Improve Intensity Estimate of Fitted Cluster Point Process Model
Update the fitted intensity of a fitted cluster point process model.
improve.kppm(object, type=c("quasi", "wclik1", "clik1"), rmax = NULL, eps.rmax = 0.01, dimyx = 50, maxIter = 100, tolerance = 1e-06, fast = TRUE, vcov = FALSE, fast.vcov = FALSE, verbose = FALSE, save.internals = FALSE)
- Fitted cluster point process model (object of class
- A character string indicating the method of estimation.
Current options are
"quasi"for, respectively, first order composite (Poisson) likelihood, weighted first order composite like
- Optional. The dependence range. Not usually specified by the user.
- Numeric. A small positive number which is used to determine
rmaxfrom the tail behaviour of the pair correlation function. Namely
rmaxis the smallest value of $r$ at which $(g(r)-1)/(g(0)-1)$ falls below
- Pixel array dimensions. See Details.
- Integer. Maximum number of iterations of iterative weighted least squares (Fisher scoring).
- Numeric. Tolerance value specifying when to stop iterative weighted least squares (Fisher scoring).
- Logical value indicating whether tapering should be used to make the
computations faster (requires the package
- Logical value indicating whether to calculate the asymptotic variance covariance/matrix.
- Logical value indicating whether tapering should be used for the
variance/covariance matrix to make the computations faster
(requires the package
Matrix). Caution: This is expected to underestimate the true asymptotic variances/cova
- A logical indicating whether the details of computations should be printed.
- A logical indicating whether internal quantities should be saved in the returned object (mostly for development purposes).
This function reestimates the intensity parameters in a fitted
type="clik1" estimates are based on the first order
composite (Poisson) likelihood, which ignores dependence between the
points. Note that
type="clik1" is mainly included for testing
purposes and is not recommended for the typical user;
instead the more efficient
improve.type="none" should be used.
type="wclik1" the dependence
structure between the points is incorporated in the estimation
procedure by using the estimated pair correlation function in the
In all cases the estimating equation is based on dividing the
observation window into small subregions and count the number of points
in each subregion. To do this the observation window is first
converted into a digital mask by
as.mask where the
resolution is controlled by the argument
computational time grows with the cube of the number of subregions, so fine
grids may take very long to compute (or even run out of memory).
- A fitted cluster point process model of class
Waagepetersen, R. (2007) An estimating function approach to inference for inhomogeneous Neyman-Scott processes, Biometrics, 63, 252-258. Guan, Y. and Shen, Y. (2010) A weighted estimating equation approach to inference for inhomogeneous spatial point processes, Biometrika, 97, 867-880. Guan, Y., Jalilian, A. and Waagepetersen, R. (2013) Quasi-likelihood for spatial Cox point processes. Submitted.
# fit a Thomas process using minimum contrast estimation method # to model interaction between points of the pattern fit0 <- kppm(bei ~ elev + grad, data = bei.extra) # fit the log-linear intensity model with quasi-likelihood method fit1 <- improve.kppm(fit0, type="quasi") # compare coef(fit0) coef(fit1)