homtestmap | R Documentation |
Compute the test statistic for the test of homogeneity of a locally-fitted Poisson or Gibbs point process model.
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)
object |
Locally-fitted point process (object of class |
... |
For |
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 ( |
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 ( |
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. |
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
.
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.
.
homtest
example(locppm) plot(H <- homtestmap(fit)) H
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