Kinhom.log {ecespa}

Simulation envelopes from the fitted values of a logistic model

Description

Computes simulation envelopes for (in-)homogeneous K-function simulating from a vector of probabilitiesn.

Usage

Kinhom.log (A, lambda=NULL, mod=NULL, lifemark="0", prob=NULL,
			r=NULL, nsim=99, correction="trans", ngrid=200)

Arguments

A

A marked point pattern with the ppp format of spatstat.

lambda

Optional. Values of the estimated intensity function as a pixel image (object of class "im" of spatstat) giving the intensity values at all locations of A.

mod

A fitted model. An object of class ppm.

lifemark

Level of the marks of A which represents the "live" or "succes" cases.

prob

Numeric vector, with length equal to the number of points of A, represeting the fitted values of a logistic model fitted to A marks.

r

Numeric vector. The values of the argument r at which the K(r) functions should be evaluated.

nsim

Number of simulated point patterns to be generated when computing the envelopes.

correction

A character item selecting any of the options "border", "bord.modif", or "translate". It specifies the edge correction to be applied when computing K-functions.

ngrid

Dimensions (ngrid by ngrid) of a rectangular grid of locations where predict.ppm would evaluate the spatial trend of the fitted models.

Details

This function is a wrapper to compute the critical envelopes for Monte Carlo test of goodness-of-fit of (in-)homogeneous K functions, simulating from the fittted values of a logistic model (i.e. a binomial GLM with logit link) fitted to the marks ("failure", "success") of a "binomially"-marked point pattern. This is particularly interesting in plant ecology when considering alternatives to the random mortality hypothesis (Kenkel 1988). This hypothesis is usually tested building Monte Carlo envelopes from the "succesful" patterns resulting from a random labelling of a "binomially"-marked point pattern (this is equivalent to a random thinning of the whole pattern irrespective of the marks). As tree mortality is rarely random but instead can be modelled as a function of a certain number of covariates, the most natural alternative to the random mortality hypothesis is the logistic mortality hypothesis, that can be tested thinning the original pattern of trees with retention probabilities defined by the fitted values of a logistic model (Batista and Maguire 1998, Olano et al. 2008).

Kinhom.log will compute the envelopes by thinning the unmarked point pattern A with retention probabilities prob. If no prob vector is provided, all points will be thinned with the same probability ( number of "live" points / number of points ), i.e. Kinhom.log will compute random thinning envelopes.

Kinhom.log will compute envelopes both to homogeneous and inhomogeneous K functions. If no lambda or mode arguments are provided, Kinhom.log assumes that the original pattern is homogeneous and will use a constant lambda to compute the inhomogeneous K (i.e. it will compute the homogeneous K). The most convenient use with inhomogeneous point patterns is to provide the argument mod with an inhomogeneous Poisson model fitted to the original pattern of 'live' points (with spatstat function ppm; see the examples). This model will be used to compute (and to update in the simulations) the inhomogeneous trend (i.e. the "lambda") of the patterns. If the argument lambda is provided but not mod, these lambda will be used as a covariate to fit an inhomogeneous Poisson model that will be used to compute (and to update in the simulations) the inhomogeneous spatial trend.

Kinhom.log will produce an object of class 'ecespa.kci' that can be easily ploted (see the examples). This is accomplished by the S3 ploth method plot.ecespa.kci; it will plot the K-function and its envelopes (actually, it will plot the most usual L-function = sqrt[K(r)/pi]-r).

Value

Kinhom.log returns an object of class ecespa.kci, basically a list with the following items:

r

Numeric vector. The values of the argument r at which the K(r) functions have been evaluated.

kia

Numeric vector. Observed (in-)homogeneous K function.

kia.s

Matrix of simulated (in-)homogeneous K functions.

datanamea

Name of point pattern A.

modnamea

Name of model mod.

type

Type of analysis. Always "Kinhom.log".

probname

Name of the vector of fitted retention probabilities prob.

modtrend

Spatial trend (formula) of the model mod.

nsim

Number of simulations.

