manylm is used to fit multivariate linear models
to high-dimensional data, such as multivariate abundance data in ecology.
This is the base model-fitting 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=1.0e-5, …)an object of class "formula" (or one that
can be coerced to that class): a symbolic description of the
model to be fitted. The details of model specification are given
under Details.
an optional data frame, list or environment (or object
coercible by as.data.frame to a data frame) containing
the variables in the model. If not found in data, the
variables are taken from environment(formula),
typically the environment from which manylm is called.
an optional vector specifying a subset of observations to be used in the fitting process.
an optional vector of weights to be used in the fitting
process. Should be NULL or a numeric vector.
If non-null, weighted least squares is used with weights
weights (that is, minimizing sum(weights*e^2)); otherwise
ordinary least squares is used.
a function which indicates what should happen
when the data contain NAs. The default is set by
the na.action setting of options, and is
na.fail if that is unset. The ‘factory-fresh’
default is na.omit. Another possible value is
NULL, no action. Value na.exclude can be useful.
the method to be used; for fitting, currently only
method = "qr" is supported; method = "model.frame" returns
the model frame (the same as with model = TRUE, see below).
logicals. If TRUE the corresponding
components of the fit (the model frame, the model matrix, the
response, the QR decomposition) are returned.
logical. If FALSE (the default in S but
not in R) a singular fit is an error.
an optional list. See the contrasts.arg
of model.matrix.default.
this can be used to specify an a priori
known component to be included in the linear predictor
during fitting. This should be NULL or a numeric vector of
length either one or equal to the number of cases.
One or more offset terms can be included in the
formula instead or as well, and if both are specified their sum is
used. See model.offset.
choice of test statistic. Can be one of "LR" (default) = likelihood ratio statistic "F" = Lawley-Hotelling trace statistic NULL = no test
This parameter is merely stored in manylm, and will be used as the default value of test in subsequent functions for inference.
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 cor.type in subsequent functions for inference.
shrinkage parameter to be used if cor.type="shrink". This parameter will be used as the default value of shrink.param in subsequent functions for inference.
the tolerance used in estimations.
additional arguments to be passed to the low level regression fitting functions (see below).
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:
a named matrix of coefficients
the residuals matrix, that is response minus fitted values.
the matrix of the fitted mean values.
the numeric rank of the fitted linear model.
(only for weighted fits) the specified weights.
the residual degrees of freedom.
the hat matrix.
the matrix (t(x)%*%x).
the test argument supplied.
the cor.type argument supplied.
the resample argument supplied.
the nBoot argument supplied.
the matched call.
the terms object used.
(only where relevant) a record of the levels of the factors used in fitting.
if requested (the default), the model frame used.
the offset used (missing if none were used).
if requested, the response matrix used.
if requested, the model matrix used.
In addition, non-null fits will have components assign and (unless not requested) qr relating to the linear fit, for use by extractor functions such as summary.manylm.
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 re-ordered so that main effects come first,
followed by the interactions, all second-order, all third-order 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.
# NOT RUN {
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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