spptest: Spatial point process testing

In myllym/spptest: Spatial point process testing

Description

The spptest library provides global envelope and deviation tests. Both type of tests are Monte Carlo tests, which demand simulations from the tested null model. Examples are mainly for spatial point processes, but the methods are applicable for any functional (or multivariate vector) data. (In the case of point processes, the functions are typically estimators of summary functions.) The main motivation for this package are the scalings for deviation tests and global envelope tests.

Details

The package supports the use of the R library spatstat for generating simulations and calculating estimators of the chosen summary function, but alternatively these can be done by any other methods, thus allowing for any models/functions.

Typical workflow

In the following, the use of the spptest library is demonstrated by its main function rank_envelope, but alternatively this step can be replaced by a call of another function for envelope or deviation test (the main options are st_envelope, qdir_envelope, deviation_test).

1) The workflow utilizing spatstat:

E.g. Say we have a point pattern, for which we would like to test a hypothesis, as a ppp object.

X <- spruces # an example pattern from spatstat

• Test complete spatial randomness (CSR):

  • Use envelope to create nsim simulations under CSR and to calculate the functions you want. Important: use the option 'savefuns=TRUE' and specify the number of simulations nsim. See the help documentation in spatstat for possible test functions (if fun not given, Kest is used, i.e. an estimator of the K function).

    Making 2499 simulations of CSR (note the number of points is not fixed here) and estimating K-function for each of them and data:

    env <- envelope(X, nsim=2499, savefuns=TRUE)

  • Perform the test

    res <- rank_envelope(env)

  • Plot the result

    plot(res)

• A goodness-of-fit of a parametric model (composite hypothesis case)

  • Fit the model to your data by means of the function ppm or kppm. See the help documentation for possible models.

  • Use dg.global_envelope to create nsim simulations from the fitted model, to calculate the functions you want, and to make an adjusted global envelope test (either rank, directional quantile or studentized global envelope test). See the detailed example in saplings.

  • Plot the result

    plot(res)

2) The random labeling test with a mark-weighted K-function

• Generate simulations (permuting marks) and estimate the chosen marked K_f-function for each pattern using the function random_labelling (requires R library marksummary available from https://github.com/myllym/).

  curve_set <- random_labelling(mpp, mtf_name = 'm', nsim=2499, r_min=1.5, r_max=9.5)

• Then do the test and plot the result

  res <- rank_envelope(curve_set); plot(res)

3) The workflow when using your own programs for simulations:

• (Fit the model and) Create nsim simulations from the (fitted) null model.

• Calculate the functions T_1(r), T_2(r), ..., T_nsim+1(r).

• Use create_curve_set to create a curve_set object from the functions T_i(r), i=1,...,s+1.

• Perform the test and plot the result

  res <- rank_envelope(curve_set) # curve_set is the 'curve_set'-object you created

  plot(res)

• Note that for calculating an adjusted global envelope test for a composite hypothesis test, you need to write some of your own code as the function dg.global_envelope allows just models that can be simulated and fitted using spatstat.

Summary

Thus, to perform a test you always first need to obtain the test function T(r) for your data (T_1(r)) and for each simulation (T_2(r), ..., T_nsim+1(r)) in one way or another. Given the set of the functions T_i(r), i=1,...,nsim+1, you can perform a test by one of the following functions provided in this library:

Envelope tests:

• rank_envelope, the completely non-parametric rank envelope test

• st_envelope, the studentised envelope test, protected against unequal variance of T(r) for different distances r

• qdir_envelope, the directional quantile envelope test, protected against unequal variance and asymmetry of T(r) for different distances r

• normal_envelope, a parametric envelope test, which uses a normal approximation of T(r)

Deviation tests (no graphical interpretation):

• deviation_test

Note that the recommended minimum number of simulations for the rank envelope test is nsim=2499, while, for the studentised and directional quantile envelope tests and deviation tests, it is nsim=99 (or 999). (For the normal test, see its documentation.)

See, in particular, rank_envelope for further examples.

Further options and functions

It is possible to modify the curve set T_1(r), T_2(r), ..., T_nsim+1(r) for the test.

(i) You can choose the interval of distances [r_min, r_max] by crop_curves.

(ii) For better visualisation, you can take T(r)-T_0(r) by residual. Here T_0(r) is the expectation of T(r) under the null hypothesis.

The function envelope_to_curve_set can be used to create a curve_set object from the object returned by envelope. An envelope object can also directly be given to the functions crop_curves and residual.

Further, as a further reminder, for composite hypotheses the library provides the function dg.global_envelope. See a detailed example in saplings.

Author(s)

Mari Myllymäki ([e-mail], [e-mail]), Henri Seijo ([e-mail], [e-mail]), Tomáš Mrkvička ([e-mail]), Pavel Grabarnik ([e-mail]), Ute Hahn ([e-mail])

References

Myllymäki, M., Grabarnik, P., Seijo, H. and Stoyan. D. (2015). Deviation test construction and power comparison for marked spatial point patterns. Spatial Statistics 11, 19-34. doi: 10.1016/j.spasta.2014.11.004

Myllymäki, M., Mrkvička, T., Grabarnik, P., Seijo, H. and Hahn, U. (2016). Global envelope tests for spatial point patterns. Journal of the Royal Statistical Society: Series B (Statistical Methodology). doi: 10.1111/rssb.12172

Mrkvička, T., Myllymäki, M. and Hahn, U. (2016). Multiple Monte Carlo testing, with applications in spatial point processes. Statistics & Computing, accepted. (Preprint: arXiv:1506.01646 [stat.ME])

myllym/spptest documentation built on May 23, 2019, noon