R: Significance Trace of Cressie-Loosmore-Ford or Maximum...

dclf.sigtrace {spatstat.core} | R Documentation

## Significance Trace of Cressie-Loosmore-Ford or Maximum Absolute Deviation Test

### Description

Generates a Significance Trace of the Diggle(1986)/ Cressie (1991)/ Loosmore and Ford (2006) test or the Maximum Absolute Deviation test for a spatial point pattern.

### Usage

    dclf.sigtrace(X, ...)
    mad.sigtrace(X, ...)
    mctest.sigtrace(X, fun=Lest, ...,
                    exponent=1, interpolate=FALSE, alpha=0.05,
                    confint=TRUE, rmin=0)

### 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"`).
`...` | Arguments passed to `envelope` or `mctest.progress`. Useful arguments include `fun` to determine the summary function, `nsim` to specify the number of Monte Carlo simulations, `alternative` to specify a one-sided test, and `verbose=FALSE` to turn off the messages.
`fun` | Function that computes the desired summary statistic for a point pattern.
`exponent` | Positive number. The exponent of the L^p distance. See Details.
`interpolate` | Logical value specifying whether to calculate the p-value by interpolation. If `interpolate=FALSE` (the default), a standard Monte Carlo test is performed, yielding a p-value of the form (k+1)/(n+1) where n is the number of simulations and k is the number of simulated values which are more extreme than the observed value. If `interpolate=TRUE`, the p-value is calculated by applying kernel density estimation to the simulated values, and computing the tail probability for this estimated distribution.
`alpha` | Significance level to be plotted (this has no effect on the calculation but is simply plotted as a reference value).
`confint` | Logical value indicating whether to compute a confidence interval for the ‘true’ p-value.
`rmin` | Optional. Left endpoint for the interval of r values on which the test statistic is calculated.

### Details

The Diggle (1986)/ Cressie (1991)/Loosmore and Ford (2006) test and the Maximum Absolute Deviation test for a spatial point pattern are described in `dclf.test`. These tests depend 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 `dclf.sigtrace` performs `dclf.test` on `X` using all possible intervals of the form [0,R], and returns the resulting p-values as a function of R.

Similarly `mad.sigtrace` performs `mad.test` using all possible intervals and returns the p-values.

More generally, `mctest.sigtrace` performs a test based on the L^p discrepancy between the curves. The deviation between two curves is measured by the pth root of the integral of the pth power of the absolute value of the difference between the two curves. The exponent p is given by the argument `exponent`. The case `exponent=2` is the Cressie-Loosmore-Ford test, while `exponent=Inf` is the MAD test.

If the argument `rmin` is given, it specifies the left endpoint of the interval defining the test statistic: the tests are performed using intervals [rmin,R] where R ≥ rmin.

The result of each command is an object of class `"fv"` that can be plotted to obtain the significance trace. The plot shows the Monte Carlo 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 (when `interpolate=FALSE`) or the delta method and normal approximation (when `interpolate=TRUE`).

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

### 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 Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.

### 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, Boca Raton, FL.

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

### See Also

`dclf.test` for the tests; `dclf.progress` for progress plots.

See `plot.fv` for information on plotting objects of class `"fv"`.

See also `dg.sigtrace`.

### Examples

      plot(dclf.sigtrace(cells, Lest, nsim=19))

[Package spatstat.core version 2.4-4 Index]