gnm (version 0.8-1)

vcov.gnm: Variance-covariance Matrix for Parameters in a Generalized Nonlinear Model

Description

This method extracts or computes a variance-covariance matrix for use in approximate inference on estimable parameter combinations in a generalized nonlinear model.

Usage

## S3 method for class 'gnm':
vcov(object, dispersion = NULL, ...)

Arguments

object

a model object of class gnm.

dispersion

...

as for vcov.

Value

• A square matrix, with number of rows/columns equal to length(coef(object)).

Details

The resultant matrix does not itself necessarily contain variances and covariances, since gnm typically works with over-parameterized model representations in which parameters are not all identified. Rather, the resultant matrix is to be used as the kernel of quadratic forms which are the variances or covariances for estimable parameter combinations. The matrix values are scaled by dispersion. If the dispersion is not specified, it is taken as 1 for the binomial and Poisson families, and otherwise estimated by the residual Chi-squared statistic divided by the residual degrees of freedom. The dispersion used is returned as an attribute of the matrix.

References

Turner, H and Firth, D (2005). Generalized nonlinear models in R: An overview of the gnm package. At http://cran.r-project.org

See Also

getContrasts, se

Examples

set.seed(1)
data(yaish)
## Fit the "UNIDIFF" mobility model across education levels
unidiff <- gnm(Freq ~ educ*orig + educ*dest +
               Mult(Exp(-1 + educ), -1 + orig:dest), family = poisson,
               data = yaish, subset = (dest != 7))
## Examine the education multipliers (differences on the log scale):
ofInterest <- grep("Mult1.Factor1", names(coef(unidiff)))
educMultipliers <- getContrasts(unidiff, rev(ofInterest))[[1]]
## Now get the same standard errors using a suitable set of
## quadratic forms, by calling vcov() directly:
cmat <- contr.sum(ofInterest)
sterrs <- sqrt(diag(t(cmat)
                     %*% vcov(unidiff)[ofInterest, ofInterest]
                     %*% cmat))
all(sterrs == (educMultipliers$SE)[-1]) ## TRUE