manylm  R Documentation 
manylm
is used to fit multivariate linear models
to highdimensional data, such as multivariate abundance data in ecology.
This is the base modelfitting function  see plot.manylm
for
assumption checking, and anova.manylm
or summary.manylm
for significance testing.
manylm( formula, data=NULL, subset=NULL, weights=NULL, na.action=options("na.action"), method="qr", model=FALSE, x=TRUE, y=TRUE, qr=TRUE, singular.ok=TRUE, contrasts=NULL, offset, test="LR" , cor.type= "I", shrink.param=NULL, tol=1.0e5, ...)
formula 
an object of class 
data 
an optional data frame, list or environment (or object
coercible by 
subset 
an optional vector specifying a subset of observations to be used in the fitting process. 
weights 
an optional vector of weights to be used in the fitting
process. Should be 
na.action 
a function which indicates what should happen
when the data contain 
method 
the method to be used; for fitting, currently only

model, x, y, qr 
logicals. If 
singular.ok 
logical. If 
contrasts 
an optional list. See the 
offset 
this can be used to specify an a priori
known component to be included in the linear predictor
during fitting. This should be 
test 
choice of test statistic. Can be one of "LR" (default) = likelihood ratio statistic "F" = LawleyHotelling trace statistic 
cor.type 
structure imposed on the estimated correlation matrix under the fitted model. Can be "I"(default), "shrink", or "R". See anova.manylm for details of its usage. This parameter will be used as the default value of 
shrink.param 
shrinkage parameter to be used if 
tol 
the tolerance used in estimations. 
... 
additional arguments to be passed to the low level regression fitting functions (see below). 
Models for manylm
are specified symbolically. For details on this
compare the details section of lm
and formula
. If the formula
includes an offset
, this is evaluated and subtracted from the
response.
See model.matrix
for some further details. The terms in
the formula will be reordered so that main effects come first,
followed by the interactions, all secondorder, all thirdorder and so
on: to avoid this pass a terms
object as the formula (see
aov
and demo(glm.vr)
for an example).
A formula has an implied intercept term. To remove this use either
y ~ x  1
or y ~ 0 + x
. See formula
for
more details of allowed formulae.
manylm
calls the lower level function manylm.fit
or manylm.wfit
for the actual numerical computations.
For programming only, you may consider doing likewise.
All of weights
, subset
and offset
are evaluated
in the same way as variables in formula
, that is first in
data
and then in the environment of formula
.
For details on arguments related to hypothesis testing (such as cor.type
and resample
) see summary.manylm
or
anova.manylm
.
manylm
returns an object of c("manylm", "mlm", "lm")
for multivariate
formula response and of of class c("lm")
for univariate response.
A manylm
object is a list containing at least the following components:
coefficients 
a named matrix of coefficients 
residuals 
the residuals matrix, that is response minus fitted values. 
fitted.values 
the matrix of the fitted mean values. 
rank 
the numeric rank of the fitted linear model. 
weights 
(only for weighted fits) the specified weights. 
df.residual 
the residual degrees of freedom. 
hat.X 
the hat matrix. 
txX 
the matrix 
test 
the 
cor.type 
the 
resample 
the 
nBoot 
the 
call 
the matched call. 
terms 
the 
xlevels 
(only where relevant) a record of the levels of the factors used in fitting. 
model 
if requested (the default), the model frame used. 
offset 
the offset used (missing if none were used). 
y 
if requested, the response matrix used. 
x 
if requested, the model matrix used. 
In addition, nonnull fits will have components assign
and
(unless not requested) qr
relating to the linear
fit, for use by extractor functions such as summary.manylm
.
Yi Wang, Ulrike Naumann and David Warton <David.Warton@unsw.edu.au>.
anova.manylm
, summary.manylm
, plot.manylm
data(spider) spiddat < log(spider$abund+1) lm.spider < manylm(spiddat~.,data=spider$x) lm.spider #Then use the plot function for diagnostic plots, and use anova or summary to #evaluate significance of different model terms.
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