vcov.gnm | R Documentation |

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

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

`object` |
a model object of class |

`dispersion` |
the dispersion parameter for the fitting family. By
default it is obtained from |

`with.eliminate` |
logical; should parts of the variance-covariance matrix corresponding to eliminated coefficients be computed? |

`...` |
as for |

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.

The dimensions of the matrix correspond to the non-eliminated
coefficients of the `"gnm"`

object. If ```
use.eliminate =
TRUE
```

then setting can sometimes give appreciable
speed gains; see `gnm`

for details of the `eliminate`

mechanism. The `use.eliminate`

argument is currently ignored if the
model has full rank.

A matrix with number of rows/columns equal to
`length(coef(object))`

. If there are eliminated coefficients and
`use.eliminate = TRUE`

, the matrix will have the following
attributes:

`covElim ` |
a matrix of covariances between the eliminated and non-eliminated parameters. |

`varElim ` |
a vector of variances corresponding to the eliminated parameters. |

The `gnm`

class includes generalized linear models, and it
should be noted that the
behaviour of `vcov.gnm`

differs from that of
`vcov.glm`

whenever `any(is.na(coef(object)))`

is
`TRUE`

. Whereas `vcov.glm`

drops all rows and columns which
correspond to `NA`

values in `coef(object)`

, `vcov.gnm`

keeps those columns (which are full of zeros, since the `NA`

represents a parameter which is fixed either by use of the
`constrain`

argument to `gnm`

or by a convention to handle
linear aliasing).

David Firth

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

`getContrasts`

, `se.gnm`

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

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