How can I improve the estimation for clustering models using kppm function in spatstat

Question

I have simulated some point pattern from Thomas and MatClust models and, I was trying to fit the parameters of the model using kppm() function from spatstat. Nevertheless, I obtained a no good estimation for the parameters. I am wondering while the estimation it is so far to the real one for the next sentence:


# simulated point point pattern
set.seed(8)
pp_obs <- rThomas(kappa = 10, mu =  10, scale = 0.05)

#--------------------------------------------------------
# Thomas fitted

mod_Thomas_fit <- kppm(pp_obs, ~ 1, "Thomas",statistic = "K",method = "mincon")
mod_Thomas_fit

Stationary cluster point process model
Fitted to point pattern dataset ‘pp_obs’
Fitted by minimum contrast
    Summary statistic: K-function

Uniform intensity:  97

Cluster model: Thomas process
Fitted cluster parameters:
      kappa       scale 
12.13783476  0.04393052 
Mean cluster size:  7.991541 points

#--------------------------------------------------------
# Thomas fitted

mod_Cluster_fit <- kppm(pp_obs, ~ 1, "MatClust",statistic = "K",method = "mincon")
mod_Cluster_fit

Stationary cluster point process model
Fitted to point pattern dataset ‘pp_obs’
Fitted by minimum contrast
    Summary statistic: K-function

Uniform intensity:  97

Cluster model: Matern cluster process
Fitted cluster parameters:
      kappa       scale 
12.52772823  0.08116434 
Mean cluster size:  7.742824 points

Someone that can I help me to improve the parameter estimation for this kind of patterns or get a good estimation.

I really appreciated your assistance.

I have used the different methods to estimate "mincon", "click2", "palm". I also implemented the "K" and "pcf" functions but, the estimation does not improve

score 1 · Answer 1 · answered Mar 18 '23 at 02:51

You don't specify what you think is wrong with the results.

You simulated a single realisation from a process with intensity 100 and parameters kappa=10, mu=10, scale=0.05. Your simulated pattern has 97 points so the estimate of intensity will always be 97, which I would consider acceptably close to 100. The first fitted model has parameters kappa=12.1, mu = 8.0, scale = 0.044, which I would consider acceptably close to the true values 10, 10, 0.05.

The parameter estimates were obtained from a single realisation of the model. The dataset is relatively small. So, we can expect moderately large errors in the parameter estimates.

It is possible to improve performance by using other arguments to kppm. For minimum contrast fits you could use statargs to modify the estimator of the K function or pair correlation function.

How can I improve the estimation for clustering models using kppm function in spatstat

1 Answers1