# vcov.kppm

##### Variance-Covariance Matrix for a Fitted Cluster Point Process Model

Returns the variance-covariance matrix of the estimates of the parameters of a fitted cluster point process model.

##### Usage

```
# S3 method for kppm
vcov(object, ...,
what=c("vcov", "corr", "fisher", "internals"),
fast = NULL, rmax = NULL, eps.rmax = 0.01,
verbose = TRUE)
```

##### Arguments

- object
A fitted cluster point process model (an object of class

`"kppm"`

.)- …
Ignored.

- what
Character string (partially-matched) that specifies what matrix is returned. Options are

`"vcov"`

for the variance-covariance matrix,`"corr"`

for the correlation matrix, and`"fisher"`

for the Fisher information matrix.- fast
Logical specifying whether tapering (using sparse matrices from Matrix) should be used to speed up calculations. Warning: This is expected to underestimate the true asymptotic variances/covariances.

- rmax
Optional. The dependence range. Not usually specified by the user. Only used when

`fast=TRUE`

.- eps.rmax
Numeric. A small positive number which is used to determine

`rmax`

from the tail behaviour of the pair correlation function when fast option (`fast=TRUE`

) is used. Namely`rmax`

is the smallest value of \(r\) at which \((g(r)-1)/(g(0)-1)\) falls below`eps.rmax`

. Only used when`fast=TRUE`

. Ignored if`rmax`

is provided.- verbose
Logical value indicating whether to print progress reports during very long calculations.

##### Details

This function computes the asymptotic variance-covariance
matrix of the estimates of the canonical (regression) parameters in the
cluster point process model `object`

. It is a method for the
generic function `vcov`

.

The result is an `n * n`

matrix where ```
n =
length(coef(model))
```

.

To calculate a confidence interval for a regression parameter,
use `confint`

as shown in the examples.

##### Value

A square matrix.

##### References

Waagepetersen, R. (2007)
Estimating functions for inhomogeneous spatial point processes
with incomplete covariate data.
*Biometrika* **95**, 351--363.

##### See Also

##### Examples

```
# NOT RUN {
data(redwood)
fit <- kppm(redwood ~ x + y)
vcov(fit)
vcov(fit, what="corr")
# confidence interval
confint(fit)
# cross-check the confidence interval by hand:
sd <- sqrt(diag(vcov(fit)))
t(coef(fit) + 1.96 * outer(sd, c(lower=-1, upper=1)))
# }
```

*Documentation reproduced from package spatstat, version 1.49-0, License: GPL (>= 2)*