAR10.presence) ~ dist(sitelocation) + dist(forestpct), data=graze, nperm=10, method="logistic")
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