spatstat (version 1.23-1)

vcov.ppm: Variance-Covariance Matrix for a Fitted Point Process Model

Description

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

Usage

## S3 method for class 'ppm':
vcov(object, \dots, what = "vcov", verbose = TRUE,
gam.action="warn", matrix.action="warn", hessian=FALSE)

Arguments

object

A fitted point process model (an object of class "ppm".)

...

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" or "Fisher"

verbose

Logical. If TRUE, a message will be printed if various minor problems are encountered.

gam.action

String indicating what to do if object was fitted by gam. Options are "fatal", "warn" and "silent".

matrix.action

String indicating what to do if the matrix is ill-conditioned (so that its inverse cannot be calculated). Options are "fatal", "warn" and "silent".

hessian

Logical. Use the negative Hessian matrix of the log pseudolikelihood instead of the Fisher information.

Value

• A square matrix.

Error messages

An error message that reports system is computationally singular indicates that the determinant of the Fisher information matrix was either too large or too small for reliable numerical calculation. This can occur either because of numerical overflow or because of collinearity in the covariates. Most commonly it occurs because of numerical overflow: to check this, rescale the coordinates of the data points and refit the model. See the Examples.

Details

This function computes the asymptotic variance-covariance matrix of the estimates of the canonical parameters in the point process model object. It is a method for the generic function vcov.

object should be an object of class "ppm", typically produced by ppm.

The canonical parameters of the fitted model object are the quantities returned by coef.ppm(object). The function vcov calculates the variance-covariance matrix for these parameters. The argument what provides three options: [object Object],[object Object],[object Object] In all three cases, the result is a square matrix. The rows and columns of the matrix correspond to the canonical parameters given by coef.ppm(object). The row and column names of the matrix are also identical to the names in coef.ppm(object).

For models fitted by maximum pseudolikelihood (which is the default in ppm), the current implementation only works for Poisson point processes. The calculations are based on standard asymptotic theory for the maximum likelihood estimator. The observed Fisher information matrix of the fitted model object is first computed, by summing over the Berman-Turner quadrature points in the fitted model. The asymptotic variance-covariance matrix is calculated as the inverse of the observed Fisher information. The correlation matrix is then obtained by normalising.

For models fitted by the Huang-Ogata method (method="ho" in the call to ppm), the implementation works for all models. A Monte Carlo estimate of the Fisher information matrix is calculated using the results of the original fit. The argument verbose makes it possible to suppress some diagnostic messages.

The asymptotic theory is not correct if the model was fitted using gam (by calling ppm with use.gam=TRUE). The argument gamaction determines what to do in this case. If gamaction="fatal", an error is generated. If gamaction="warn", a warning is issued and the calculation proceeds using the incorrect theory for the parametric case, which is probably a reasonable approximation in many applications. If gamaction="silent", the calculation proceeds without a warning. If hessian=TRUE then the negative Hessian (second derivative) matrix of the log pseudolikelihood, and its inverse, will be computed. For non-Poisson models, this is not a valid estimate of variance, but is useful for other calculations.

Examples

X <- rpoispp(42)
  fit <- ppm(X, ~ x + y)
  vcov(fit)
  vcov(fit, what="Fish")

  # example of singular system
  data(demopat)
  m <- ppm(demopat, ~polynom(x,y,2))
  try(v <- vcov(m))
  # rescale x, y coordinates to range [0,1] x [0,1] approximately
  demopat <- rescale(demopat, 10000)
  m <- ppm(demopat, ~polynom(x,y,2))
  v <- vcov(m)