plot.bermantest: Plot Result of Berman Test

Description

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

Usage

# S3 method for bermantest
plot(x, ...,
                   lwd=par("lwd"), col=par("col"), lty=par("lty"),
                   lwd0=lwd, col0=2, lty0=2)

Arguments

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 berman.test.

For the Z1 test (i.e. if x was computed using berman.test( ,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 berman.test( ,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

   plot(berman.test(cells, "x"))

   if(require("spatstat.model")) {
     # 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 <- berman.test(fit0, xcoord, "Z1")
   
     # plot result of test
     plot(k, col="red", col0="green")

     # Z2 test
     k2 <- berman.test(fit0, xcoord, "Z2")
     plot(k2, col="red", col0="green")
   }