saplings {GET}

Saplings data set

Description

Saplings data set

Usage

data("saplings")

Format

A data.frame containing the locations (x- and y-coordinates) of 123 trees in an area of 75 m x 75 m.

Details

A pattern of small trees (height <= 15 m) originating from an uneven aged multi-species broadleaf nonmanaged forest in Kaluzhskie Zaseki, Russia.

The pattern is a sample part of data collected over 10 ha plot as a part of a research program headed by project leader Prof. O.V. Smirnova.

References

Grabarnik, P. and Chiu, S. N. (2002) Goodness-of-fit test for complete spatial randomness against mixtures of regular and clustered spatial point processes. Biometrika, 89, 411–421.

van Lieshout, M.-C. (2010) Spatial point process theory. In Handbook of Spatial Statistics (eds. A. E. Gelfand, P. J. Diggle, M. Fuentes and P. Guttorp), Handbooks of Modern Statistical Methods. Boca Raton: CRC Press.

Myllymäki, M., Mrkvička, T., Grabarnik, P., Seijo, H. and Hahn, U. (2017). Global envelope tests for spatial point patterns. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 79: 381-404. doi: 10.1111/rssb.12172

See Also

adult_trees

Examples

# This is an example analysis of the saplings data set
#=====================================================
# Example of Myllymaki et al. (2017, Supplement S4).
if(require("spatstat.explore", quietly=TRUE)) {
  data("saplings")
  saplings <- as.ppp(saplings, W=square(75))

  # First choose the r-distances for L (r) and J (rJ) functions, respectively.
  nr <- 500
  rmin <- 0.3; rminJ <- 0.3
  rmax <- 10; rmaxJ <- 6
  rstep <- (rmax-rmin)/nr; rstepJ <- (rmaxJ-rminJ)/nr
  r <- seq(0, rmax, by=rstep)
  rJ <- seq(0, rmaxJ, by=rstepJ)

  #-- CSR test --# (a simple hypothesis)
  #--------------#
  # First, a CSR test using the L(r)-r function:
  # Note: CSR is simulated by fixing the number of points and generating nsim simulations
  # from the binomial process, i.e. we deal with a simple hypothesis.
  nsim <- 999 # Number of simulations
  
  env <- envelope(saplings, nsim=nsim,
   simulate=expression(runifpoint(ex=saplings)), # Simulate CSR
   fun="Lest", correction="translate", # T(r) = estimator of L with translational edge correction
   transform=expression(.-r),          # Take the L(r)-r function instead of L(r)
   r=r,                                # Specify the distance vector
   savefuns=TRUE)                      # Save the estimated functions
  # Crop the curves to the interval of distances [rmin, rmax]
  # (at the same time create a curve_set from 'env')
  curve_set <- crop_curves(env, r_min=rmin, r_max=rmax)
  # Perform a global envelope test
  res <- global_envelope_test(curve_set, type="erl") # type="rank" and larger nsim was used in S4.
  # Plot the result.
  plot(res) + ggplot2::ylab(expression(italic(hat(L)(r)-r)))

  # -> The CSR hypothesis is clearly rejected and the rank envelope indicates clear
  # clustering of saplings. Next we explore the Matern cluster process as a null model.
}

if(require("spatstat.model", quietly=TRUE)) {
  #-- Testing the Matern cluster process --# (a composite hypothesis)
  #----------------------------------------#
  # Fit the Matern cluster process to the pattern (using minimum contrast estimation with the pair
  # correction function)
  fitted_model <- kppm(saplings~1, clusters="MatClust", statistic="pcf")
  summary(fitted_model)

  nsim <- 19 # 19 just for experimenting with the code!!
  #nsim <- 499 # 499 is ok for type = 'qdir' (takes > 1 h)

  # Make the adjusted directional quantile global envelope test using the L(r)-r function
  # (For the rank envelope test, choose type = "rank" instead and increase nsim.)
  adjenvL <- GET.composite(X=fitted_model,
                     fun="Lest", correction="translate",
                     transform=expression(.-r), r=r,
                     type="qdir", nsim=nsim, nsimsub=nsim,
                     r_min=rmin, r_max=rmax)
  # Plot the test result
  plot(adjenvL) + ggplot2::ylab(expression(italic(L(r)-r)))

  # From the test with the L(r)-r function, it appears that the Matern cluster model would be
  # a reasonable model for the saplings pattern.
  # To further explore the goodness-of-fit of the Matern cluster process, test the
  # model with the J function:
  # This takes quite some time if nsim is reasonably large.
  adjenvJ <- GET.composite(X=fitted_model,
                     fun="Jest", correction="none", r=rJ,
                     type="qdir", nsim=nsim, nsimsub=nsim,
                     r_min=rminJ, r_max=rmaxJ)
  # Plot the test result
  plot(adjenvJ) + ggplot2::ylab(expression(italic(J(r))))
  # -> the Matern cluster process not adequate for the saplings data

  # Test with the two test functions jointly
  adjenvLJ <- GET.composite(X=fitted_model,
                     testfuns=list(L=list(fun="Lest", correction="translate",
                                          transform=expression(.-r), r=r),
                                   J=list(fun="Jest", correction="none", r=rJ)),
                     type="erl", nsim=nsim, nsimsub=nsim,
                     r_min=c(rmin, rminJ), r_max=c(rmax, rmaxJ),
                     save.cons.envelope=TRUE)
  plot(adjenvLJ)
}