Options for General Correlation Structure in nlme (R)

Question

I am trying to decide what covariance structure top specify for a mixed model in R. When comparing two models with an unstructured covariance (corSymm) i can specify whether or not to allow coefficients to vary.

Here is my syntax

str(lCtr <- lmeControl(opt = "optim"))
m1 <- lme(y ~  Time, random = ~ 1 + Time | id, data=sdata, na.action = na.exclude, 
           correlation = corSymm(fixed = FALSE), control = lCtr)
m2 <-  lme(y ~ Time, random = ~ 1 + Time | id, data=sdata, na.action = na.exclude,
           correlation = corSymm(fixed = TRUE), control = lCtr)
-2*logLik(m1)
-2*logLik(m2)

and results

'log Lik.' 1336.108 (df=21)
'log Lik.' 1354.123 (df=6)

What confuses me is why i get more degrees of freedom when I specify that the coefficients are allowed to vary than the other way. What does it mean that the coefficients are allowed to vary?

Is there a better way to specify an unstructured covariance for the model?

Answer 1

The degrees of freedom refers to the number of parameters that are estimated to determine the likelihood. See df = p + length(coef(object[["modelStruct"]])) + as.integer(!fixSig)) in the last line in the code of the function below.

> getAnywhere(logLik.lme)
A single object matching ‘logLik.lme’ was found
It was found in the following places
  registered S3 method for logLik from namespace nlme
  namespace:nlme
with value

function (object, REML, ...) 
{
    fixSig <- attr(object[["modelStruct"]], "fixedSigma")
    fixSig <- !is.null(fixSig) && fixSig
    od <- object$dims
    p <- od$ncol[[od$Q + 1L]]
    N <- od$N
    estM <- object$method
    if (missing(REML)) 
        REML <- estM == "REML"
    val <- object[["logLik"]]
    if (REML && (estM == "ML")) {
        val <- val + (p * (log(2 * pi) + 1L) + (N - p) * log(1 - 
            p/N) + sum(log(abs(svd.d(object$varFix)))))/2
    }
    if (!REML && (estM == "REML")) {
        val <- val - (p * (log(2 * pi) + 1L) + N * log(1 - p/N) + 
            sum(log(abs(svd.d(object$varFix)))))/2
    }
    structure(val, class = "logLik", nall = N, nobs = N - REML * 
        p, df = p + length(coef(object[["modelStruct"]])) + as.integer(!fixSig))
}
<bytecode: 0x47df7dd8>
<environment: namespace:nlme>