R: Maximum likelihood estimation for Markov point process models.

newtonraphson.mpp {MppMLE}

R Documentation

Maximum likelihood estimation for Markov point process models.

Description

Maximum likelihood estimation for Markov point process models using Newton-Raphson with MCMC estimates of score and observed information.

Usage

newtonraphson.mpp(inhompar,interactpar,interactradii=c(),smpsize,space,data,border=0,model,trustfactor=100,torus=F,stopcrit=10e-8,L=c(),constraint=T,fix=c())

Arguments

`inhompar, interactpar, interactradii`	parameters for Markov point processes, see details on models
`smpsize`	size of MCMC sample used for estimation of score and observed information
`space`	specifies subsampling of birth-death Markov chain
`data`	a `ppp` `spatstat` object
`border`	border correction. The reduced observation window is obtained by trimming off a margin of width `border` from the observation window of the data pattern. If zero, no border correction is used
`model`	specifies the type of Markov point process being fitted, see details
`trustfactor`	Parameter used when evaluating the adequacy of importance sampling, see Moeller and Waagepetersen (2003) p. 148
`torus`	if true, toroidal edge correction is used
`stopcrit`	Newton-Raphson iterations stop when Euclidean distance between two consecutive parameter estimates and norm of score is less than stopcrit (if some parameters are constrained only the first criterion is used)
`L`	contrast matrix to calculate Wald statistic, see Moeller and Waagepetersen (2003) p. 150.
`constraint`	if true, interaction parameters are constrained to be non-positive
`fix`	if not equal to `c()` it can be used to fix parameters at the starting values. In that case it should be a vector of `T`'s or `F`'s of length equal to the total number of parameters in `inhompar` and `interactpar`

Details

This function computes maximum likelihood estimates for a Markov point process model using Newton-Raphson updates where the score and information matrix is estimated using MCMC. Interaction parameters are for the exponential family representation.

Note the MCMC simulation procedure terminates if the simulated number of points exceeds 5000.

data

The observation window must be of type rectangular

models

0 is the multiscale process. In this case interactradii[1] specifies the maximal interaction range and interactionradii[2] specifies the number of intervals (of same length) with different interaction parameters. The interaction parameters are given in interactpar. The vector inhompar should have one component: the first order interaction potential (AKA the chemical activity).

1 implements the overlap process used for Norwegian spruces data in Moeller and Waagepetersen (2003). In this case interactradii[0] specifies the factor for computing influence zones.

2 is a multitype (0 or 1) Strauss process where inhompar contains coefficients for a fourth-order polynomial in the y coordinate while interactpar contains 3 interactionparameters for interactions between type 0 points, between type 0 and type 1 points, and between type 1 points. The interaction radius is given in interactradii.

3 is as 2 but only one interactionparameter is used regardless of type of the points.

4 is the hierarchical model used for ants's nests in Moeller and Waagepetersen (2006).

Value

A list with components: the sufficient statistics, the gradient, the observed information, the parameter estimate, the number of MCMC samples used, and the Wald statistic.

Author(s)

Rasmus Waagepetersen rw@math.aau.dk http://www.math.aau.dk/~rw

References

Moeller, J. and Waagepetersen, R. (2003) Statistical inference and simulation of spatial point processes. Chapman & Hall/CRC Press, Boca Raton.

Moeller, J. and Waagepetersen, R. (2006) Modern statistics for spatial point processes. (prepared as a discussion paper for Scandinavian Journal of Statistics).