[R-sig-eco] calculating standard error of coefficients from adonis model

[Rafter]

I apologize that this seems to be a half function-specific, half stats
question. My stats knowledge is basic in terms of working with formulae, but
pretty decent conceptually. 

I'm conducting a set of multivariate analyses using adonis.
Predictor variables are mixed continuous and categorical. I'm using the same
predictors to fit 3 models to 3 sets of response variables - each set being
all binary, ordinal, or continuous (count) data.

I would like to display results by plotting the coefficients with confidence
intervals, as discussed here: http://tables2graphs.com/doku.php, and walked
through here: https://gist.github.com/dsparks/4332698. (The approaches
outlined at those links would need to be modified for multivariate models -
that's not my concern.)

I've searched a good chunk of several days on the following questions,
without much luck:
(1) Does it make sense to even consider coefficient SEs with a permutational
distance-based method such as adonis?
(2) (If so) How could I calculate coefficient SEs from the adonis output
and/or the raw data?

Looking at this formula for coefficient SE (found here:
http://stattrek.com/regression/slope-confidence-interval.aspx)

SE = sb1 = sqrt [ Σ(yi - ŷi)2 / (n - 2) ] / sqrt [ Σ(xi - x)2 ]
"where yi is the value of the dependent variable for observation i, ŷi is
estimated value of the dependent variable for observation i, xi is the
observed value of the independent variable for observation i, x is the mean
of the independent variable, and n is the number of observations."

I run into confusion with the mixed nature of the data, and come up with the
following questions:
(1) Could I use the term-level MSE from the anova table for the first half
of that equation? Otherwise (if it would need to be recalculated for each
factor level) I'm stuck at adonis' lack of a predict function.
(2) If so, can the second half of the equation be calculated using the
coding in the model.matrix for the factors? Or is R doing something sneaky
with the coding that I don't understand, rather than using it in as a set of
values in a straightforward way?

Any help or guidance is greatly appreciate. Thank you for your time and
consideration!

Warmly,
Rafter
 



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