profile.mlegc {gcKrig}

Profile Likelihood Based Confidence Interval of Parameters for Gaussian Copula Models in Geostatistical Count Data

Description

This function computes the (approximate) profile likelihood based confidence interval. The algorithm starts by choosing two starting points at different sides of the MLE and using an iterative process to find the approximate lower and upper bound.

Usage

## S3 method for class 'mlegc'
profile(fitted, par.index, alpha = 0.05, start.point = NULL,
        method = 'GQT', nrep = 1000, seed = 12345, ...)
          

Arguments

fitted

an object of class mlegc, typically inherited from function mlegc.

par.index

the index of the parameter which should be profiled.

alpha

the significance level, default is 0.05 which corresponds to 95 percent confidence interval.

start.point

numeric vector of length 2 indicating the starting points for finding the left and right bound. If start.point = NULL then the default starting points will be used.

method

Two methods are implemented. If method = 'GHK' then the simulated likelihood will be used, if method = 'GQT' then the surrogate likelihood will be used.

nrep

the Monte Carlo size of the importance sampling algorithm for likelihood approximation; only need to be specified if method = 'GHK'.

seed

seed of the pseudorandom generator used in Monte Carlo simulation; only need to be specified if method = 'GHK'.

...

other arguments passed.

Value

Lower and upper bounds of the approximate confidence interval.

Author(s)

Zifei Han [e-mail]

References

Masarotto, G. and Varin, C. (2012) Gaussian copula marginal regression. Electronic Journal of Statistics 6:1517-1549. https://projecteuclid.org/euclid.ejs/1346421603.

Masarotto, G. and Varin C. (2017). Gaussian Copula Regression in R. Journal of Statistical Software, 77(8), 1–26. doi: 10.18637/jss.v077.i08.

Han, Z. and De Oliveira, V. (2018) gcKrig: An R Package for the Analysis of Geostatistical Count Data Using Gaussian Copulas. Journal of Statistical Software, 87(13), 1–32. doi: 10.18637/jss.v087.i13.

See Also

mlegc

Examples

## Not run: 
data(LansingTrees)
Treefit4 <- mlegc(y = LansingTrees[,3], x = LansingTrees[,4],
                    locs = LansingTrees[,1:2], marginal = zip.gc(link = 'log'),
                    corr = matern.gc(kappa = 0.5, nugget = TRUE), method = 'GHK')
summary(Treefit4)

profile(Treefit4, 1, 0.05,  method = 'GHK', nrep = 1000, seed = 12345)
profile(Treefit4, 2, 0.05,  method = 'GHK', nrep = 1000, seed = 12345)
profile(Treefit4, 3, 0.05,  method = 'GHK', nrep = 1000, seed = 12345)
profile(Treefit4, 4, 0.05,  method = 'GHK', nrep = 1000, seed = 12345)
profile(Treefit4, 5, 0.05, method = 'GHK', nrep = 1000, seed = 12345)

## End(Not run)