| gaussianff {VGAM} | R Documentation |
Fits a generalized linear model to a response with Gaussian (normal) errors. The dispersion parameter may be known or unknown.
gaussianff(dispersion = 0, parallel = FALSE, zero = NULL)
parallel |
A logical or formula. If a formula, the response of the formula should
be a logical and the terms of the formula indicates whether or not
those terms are parallel.
|
dispersion |
Dispersion parameter.
If 0 then it is estimated and the moment estimate is put in
object@misc$dispersion; it is assigned the value
sum_{i=1}^n (y_i - eta_i)^T W_i (y_i - eta_i) / (nM-p)
where p is the total number of parameters estimated
(for RR-VGLMs the value used is the number of columns in the large
X model matrix; this may not be correct).
If the argument is assigned a positive quantity then it is assumed to
be known with that value.
|
zero |
An integer-valued vector specifying which linear/additive predictors
are modelled as intercepts only. The values must be from the set
{1,2,...,M} where M is the number of columns of the
matrix response.
|
This function is usually used in conjunction with vglm, else
vlm is recommended instead.
The notation M is used to denote the number of
linear/additive predictors.
This function can handle any finite M, and the default is to
use ordinary least squares.
A vector linear/additive model can be fitted by minimizing
sum_{i=1}^n (y_i - eta_i)^T W_i (y_i - eta_i)
where y_i is a M-vector,
eta_i is the vector of linear/additive predictors.
The W_i is any positive-definite matrix, and the default is the
order-M identity matrix.
The W_i can be inputted using the weights argument of
vlm/vglm/vgam etc., and the
format is the matrix-band format whereby it is a n * A matrix with the diagonals are passed first, followed by next
the upper band, all the way to the (1,M) element. Here, A
has maximum value of M(M+1)/2 and a minimum value of M.
Usually the weights argument of
vlm/vglm/vgam/rrvglm
is just a vector,
in which case each element is multiplied by a order-M
identity matrix.
If in doubt, type something like weights(object, type="working")
after the model has been fitted.
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
rrvglm
and vgam.
This VGAM family function is supposed to be similar to
gaussian but is is not compatible with
glm.
The "ff" in the name is added to avoid any masking problems.
Thomas W. Yee
McCullagh, P. and Nelder, J. A. (1989) Generalized Linear Models, 2nd ed. London: Chapman & Hall.
Yee, T. W. and Wild, C. J. (1996) Vector generalized additive models. Journal of the Royal Statistical Society, Series B, Methodological, 58, 481–493.
normal1,
vlm,
vglm,
vgam,
rrvglm.
d = data.frame(x = sort(runif(n <- 40)))
d = transform(d, y1 = 1 + 2*x + rnorm(n, sd=0.1),
y2 = 3 + 4*x + rnorm(n, sd=0.1),
y3 = 7 + 4*x + rnorm(n, sd=0.1))
fit = vglm(cbind(y1,y2) ~ x, gaussianff, data=d)
coef(fit, matrix=TRUE)
# For comparison:
coef( lmfit <- lm(y1 ~ x, data=d))
coef(glmfit <- glm(y2 ~ x, data=d, gaussian))
vcov(fit)
vcov(lmfit)
t(weights(fit, type="prior")) # Unweighted observations
weights(fit, type="working")[1:4,] # Identity matrices
# Reduced-rank VLM (rank-1)
fit2 = rrvglm(cbind(y1,y2,y3) ~ x, gaussianff, data=d)
Coef(fit2)