vegan (version 2.4-2)

as.mlm.cca: Refit Constrained Ordination as a Multiple Response Linear Model

Description

Functions refit results of constrained ordination (cca, rda, capscale) as a multiple response linear model (lm). This allows finding influence statistics (influence.measures). This also allows deriving several other statistics, but most of these are biased and misleading, since refitting ignores a major component of variation in constrained ordination.

Usage

as.mlm(x)

Arguments

x

Constrained ordination result.

Value

Function returns an object of multiple response linear model of class "mlm" documented with lm.

Details

Popular algorithm for constrained ordination is based on iteration with regression where weighted averages of sites are used as dependent variables and constraints as independent variables. Statistics of linear regression are a natural by-product in this algorithm. Constrained ordination in vegan uses different algorithm, but to obtain linear regression statistics you can refit an ordination result as a multiple response linear model (lm). This regression ignores residual unconstrained variation in the data, and therefore estimates of standard error are strongly biased and much too low. You can get statistics like $t$-values of coefficients, but you should not use these because of this bias. Some useful information you can get with refitted models are statistics for detecting influential observations (influence.measures including cooks.distance, hatvalues).

See Also

cca, rda, capscale, cca.object, lm, summary.mlm, influence.measures.

Examples

data(varespec)
data(varechem)
mod <- cca(varespec ~ Al + P + K, data=varechem)
lmod <- as.mlm(mod)
## Coefficients
lmod
coef(mod)
## Influential observations
influence.measures(lmod)
plot(mod, type = "n")
points(mod, cex = 10*hatvalues(lmod), pch=16, xpd = TRUE)
text(mod, display = "bp", col = "blue")