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.
## S3 method for class 'ppm': vcov(object, \dots, what = "vcov", verbose = TRUE, gam.action="warn", matrix.action="warn", hessian=FALSE)
- A fitted point process model (an object of class
- Character string (partially-matched)
that specifies what matrix is returned.
"vcov"for the variance-covariance matrix,
"corr"for the correlation matrix, and
- Logical. If
TRUE, a message will be printed if various minor problems are encountered.
- String indicating what to do if
objectwas fitted by
gam. Options are
- String indicating what to do if the matrix
is ill-conditioned (so that its inverse cannot be calculated).
- Logical. Use the negative Hessian matrix of the log pseudolikelihood instead of the Fisher information.
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
object should be an object of class
The canonical parameters of the fitted model
are the quantities returned by
vcov calculates the variance-covariance matrix
for these parameters.
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
For models fitted by maximum pseudolikelihood (which is the
ppm), the current implementation only works
for Poisson point processes.
The calculations are based on standard asymptotic theory for the maximum
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
For models fitted by the Huang-Ogata method (
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.
verbose makes it possible to suppress some
The asymptotic theory is not correct if the model was fitted using
gam (by calling
gamaction determines what to do in this case.
gamaction="fatal", an error is generated.
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.
gamaction="silent", the calculation proceeds without a
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.
- A square matrix.
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.
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)