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
sum_{i=1}^n (y_i - eta_i)^T W_i (y_i - η_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 - η_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.
uninormal
,
huber2
,
lqnorm
,
binormal
,
SURff
.
vlm
,
vglm
,
vgam
,
rrvglm
.
gdata <- data.frame(x2 = sort(runif(n <- 40))) gdata <- transform(gdata, y1 = 1 + 2*x2 + rnorm(n, sd = 0.1), y2 = 3 + 4*x2 + rnorm(n, sd = 0.1), y3 = 7 + 4*x2 + rnorm(n, sd = 0.1)) fit <- vglm(cbind(y1,y2) ~ x2, gaussianff, data = gdata) coef(fit, matrix = TRUE) # For comparison: coef( lmfit <- lm(y1 ~ x2, data = gdata)) coef(glmfit <- glm(y2 ~ x2, data = gdata, gaussian)) vcov(fit) vcov(lmfit) t(weights(fit, type = "prior")) # Unweighted observations head(weights(fit, type = "working")) # Identity matrices # Reduced-rank VLM (rank-1) fit2 <- rrvglm(cbind(y1, y2, y3) ~ x2, gaussianff, data = gdata) Coef(fit2)