Using R INLA hyperparameter to.theta and from.theta functions

Question

R-INLA model hyperparameters have to.theta and from.theta functions that appear to be for converting between different parameterisations. It would be convenient to use those conversion functions but how does one do so?

Example with ar1

From the ar1 documentation (http://www.math.ntnu.no/inla/r-inla.org/doc/latent/ar1.pdf):

The parameter rho is represented as theta_2 = log((1 + rho)/(1 - rho))

and further down under hyper, theta2 we have to.theta 'function(x) log((1+x)/(1-x))'. It would be nice if we could use that to convert between rho and theta_2.

Let's try using an example

library(INLA)
# Example from ar1 documentation (http://www.math.ntnu.no/inla/r-inla.org/doc/latent/ar1.pdf)

#simulate data
n = 100
rho = 0.8
prec = 10
## note that the marginal precision would be
marg.prec = prec * (1-rho^2)
E=sample(c(5,4,10,12),size=n,replace=T)
eta = as.vector(arima.sim(list(order = c(1,0,0), ar = rho), n = n,sd=sqrt(1/prec)))
y=rpois(n,E*exp(eta))
data = list(y=y, z=1:n, E=E)
## fit the model
formula = y~f(z,model="ar1")
result = inla(formula,family="poisson", data = data, E=E)

That runs fine. Can we use to.theta like this?

formula.to.theta = y~f(z,model="ar1", 
                       hyper = list(rho = list(initial = to.theta(0.25))))
result = inla(formula.to.theta,family="poisson", data = data, E=E)
# Error in to.theta(0.25) : could not find function "to.theta" 

So we can't use it like that. Is there another way to specify formula.to.theta that would work?

Answer 1

Pretty sure the answer to your question is "no". The Documentation is saying, not that there are functions by those names in the package, but rather that the hyper hyperparameter element will have functions by those names with values as given in the documentation. There is no reason to think that pasting those names after formula. would result in a meaningful function. Here is how to examine the value of from.theta in the environment of a specific call to the f-function:

library(INLA)
eval( f(z, model = "ar1") )$hyper$theta3$from.theta
===== result ========
function (x) 
x
<environment: 0x7fdda6214040>
attr(,"inla.read.only")
[1] TRUE

The result from f( , "ar1") actually has three theta's each with a to and from function. You may be trying to change the hyper$thetax$param value which does not have an attr(,"inla.read.only") value of TRUE.

It would probably be more informative for you to execute this:

eval( f(z, model = "ar1") )$hyper