weightsvglm {VGAM} | R Documentation

## 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 R package 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 at convergence may or may not assign the latest value of quantities such as the mean and weights.
`deriv.arg` | Logical. If `TRUE` then a list with components `deriv` and `weights` is returned. See below for more details.
`...` | Currently ignored.

### 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.

### 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`.

`deriv` | Typically 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.
`weights` | The working weights.

### Note

This function is intended to be similar to `weights.glm` (see `glm`).

### Author(s)

Thomas W. Yee

### 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.

### See Also

`glm`, `vglmff-class`, `vglm`.

### Examples

    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

[Package VGAM version 1.0-3 Index]