R: Dao-Genton Adjusted Goodness-Of-Fit Test

dg.test {spatstat} | R Documentation

## Dao-Genton Adjusted Goodness-Of-Fit Test

### Description

Performs the Dao and Genton (2014) adjusted goodness-of-fit test of spatial pattern.

### Usage

    dg.test(X, ...,
            exponent = 2, nsim=19, nsimsub=nsim-1,
            alternative=c("two.sided", "less", "greater"),
            reuse = TRUE, leaveout=1, interpolate = FALSE,
            savefuns=FALSE, savepatterns=FALSE,
            verbose = TRUE)

### Arguments

`X` | Either a point pattern dataset (object of class `"ppp"`, `"lpp"` or `"pp3"`) or a fitted point process model (object of class `"ppm"`, `"kppm"`, `"lppm"` or `"slrm"`).
`...` | Arguments passed to `dclf.test` or `mad.test` or `envelope` to control the conduct of the test. Useful arguments include `fun` to determine the summary function, `rinterval` to determine the range of r values used in the test, and `use.theory` described under Details.
`exponent` | 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.
`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.
`reuse` | Logical value indicating whether to re-use the first stage simulations at the second stage, as described by Dao and Genton (2014).
`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).
`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 value indicating whether to print progress reports.

### Details

Performs the Dao-Genton (2014) adjusted Monte Carlo goodness-of-fit test, in the equivalent form described by Baddeley et al (2014).

If `X` is a point pattern, the null hypothesis is CSR.

If `X` is a fitted model, the null hypothesis is that model.

The argument `use.theory` passed to `envelope` determines whether to compare the summary function for the data to its theoretical value for CSR (`use.theory=TRUE`) or to the sample mean of simulations from CSR (`use.theory=FALSE`).

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).

The Dao-Genton test is biased when the significance level is very small (small p-values are not reliable) and we recommend `bits.test` in this case.

### Value

A hypothesis test (object of class `"htest"` which can be printed to show the outcome of the test.

### 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

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.

Baddeley, A., Diggle, P.J., Hardegen, A., Lawrence, T., Milne, R.K. 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. (2017) On two-stage Monte Carlo tests of composite hypotheses. Computational Statistics and Data Analysis, in press.

### See Also

`bits.test`, `dclf.test`, `mad.test`

### Examples

     ns <- if(interactive()) 19 else 4
     dg.test(cells, nsim=ns)
     dg.test(cells, alternative="less", nsim=ns)
     dg.test(cells, nsim=ns, interpolate=TRUE)

[Package spatstat version 1.63-3 Index]