Description Usage Arguments Details Value Author(s) See Also Examples
This help page documents a few functions for exact evaluation of the log-likelihood and profile log-likelihood for a direct CAR model, the maximum pseudo-likelihood estimator, and least square estimators for beta and sigma given the spatial coefficient rho in the CAR covariance matrix. The exact evaluation computes the log determinant in the log-likelihood function with eigen-values of the spatial weight matrix.
1 2 3 4 5 6 7 | loglik.dCAR(pars, data, rho.cons = c(-0.249, 0.249))
ploglik.dCAR(rho, data)
get.beta.lm(rho, data)
sigmabeta(rho, data)
mple.dCAR(data, tol = 1e-06, rho0=0)
|
pars |
the parameter value to be evaluated |
rho |
the value of the spatial coefficient in the CAR covariance to be evaluated |
data |
a list containing the following objects:
|
rho.cons |
rho domain interval |
tol |
tolerance for the relative difference for two consequtive iterations in finding the MPLE; default set to be = 1e-06 |
rho0 |
starting value for iteratively finding the MPLE; default value set to be 0. |
The eigen-values can be supplied in the data
list if the
likelihood for the same data is going to be evaluated many times; if not
supplied the function use the function eigen
to find the
eigen-values of the weight matrix.
loglik.dCAR
and ploglik.dCAR
return a numeric value
of the log-likelihood evaluation. get.beta.lm
, sigmabeta
and mple
return a numeric array of the estimates.
Zhe Sha zhesha1006@gmail.com
CAR.simLM
, get.beta.glm
, mcl.dCAR
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 | ## Simulate data from a torus
set.seed(30)
n.torus <- 20
rho <- 0.15
sigma <- 1.5
beta <- c(1, 2)
XX <- cbind(rep(1, n.torus^2), log(1:n.torus^2))
mydata <- CAR.simTorus(n.torus, n.torus, rho, 1/sigma)
y <- XX %*% beta + mydata$X
mydata$data.vec <- data.frame(y=y, XX[,-1])
## evaluate the log-likelihood without lambda
loglik.dCAR(pars = c(0.1, 1, 0.9, 2.1), data = mydata)
## evaluate the log-likelihood with lamda
lambda <- eigen(mydata$W, symmetric = TRUE, only.values=TRUE)$values
mydata$lambda <- lambda
loglik.dCAR(pars = c(0.1, 1, 0.9, 2.1), data = mydata)
## evaluate the profile log-likelihood of rho
ploglik.dCAR(rho = 0.1, data = mydata)
## given rho = 0.1, find the least square estimates for beta and sigma
get.beta.lm(rho = 0.1, data = mydata)
sigmabeta(rho = 0.1, data = mydata)
## find the maximum pseudo-likelihood estimates
mple.dCAR(data = mydata)
|
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