vcov.kppm

A fitted cluster point process model (an object of class
 <code>"kppm"</code>.)

object

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Character string (partially-matched)
 that specifies what matrix is returned.
 Options are <code>"vcov"</code> for the variance-covariance matrix,
 <code>"corr"</code> for the correlation matrix, and
 <code>"fisher"</code> for the Fisher information matrix.

what

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.

fast

Optional. The dependence range. Not usually specified by the
 user. Only used when <code>fast=TRUE</code>.

rmax

Numeric. A small positive number which is used to determine <code>rmax</code>
 from the tail behaviour of the pair correlation function when fast
 option (<code>fast=TRUE</code>) is used. Namely
 <code>rmax</code> is the smallest value of \(r\)
 at which \((g(r)-1)/(g(0)-1)\)
 falls below <code>eps.rmax</code>.
 Only used when <code>fast=TRUE</code>.
 Ignored if <code>rmax</code> is provided.

eps.rmax

Logical value indicating whether to print progress reports
 during very long calculations.

verbose

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

models

methods

spatial

Comprehensive open-source toolbox for analysing Spatial Point Patterns. Focused mainly on two-dimensional point patterns, including multitype/marked points, in any spatial region. Also supports three-dimensional point patterns, space-time point patterns in any number of dimensions, point patterns on a linear network, and patterns of other geometrical objects. Supports spatial covariate data such as pixel images.
Contains over 2000 functions for plotting spatial data, exploratory data analysis, model-fitting, simulation, spatial sampling, model diagnostics, and formal inference.
Data types include point patterns, line segment patterns, spatial windows, pixel images, tessellations, and linear networks.
Exploratory methods include quadrat counts, K-functions and their simulation envelopes, nearest neighbour distance and empty space statistics, Fry plots, pair correlation function, kernel smoothed intensity, relative risk estimation with cross-validated bandwidth selection, mark correlation functions, segregation indices, mark dependence diagnostics, and kernel estimates of covariate effects. Formal hypothesis tests of random pattern (chi-squared, Kolmogorov-Smirnov, Monte Carlo, Diggle-Cressie-Loosmore-Ford, Dao-Genton, two-stage Monte Carlo) and tests for covariate effects (Cox-Berman-Waller-Lawson, Kolmogorov-Smirnov, ANOVA) are also supported.
Parametric models can be fitted to point pattern data using the functions ppm(), kppm(), slrm(), dppm() similar to glm(). Types of models include Poisson, Gibbs and Cox point processes, Neyman-Scott cluster processes, and determinantal point processes. Models may involve dependence on covariates, inter-point interaction, cluster formation and dependence on marks. Models are fitted by maximum likelihood, logistic regression, minimum contrast, and composite likelihood methods.
A model can be fitted to a list of point patterns (replicated point pattern data) using the function mppm(). The model can include random effects and fixed effects depending on the experimental design, in addition to all the features listed above.
Fitted point process models can be simulated, automatically. Formal hypothesis tests of a fitted model are supported (likelihood ratio test, analysis of deviance, Monte Carlo tests) along with basic tools for model selection (stepwise(), AIC()). Tools for validating the fitted model include simulation envelopes, residuals, residual plots and Q-Q plots, leverage and influence diagnostics, partial residuals, and added variable plots.

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

Description

Usage

Arguments

Value

Details

References

See Also

Examples