Description Usage Arguments Details Value Author(s) References See Also Examples
manyglm
is used to fit generalized linear models to high-dimensional data, such as multivariate abundance data in ecology. This is the base model-fitting function - see plot.manyglm
for assumption checking, and anova.manyglm
or summary.manyglm
for significance testing.
1 2 3 4 5 6 | manyglm(formula, family="negative.binomial", K=1, data=NULL, subset=NULL,
na.action=options("na.action"), theta.method = "PHI", model = FALSE,
x = TRUE, y = TRUE, qr = TRUE, cor.type= "I", shrink.param=NULL,
tol=sqrt(.Machine$double.eps), maxiter=25, maxiter2=10,
show.coef=FALSE, show.fitted=FALSE, show.residuals=FALSE,
show.warning=FALSE, offset, ... )
|
formula |
an object of class |
family |
a description of the error distribution function to be used
in the model. At the moment, this must be a character string naming one
of the following members of the exponential family: 'gaussian', 'poisson',
'binomial', 'negative.binomial'. Further improvement will include options
of specifying the link function and calling to a family function defined
in |
K |
number of trials in binomial regression. By default, K=1 for presence-absence data using logistic regression. |
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. |
na.action |
a function which indicates what should happen
when the data contain |
theta.method |
the method used for the estimation of the overdisperson
parameter theta, such that the mean-variance relationship is V=m+m^2/theta for
the negative binomial family. Here offers three options |
model, x, y, qr |
logicals. If |
cor.type |
the structure imposed on the estimated correlation
matrix under the fitted model. Can be "I"(default), "shrink", or "R".
See Details. This parameter is merely stored in |
shrink.param |
shrinkage parameter to be used if |
tol |
the tolerance used in estimation. |
maxiter |
maximum allowed iterations in the weighted least square estimation of beta. The default value is 25. |
maxiter2 |
maximum allowed iterations in the internal ML estimations of negative binomial regression. The default value is 10. |
show.coef, show.fitted, show.residuals, show.warning |
logical. Whether to show model coefficients, fitted values, standardized pearson residuals, or operation warnings. |
offset |
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 equal to NROW (i.e. number of observations) or a matrix of NROW times p (i.e. number of species). |
... |
further arguments passed to or from other methods. |
manyglm
is used to calculate the parameter estimates of generalised linear models fitted to each of many variables simultaneously as in Warton et. al. (2012) and Wang et.al.(2012). Models for manyglm
are specified symbolically. For details on how to specify a formula see the details section of lm
and formula
.
Generalised linear models are designed for non-normal data for which a distribution can be specified that offers a reasonable model for data, as specified using the argument family
. The manyglm
function currently only accepts a character argument that takes one of three possible values. Count data can be analysed using family="poisson"
if the data is not "overdispersed" (that is, if the variance is not larger than the mean), although for multivariate abundance data it has been shown that the negative binomial distribution (family="negative.binomial"
) is a good choice of model for counts (Warton (2005)). In both cases, a log-link is used. For binary (presence/absence) data, family="binomial"
should be used, which uses a logit-link ("logistic regression"). If another link function or family is desired, this can be specified using the manyany
function, which accepts regular family
arguments.
The negative binomial function requires knowledge of the overdispersion parameter (theta
) in order to fit a generalised linear model. However, it is usual not to have knowledge of the value of theta
. So we estimate a separate theta
for each variable from the data. The method of estimating theta
is controlled by theta.method
for negative binomial distributions.
cor.type
is the structure imposed on the estimated correlation
matrix under the fitted model. Possible values are:
"I"
(default) = independence is assumed (correlation matrix is the identity)
"shrink"
= sample correlation matrix is shrunk towards I to improve its stability.
"R"
= unstructured correlation matrix is used. (Only available when N>p.)
If cor.type=="shrink"
, a numerical value will be assigned to shrink.param
either through the argument or by internal estimation. The working horse function for the internal estimation is ridgeParamEst
, which is based on cross-validation (Warton 2008). The validation groups are chosen by random assignment, so some slight variation in the estimated values may be observed in repeat analyses. See ridgeParamEst
for more details. The shrinkage parameter can be any value between 0 and 1 (0="I" and 1="R", values closer towards 0 indicate more shrinkage towards "I").
manyglm
returns an object inheriting from "manyglm"
,
"manylm"
and "mglm".
The function summary
(i.e. summary.manyglm
) can be used to obtain or print a summary of the results and the function
anova
(i.e. anova.manyglm
) to produce an
analysis of variance table, although note that these functions use resampling so they can take a while to fit.
