homtestmap {spatstat.local}

Test Statistic for Homogeneity Test

Description

Compute the test statistic for the test of homogeneity of a locally-fitted Poisson or Gibbs point process model.

Usage

homteststat(object, ..., verbose = FALSE)

homtestmap(object, ...,
           what=c("components", "statistic", "pvalue"),
           test = c("score", "taylor", "likelihood"),
           ladjust=c("none", "moment", "PSS"),
           calibrate=c("chisq", "Satterthwaite", "firstmoment"),
           simple = !is.null(theta0),
           theta0 = NULL,
           poolmoments=NULL,
           sigma = NULL, 
           saveall = FALSE, 
           use.fft = TRUE,
           verbose = TRUE)

## S3 method for class 'homtestmap'
update(object, ..., 
           what=NULL, test=NULL, ladjust=NULL,
           calibrate=NULL, saveall=FALSE, poolmoments=NULL)

Arguments

object

Locally-fitted point process (object of class "locppm") or an object previously computed by homtestmap.

...

For homteststat, arguments passed to homtestmap. For homtestmap, additional unmatched arguments are ignored.

what

Character string (partially matched) indicating whether to return the vector components of the local test statistic, or the value of the local test statistic, or the local p-values.

test

Character string (partially matched) indicating whether to perform the local score test (test="score"), or the local composite likelihood ratio test approximately (test="taylor") or exactly (test="likelihood").

ladjust

Character string (partially matched) specifying an adjustment to the composite likelihood ratio test statistic.

calibrate

Character string (partially matched) specifying how to calculate p-values from the test statistic.

simple

Logical value indicating whether to treat the fitted model as a simple null hypothesis (simple=TRUE) or as an estimate of the parameters in a composite null hypothesis (simple=FALSE, the default).

theta0

Coefficient vector specifying a simple null hypothesis.

poolmoments

Logical value indicating how to calculate the reference distribution for the likelihood ratio test statistic (and thus how to calculate p-values). See Details.

sigma

Smoothing bandwidth.

saveall

Logical value indicating whether to compute a complete set of sufficient statistics and save them as an attribute of the result. See Details.

use.fft

For software testing purposes only. Logical value indicating whether to use data computed by the Fast Fourier Transform.

verbose

Logical value indicating whether to print progress reports.

Details

These functions are used by homtest to perform a Monte Carlo test of the null hypothesis of homogeneity (i.e.\ constant parameter values) for the locally-fitted Poisson point process or Gibbs point process object.

The function homtestmap computes either the local likelihood ratio test statistic or the local score test statistic. If what="statistic", then the result is a scalar-valued function giving the local values of the test statistic. If what="pvalue", the result is a scalar-valued function p(v) giving the local p-value at each location v. If what="components", the result is a vector-valued function T(v) containing the components of the quadratic form; the squared norm of T(v) is equal to the desired test statistic at each location v.

If saveall=TRUE, then a complete set of sufficient statistics is calculated and stored as an attribute of the result. This makes it possible to compute all of the statistics and p values described above.

The function update.homtestmap, a method for the generic function update, converts an object of class "homtestmap" from one of these formats to another, where possible. Except in trivial cases, this requires that the "homtestmap" object was computed with saveall=TRUE.

The function homteststat computes the mean of the local test statistic or the mean of the local p-values over the observation window.

To compute the p-values when test="likelihood" or test="taylor", the values of the local likelihood ratio test statistic are referred to a gamma distribution whose first two moments are estimated from the data. If poolmoments=FALSE, the local estimates of the moments are used; if poolmoments=TRUE, the spatial average of these estimates is used. The default is to use pooling whenever it is theoretically justified, namely when the template model is a stationary point process.

Finer control over the computation is possible using the arguments ... passed to locppm.

Value

For homteststat, a numeric value giving the test statistic.

For homtestmap and update.homtestmap, a spatially-sampled function object (class "ssf"; see ssf). This object also belongs to the special class "homtestmap" which has a print method.

Author(s)

Adrian Baddeley [e-mail].

References

Baddeley, A. (2017) Local composite likelihood for spatial point patterns. Spatial Statistics 22, 261–295. DOI: 10.1016/j.spasta.2017.03.001

Baddeley, A., Rubak, E. and Turner, R. (2015) Spatial Point Patterns: Methodology and Applications with R. Chapman and Hall/CRC Press.

See Also

homtest

Examples

   example(locppm)
   plot(H <- homtestmap(fit))
   H