spMC (version 0.3.2)

tpfit: One-dimensional Model Parameters Estimation

Description

The function estimates the model parameters of a 1-D continuous lag spatial Markov chain. Transition rates matrix along a user defined direction and proportions of categories are computed.

Usage

tpfit(data, coords, direction, method = "ml",
      tolerance = pi/8, max.it = 9000, mle = "trm", ...)

Value

An object of the class tpfit is returned. The function print.tpfit is used to print the fitted model. The object is a list with the following components:coefficientsthe transition rates matrix computed for the user defined direction.propa vector containing the proportions of each observed category.tolerancea numerical value which denotes the tolerance angle (in radians).

Rdversion

1.1

Details

A 1-D continuous-lag spatial Markov chain is probabilistic model which involves a transition rate matrix $R$ computed for the direction $\phi$. It defines the transition probability $\Pr(Z(s + h) = z_k | Z(s) = z_j)$ through the entry $t_{jk}$ of the following matrix $$T = \mbox{expm} (h R),$$ where $h$ is a positive lag value.

Three methods are available to calculate entries of the transition rate matrix. The mean length method is performed by the use of the function tpfit_ml, the iterated least squares are applied through the function tpfit_ils, while the function tpfit_me implements the maximum entropy method.

References

Carle, S. F., Fogg, G. E. (1997) Modelling Spatial Variability with One and Multidimensional Continuous-Lag Markov Chains. Mathematical Geology, 29(7), 891-918.

Sartore, L. (2010) Geostatistical models for 3-D data. M.Phil. thesis, Ca' Foscari University of Venice.

See Also

predict.tpfit, print.tpfit, multi_tpfit, transiogram

Examples

data(ACM)

# Estimate the parameters of a 
# one-dimensional MC model
tpfit(ACM$MAT5, ACM[, 1:3], c(0, 0, 1))