Warning

As this implementation involves the use of images as the means of evaluation of the (inhomogeneous) spatial trend, and a mask based on those images will be used as the point pattern window, the "Ripley's" or "isotropic" edge correction can not be employed.

Author(s)

Marcelino de la Cruz Rot

References

Batista, J.L.F. and Maguire, D.A. 1998. Modelling the spatial structure of tropical forests. For. Ecol. Manag., 110: 293-314.

Kenkel, N.C. 1988. Pattern of self-thinning in Jack Pine: testing the random mortality hypothesis. Ecology, 69: 1017-1024.

Olano, J.M., Laskurain, N.A., Escudero, A. and De la Cruz, M. 2009. Why and where adult trees die in a secondary temperate forest? The role of neighbourhood. Annals of Forest Science, 66: 105. doi:10.1051/forest:2008074.

Examples

  
   
   data(quercusvm)
   
   # set the number of simulations (nsim=199 or larger for real analyses)
   nsim<- 19

   # read fitted values from logistic model:
   
   
   probquercus <-c(0.99955463, 0.96563477, 0.97577094, 0.97327199, 0.92437309,
   0.84023396, 0.94926682, 0.89687281, 0.99377915, 0.74157478, 0.95491518,
   0.72366493, 0.66771787, 0.77330148, 0.67569082, 0.9874892, 0.7918891, 
   0.73246803, 0.81614635, 0.66446411, 0.80077908, 0.98290508, 0.54641754,
   0.53546689, 0.73273626, 0.7347013, 0.65559655, 0.89481468, 0.63946334,
   0.62101995, 0.78996371, 0.93179582, 0.80160346, 0.82204428, 0.90050059,
   0.83810669, 0.92153079, 0.47872421, 0.24697004, 0.50680935, 0.6297911, 
   0.46374812, 0.65672284, 0.87951682, 0.35818237, 0.50932432, 0.92293014,
   0.48580241, 0.49692053, 0.52290553, 0.7317549, 0.32445982, 0.30300865,
   0.73599359, 0.6206056, 0.85777043, 0.65758613, 0.50100406, 0.31340849, 
   0.22289286, 0.40002879, 0.29567678, 0.56917817, 0.56866864, 0.27718552,
   0.4910667, 0.47394411, 0.40543788, 0.29571349, 0.30436276, 0.47859015,
   0.31754526, 0.42131675, 0.37468782, 0.73271225, 0.26786274, 0.59506388, 
   0.54801851, 0.38983575, 0.64896835, 0.37282031, 0.67624306, 0.29429766,
   0.29197755, 0.2247629, 0.40697843, 0.17022391, 0.26528042, 0.24373722,
   0.26936163, 0.13052254, 0.19958585, 0.18659692, 0.36686678, 0.47263005,
   0.39557661, 0.68048997, 0.74878567, 0.88352322, 0.93851375)
   
  

   ################################ 
   ## Envelopes for an homogeneous point pattern:
   
   cosap <- Kinhom.log(A=quercusvm, lifemark="0",  prob=probquercus, nsim=nsim)

   plot(cosap)

   
   ################################ 
   ## Envelopes for an inhomogeneous point pattern:
   
   ## First, fit an inhomogeneous Poisson model to alive trees :
   
   quercusalive <- unmark(quercusvm[quercusvm$marks == 0])

    mod2 <- ppm(quercusalive, ~polynom(x,y,2))

    ## Now use mod2 to estimate lambda for K.inhom:
    
    cosapm <- Kinhom.log(A=quercusvm, lifemark="0", prob=probquercus, 
                                   nsim=nsim, mod=mod2)

   
   ################################ 
   ## An example of homogeneous random thinning:
      
   cosa <- Kinhom.log(A=quercusvm, lifemark="0", nsim=nsim)
   
   plot(cosa)