VGAM (version 1.0-4)

weightsvglm: Prior and Working Weights of a VGLM fit


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


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



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


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


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


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 at convergence may or may not assign the latest value of quantities such as the mean and weights.


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

Currently ignored.


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.


Typically the first derivative of the log-likelihood with respect to the linear predictors. For example, this is the variable in, or equivalently, the matrix returned in the "deriv" slot of a VGAM family function.


The working weights.


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.


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.

See Also

glm, vglmff-class, vglm.


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

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

wwt <- weights(fit, type = "working", deriv = TRUE)  # In matrix-band format
wz <- m2a(wwt$weights, M = M)  # In array format
wzinv <- array(apply(wz, 3, solve), c(M, M, nn))
wresid <- matrix(NA, nn, M)  # Working residuals
for (ii in 1:nn)
  wresid[ii, ] <- wzinv[, , ii, drop = TRUE] %*% wwt$deriv[ii, ]
max(abs(c(resid(fit, type = "work")) - c(wresid)))  # Should be 0

(zedd <- predict(fit) + wresid)  # Adjusted dependent vector
# }

Run the code above in your browser using DataCamp Workspace