Variance-Covariance Matrix for a Fitted Point Process Model

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

models, methods, spatial
## S3 method for class 'ppm':
vcov(object, \dots, what = "vcov", verbose = TRUE)
A fitted point process model (an object of class "ppm".)
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"
Logical. If TRUE, a message will be printed if various minor problems are encountered.

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 current implementation only works for Poisson point processes.

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] The calculations are based on standard asymptotic theory for the maximum likelihood estimator. In all cases, 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.

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).

The argument verbose makes it possible to suppress some diagnostic messages.


  • A square matrix.

  • vcov.ppm
X <- rpoispp(42)
  fit <- ppm(X, ~ x + y)
  vcov(fit, what="Fish")
Documentation reproduced from package spatstat, version 1.9-1, License: GPL version 2 or newer

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