Unable to extract AR(p) values from the GAMM function in mgcv

Question

I am using generalized additive models in R with an correlated structure on the residuals, however I am unable to extract the actual coefficients of the AR(p) structure even though they are provide in the output. Here is an example of an output and I am interested in being able to extract the Phi value of 0.6100947.

>GAM_sim1<-(gamm(y_sim~s(x_sim, bs="cs", k=40), correlation = corARMA(p=length(AR))))
>GAM_sim1$lme

Linear mixed-effects model fit by maximum likelihood
  Data: strip.offset(mf) 
  Log-likelihood: -250.7398
  Fixed: y ~ X - 1 
        X 
-7.442257 

Random effects:
 Formula: ~Xr - 1 | g
 Structure: pdIdnot
               Xr1        Xr2        Xr3        Xr4        Xr5        Xr6        Xr7        Xr8
StdDev: 0.01667312 0.01667312 0.01667312 0.01667312 0.01667312 0.01667312 0.01667312 0.01667312
               Xr9       Xr10       Xr11       Xr12       Xr13       Xr14       Xr15       Xr16
StdDev: 0.01667312 0.01667312 0.01667312 0.01667312 0.01667312 0.01667312 0.01667312 0.01667312
              Xr17       Xr18       Xr19       Xr20       Xr21       Xr22       Xr23       Xr24
StdDev: 0.01667312 0.01667312 0.01667312 0.01667312 0.01667312 0.01667312 0.01667312 0.01667312
              Xr25       Xr26       Xr27       Xr28       Xr29       Xr30       Xr31       Xr32
StdDev: 0.01667312 0.01667312 0.01667312 0.01667312 0.01667312 0.01667312 0.01667312 0.01667312
              Xr33       Xr34       Xr35       Xr36       Xr37       Xr38       Xr39 Residual
StdDev: 0.01667312 0.01667312 0.01667312 0.01667312 0.01667312 0.01667312 0.01667312 1.557552

Correlation Structure: AR(1)
 Formula: ~1 | g 
 Parameter estimate(s):
      Phi 
0.6100947 
Number of Observations: 151
Number of Groups: 1 

The summary above can be shorten even more by using,

>GAM_sim1$lme$modelStruct$corStruct
Correlation structure of class corAR1 representing
      Phi 
0.6100947

And now this is where the fun happens as when I try to extract this value, I get a completely different value and no further information is given.

>GAM_sim1$lme$modelStruct$corStruct[1]
[1] 1.418144

I haven't been able to figure out where the 1.4 comes from and even if I expand this out to auto-correlated errors of an AR(2) then the same situation happens when I try to extract the two Phi values.

> GAM_sim2<-(gamm(y_sim~s(x_sim, bs="cs", k=40), correlation = corARMA(p=2)))
> GAM_sim2$lme$modelStruct$corStruct
Correlation structure of class corARMA representing
     Phi1      Phi2 
0.5257324 0.1708431 
> GAM_sim2$lme$modelStruct$corStruct[1:2]
[1] 1.496342 0.345070

Does anyone know how to extract the AR values from the GAMM function in the mgcv package as I haven't been able to get a proper answer in the documentation?

Thank you

Answer 1

Try coef(GAM_sim2$lme$modelStruct$corStruct, unconstrained = FALSE).

I found this by looking through the {nlme} functions nlme:::print.corStruct and nlme:::coef.corAR1. The latter function is

function (object, unconstrained = TRUE, ...) 
{
    if (unconstrained) {
        if (attr(object, "fixed")) {
            return(numeric(0))
        }
        else {
            return(as.vector(object))
        }
    }
    aux <- exp(as.vector(object))
    aux <- c((aux - 1)/(aux + 1))
    names(aux) <- "Phi"
    aux
}

Not sure exactly sure why the transform is doing that. It resembles a hyperbolic tangent function.