The generic accessor functions coefficients
,
fitted.values
and residuals
can be used to
extract various useful features of the value returned by manyglm
.
An object of class "manyglm"
is a list containing at least the
following components:
coefficients |
a named matrix of coefficients. |
var.coefficients |
the estimated variances of each coefficient. |
fitted.values |
the matrix of fitted mean values, obtained by transforming the linear predictors by the inverse of the link function. |
linear.predictor |
the linear fit on the scale of the linear predictor. |
residuals |
the matrix of working residuals, that is the Pearson residuals standardized by the leverage adjustment h obtained from the diagonal elements of the hat matrix H. |
PIT.residuals |
probability integral transform (PIT) residuals - for a model that fits well these should be approximately standard uniform values evenly scattered between 0 and 1. Their calculation involves some randomisation, so different fits will return slightly different values for PIT residuals. |
sqrt.1_Hii |
the matrix of scale terms used to standardize the Pearson reidusals. |
var.estimator |
the estimated variance of each observation, computed using the corresponding family function. |
sqrt.weight |
the matrix of square root of working weights, estimated for the corresponding family function. |
theta |
the estimated nuisance parameters accounting for overdispersion |
two.loglike |
two times the log likelihood. |
deviance |
up to a constant, minus twice the maximized log-likelihood. Where sensible, the constant is chosen so that a saturated model has deviance zero. |
iter |
the number of iterations of IWLS used. |
data |
a data frame storing the input data. |
stderr.coefficients |
the estimated standard error of each coefficient. |
phi |
the inverse of theta |
tol |
the tolerance used in estimations. |
maxiter,maxiter2,family,theta.method,cor.type,formula |
arguments supplied in the |
aic |
a vector returning Akaike's An Information Criterion for each response variable - minus twice the maximized log-likelihood plus twice the number of coefficients. |
AICsum |
the sum of the AIC's over all variables. |
shrink.param |
the shrink parameter to be used in subsequent inference. |
call |
the matched call. |
terms |
the |
rank |
the numeric rank of the fitted linear model. |
xlevels |
(where relevant) a record of the levels of the factors used in fitting. |
df.residual |
the residual degrees of freedom. |
x |
if the argument |
y |
if the argument |
model |
if the argument |
qr |
if the argument |
show.coef,show.fitted,show.residuals |
arguments supplied in the |
offset |
the |
Yi Wang, Ulrike Naumann and David Warton <David.Warton@unsw.edu.au>.
Lawless, J. F. (1987) Negative binomial and mixed Poisson regression, Canadian Journal of Statistics 15, 209-225.
Hilbe, J. M. (2008) Negative Binomial Regression, Cambridge University Press, Cambridge.
Warton D.I. (2005) Many zeros does not mean zero inflation: comparing the goodness of-fit of parametric models to multivariate abundance data, Environmetrics 16(3), 275-289.
Warton D.I. (2008). Penalized normal likelihood and ridge regularization of correlation and covariance matrices. Journal of the American Statistical Association 103, 340-349.
Warton D.I. (2011). Regularized sandwich estimators for analysis of high dimensional data using generalized estimating equations. Biometrics, 67(1), 116-123.
Warton D. I., Wright S., and Wang, Y. (2012). Distance-based multivariate analyses confound location and dispersion effects. Methods in Ecology and Evolution, 3(1), 89-101.
Wang Y., Neuman U., Wright S. and Warton D. I. (2012). mvabund: an R package for model-based analysis of multivariate abundance data. Methods in Ecology and Evolution. online 21 Feb 2012.
anova.manyglm
, summary.manyglm
, residuals.manyglm
, plot.manyglm
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | data(spider)
spiddat <- mvabund(spider$abund)
X <- spider$x
#To fit a log-linear model assuming counts are poisson:
glm.spid <- manyglm(spiddat~X, family="poisson")
glm.spid
summary(glm.spid, resamp="residual")
#To fit a binomial regression model to presence/absence data:
pres.abs <- spiddat
pres.abs[pres.abs>0] = 1
X <- data.frame(spider$x) #turn into a data frame to refer to variables in formula
glm.spid.bin <- manyglm(pres.abs~soil.dry+bare.sand+moss, data=X, family="binomial")
glm.spid.bin
drop1(glm.spid.bin) #AICs for one-term deletions, suggests dropping bare.sand
glm2.spid.bin <- manyglm(pres.abs~soil.dry+moss, data=X, family="binomial")
drop1(glm2.spid.bin) #backward elimination suggests settling on this model.
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