weightsvglm: Prior and Working Weights of a VGLM fit

Description

Returns either the prior weights or working weights of a VGLM object.

Usage

weightsvglm(object, type = c("prior", "working"),
            matrix.arg = TRUE, ignore.slot = FALSE,
            deriv.arg = FALSE, ...)

Arguments

object

a model object from the VGAM Rpackage that inherits from a vector generalized linear model (VGLM), e.g., a model of class "vglm".

type

Character, which type of weight is to be returned? The default is the first one.

matrix.arg

Logical, whether the answer is returned as a matrix. If not, it will be a vector.

ignore.slot

Logical. If TRUE then object@weights is ignored even if it has been assigned, and the long calculation for object@weights is repeated. This may give a slightly different answer because of the final IRLS step

deriv.arg

Logical. If TRUE then a list with components deriv and weights is returned. See below for more details.

...

Currently ignored.

Value

If type="working" and deriv=TRUE then a list is returned with the two components described below. Otherwise the prior or working weights are returned depending on the value of type.
derivTypically the first derivative of the log-likelihood with respect to the linear predictors. For example, this is the variable deriv.mu in vglm.fit(), or equivalently, the matrix returned in the "deriv" slot of a VGAM family function.
weightsThe working weights.

Details

Prior weights are usually inputted with the weights argument in functions such as vglm and vgam. It may refer to frequencies of the individual data or be weight matrices specified beforehand.

Working weights are used by the IRLS algorithm. They correspond to the second derivatives of the log-likelihood function with respect to the linear predictors. The working weights correspond to positive-definite weight matrices and are returned in matrix-band form, e.g., the first $M$ columns correspond to the diagonals, etc.

References

Yee, T. W. and Hastie, T. J. (2003) Reduced-rank vector generalized linear models. Statistical Modelling, 3, 15--41.

Chambers, J. M. and T. J. Hastie (eds) (1992) Statistical Models in S. Wadsworth & Brooks/Cole.

Examples

Run this code

data(pneumo)
pneumo = transform(pneumo, let=log(exposure.time))
(fit = vglm(cbind(normal, mild, severe) ~ let,
           cumulative(parallel=TRUE, reverse=TRUE), pneumo))
fit@y                      # These are sample proportions 
weights(fit, type="prior", matrix=FALSE) # Number of observations

# Look at the working residuals
n = nrow(model.matrix(fit, type="lm"))
M = ncol(predict(fit))

temp = weights(fit, type="working", deriv=TRUE)
wz = m2adefault(temp$weights, M=M)  # In array format
wzinv = array(apply(wz, 3, solve), c(M,M,n))
wresid = matrix(NA, n, M)  # working residuals 
for(i in 1:n)
    wresid[i,] = wzinv[,,i,drop=TRUE] %*% temp$deriv[i,]
max(abs(c(resid(fit, type="w")) - c(wresid))) # Should be 0

z = predict(fit) + wresid  # Adjusted dependent vector 
z

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