plot.bermantest: Plot Result of Berman Test

Description

Plot the result of Berman's test of goodness-of-fit

Usage

## S3 method for class 'bermantest':
plot(x, ...,
                   lwd=par("lwd"), col=par("col"), lty=par("lty"),
                   lwd0=lwd, col0=col, lty0=lty)

Arguments

Object to be plotted. An object of class "bermantest" produced by bermantest.

...

extra arguments that will be passed to the plotting function plot.ecdf.

col,lwd,lty

The width, colour and type of lines used to plot the empirical distribution.

col0,lwd0,lty0

The width, colour and type of lines used to plot the predicted distribution.

Value

NULL.

Details

This is the plot method for the class "bermantest". An object of this class represents the outcome of Berman's test of goodness-of-fit of a spatial Poisson point process model, computed by bermantest.

For the Z1 test (i.e. if x was computed using bermantest( ,which="Z1")), the plot displays the two cumulative distribution functions that are compared by the test: namely the empirical cumulative distribution function of the covariate at the data points, $\hat F$, and the predicted cumulative distribution function of the covariate under the model, $F_0$, both plotted against the value of the covariate. Two vertical lines show the mean values of these two distributions. If the model is correct, the two curves should be close; the test is based on comparing the two vertical lines.

For the Z2 test (i.e. if x was computed using bermantest( ,which="Z2")), the plot displays the empirical cumulative distribution function of the values $U_i = F_0(Y_i)$ where $Y_i$ is the value of the covariate at the $i$-th data point. The diagonal line with equation $y=x$ is also shown. Two vertical lines show the mean of the values $U_i$ and the value $1/2$. If the model is correct, the two curves should be close. The test is based on comparing the two vertical lines.

Examples

Run this code

# synthetic data: nonuniform Poisson process
   X <- rpoispp(function(x,y) { 100 * exp(-x) }, win=square(1))

   # fit uniform Poisson process
   fit0 <- ppm(X, ~1)

   # test covariate = x coordinate
   xcoord <- function(x,y) { x }

   # test wrong model
   k <- bermantest(fit0, xcoord, "Z1")

   # plot result of test
   plot(k, col="red", col0="green")

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