berman.test.lpp: Berman's Tests for Point Process Model on a Network

Description Usage Arguments Details Value Warning Author(s) References See Also Examples

View source: R/bermanlpp.R

Description

Tests the goodness-of-fit of a Poisson point process model on a linear network, using the approach of Berman (1986).

Usage

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## S3 method for class 'lpp'
berman.test(X, covariate,
                         which = c("Z1", "Z2"),
        alternative = c("two.sided", "less", "greater"), ...)

## S3 method for class 'lppm'
berman.test(model, covariate,
                         which = c("Z1", "Z2"),
               alternative = c("two.sided", "less", "greater"), ...)

Arguments

X

A point pattern (object of class "lpp").

model

A fitted point process model (object of class "lppm").

covariate

The spatial covariate on which the test will be based. An image (object of class "im" or "linim") or a function.

which

Character string specifying the choice of test.

alternative

Character string specifying the alternative hypothesis.

...

Additional arguments controlling the pixel resolution (arguments dimyx and eps passed to as.mask) or other undocumented features.

Details

These functions perform a goodness-of-fit test of a Poisson point process model fitted to point pattern data. The observed distribution of the values of a spatial covariate at the data points, and the predicted distribution of the same values under the model, are compared using either of two test statistics Z[1] and Z[2] proposed by Berman (1986). The Z[1] test is also known as the Lawson-Waller test.

The function berman.test is generic, with methods for point patterns ("ppp" or "lpp") and point process models ("ppm" or "lppm").

See the help file for berman.test for information on the generic function and the methods for data in two-dimensional space, classes "ppp" and "ppm".

This help file describes the methods for data on a linear network, classes "lpp" and "lppm".

The test is performed by comparing the observed distribution of the values of a spatial covariate at the data points, and the predicted distribution of the same covariate under the model. Thus, you must nominate a spatial covariate for this test.

The argument covariate should be either a function(x,y) or a pixel image (object of class "im" containing the values of a spatial function. If covariate is an image, it should have numeric values, and its domain should cover the observation window of the model. If covariate is a function, it should expect two arguments x and y which are vectors of coordinates, and it should return a numeric vector of the same length as x and y.

First the original data point pattern is extracted from model. The values of the covariate at these data points are collected.

Next the values of the covariate at all locations in the observation window are evaluated. The point process intensity of the fitted model is also evaluated at all locations in the window.

In both cases the null distribution of the test statistic is the standard normal distribution, approximately.

The return value is an object of class "htest" containing the results of the hypothesis test. The print method for this class gives an informative summary of the test outcome.

Value

An object of class "htest" (hypothesis test) and also of class "bermantest", containing the results of the test. The return value can be plotted (by plot.bermantest) or printed to give an informative summary of the test.

Warning

The meaning of a one-sided test must be carefully scrutinised: see the printed output.

Author(s)

\spatstatAuthors

.

References

Berman, M. (1986) Testing for spatial association between a point process and another stochastic process. Applied Statistics 35, 54–62.

Lawson, A.B. (1993) On the analysis of mortality events around a prespecified fixed point. Journal of the Royal Statistical Society, Series A 156 (3) 363–377.

Waller, L., Turnbull, B., Clark, L.C. and Nasca, P. (1992) Chronic Disease Surveillance and testing of clustering of disease and exposure: Application to leukaemia incidence and TCE-contaminated dumpsites in upstate New York. Environmetrics 3, 281–300.

See Also

cdf.test, quadrat.test, ppm lppm

Examples

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   #' test of complete randomness
   berman.test(spiders, "x")
   #' test of fitted model
   fit <- lppm(spiders ~ x)
   berman.test(fit, "y", "Z2")

spatstat.linnet documentation built on July 17, 2021, 9:07 a.m.