dg.sigtrace {spatstat.explore}

Significance Trace of Dao-Genton Test

Description

Generates a Significance Trace of the Dao and Genton (2014) test for a spatial point pattern.

Usage

  dg.sigtrace(X, fun = Lest, ...,
              exponent = 2, nsim = 19, nsimsub = nsim - 1,
              alternative = c("two.sided", "less", "greater"),
              rmin=0, leaveout=1,
              interpolate = FALSE, confint = TRUE, alpha = 0.05,
              savefuns=FALSE, savepatterns=FALSE, verbose=FALSE)

Arguments

X

Either a point pattern (object of class "ppp", "lpp" or other class), a fitted point process model (object of class "ppm", "kppm" or other class) or an envelope object (class "envelope").

fun

Function that computes the desired summary statistic for a point pattern.

...

Arguments passed to envelope.

exponent

Positive number. Exponent used in the test statistic. Use exponent=2 for the Diggle-Cressie-Loosmore-Ford test, and exponent=Inf for the Maximum Absolute Deviation test. See Details.

nsim

Number of repetitions of the basic test.

nsimsub

Number of simulations in each basic test. There will be nsim repetitions of the basic test, each involving nsimsub simulated realisations, so there will be a total of nsim * (nsimsub + 1) simulations.

alternative

Character string specifying the alternative hypothesis. The default (alternative="two.sided") is that the true value of the summary function is not equal to the theoretical value postulated under the null hypothesis. If alternative="less" the alternative hypothesis is that the true value of the summary function is lower than the theoretical value.

rmin

Optional. Left endpoint for the interval of r values on which the test statistic is calculated.

leaveout

Optional integer 0, 1 or 2 indicating how to calculate the deviation between the observed summary function and the nominal reference value, when the reference value must be estimated by simulation. See Details.

interpolate

Logical value indicating whether to interpolate the distribution of the test statistic by kernel smoothing, as described in Dao and Genton (2014, Section 5).

confint

Logical value indicating whether to compute a confidence interval for the ‘true’ p-value.

alpha

Significance level to be plotted (this has no effect on the calculation but is simply plotted as a reference value).

savefuns

Logical flag indicating whether to save the simulated function values (from the first stage).

savepatterns

Logical flag indicating whether to save the simulated point patterns (from the first stage).

verbose

Logical flag indicating whether to print progress reports.

Details

The Dao and Genton (2014) test for a spatial point pattern is described in dg.test. This test depends on the choice of an interval of distance values (the argument rinterval). A significance trace (Bowman and Azzalini, 1997; Baddeley et al, 2014, 2015; Baddeley, Rubak and Turner, 2015) of the test is a plot of the p-value obtained from the test against the length of the interval rinterval.

The command dg.sigtrace effectively performs dg.test on X using all possible intervals of the form [0,R], and returns the resulting p-values as a function of R.

The result is an object of class "fv" that can be plotted to obtain the significance trace. The plot shows the Dao-Genton adjusted p-value (solid black line), the critical value 0.05 (dashed red line), and a pointwise 95% confidence band (grey shading) for the ‘true’ (Neyman-Pearson) p-value. The confidence band is based on the Agresti-Coull (1998) confidence interval for a binomial proportion.

If X is an envelope object and fun=NULL then the code will re-use the simulated functions stored in X.

If the argument rmin is given, it specifies the left endpoint of the interval defining the test statistic: the tests are performed using intervals [r_{\mbox{\scriptsize min}},R] where R \ge r_{\mbox{\scriptsize min}}.

The argument leaveout specifies how to calculate the discrepancy between the summary function for the data and the nominal reference value, when the reference value must be estimated by simulation. The values leaveout=0 and leaveout=1 are both algebraically equivalent (Baddeley et al, 2014, Appendix) to computing the difference observed - reference where the reference is the mean of simulated values. The value leaveout=2 gives the leave-two-out discrepancy proposed by Dao and Genton (2014).

Value

An object of class "fv" that can be plotted to obtain the significance trace.

Author(s)

Adrian Baddeley, Andrew Hardegen, Tom Lawrence, Robin Milne, Gopalan Nair and Suman Rakshit. Implemented by Adrian Baddeley [e-mail], Rolf Turner [e-mail] and Ege Rubak [e-mail].

References

Agresti, A. and Coull, B.A. (1998) Approximate is better than “Exact” for interval estimation of binomial proportions. American Statistician 52, 119–126.

Baddeley, A., Diggle, P., Hardegen, A., Lawrence, T., Milne, R. and Nair, G. (2014) On tests of spatial pattern based on simulation envelopes. Ecological Monographs 84(3) 477–489.

Baddeley, A., Hardegen, A., Lawrence, L., Milne, R.K., Nair, G.M. and Rakshit, S. (2015) Pushing the envelope: extensions of graphical Monte Carlo tests. Unpublished manuscript.

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

Bowman, A.W. and Azzalini, A. (1997) Applied smoothing techniques for data analysis: the kernel approach with S-Plus illustrations. Oxford University Press, Oxford.

Dao, N.A. and Genton, M. (2014) A Monte Carlo adjusted goodness-of-fit test for parametric models describing spatial point patterns. Journal of Graphical and Computational Statistics 23, 497–517.

See Also

dg.test for the Dao-Genton test, dclf.sigtrace for significance traces of other tests.

Examples

  ns <- if(interactive()) 19 else 5
  plot(dg.sigtrace(cells, nsim=ns))