[R] lme invocation

[Douglas Bates]

For convenience lme offers several different ways of specifying the
formula and nesting structure of the random effects.  The default
random effects have the same model matrix as the fixed effects and the
default grouping variable.  If the model matrix has more than one
column the default structure for the variance-covariance of the random
effects is a general positive-definite symmetric (pdSymm) structure.
The default parameterization for pdSymm is pdLogChol

Orthodont is a groupedData object that carries information on the
grouping structure.  The default grouping variable is Subject.  Hence
the following specifications should be equivalent after 
  fixed = distance ~ age, data = Orthodont

 random = list(Subject = pdLogChol(~ age))
 random = list(Subject = pdSymm(~ age))
 random = ~ age | Subject
 random = ~ age
 no random specification

I'm not sure why you got different answers between your first and
second specifications.  It may be that there is a route through the
code that picks up a parameterization for pdSymm other than
pdLogChol.  The default in S-PLUS was pdMatrixLog but we changed that
in the R implementation because it is difficult (perhaps impossible)
to get an analytic gradient of the matrix exponential.

(Ted Harding) <Ted.Harding at nessie.mcc.ac.uk> writes:

> I'm trying to understand the model specification formalities
> for 'lme', and the documentation is leaving me a bit confused.
> 
> Specifically, using the example dataset 'Orthodont' in the
> 'nlme' package, first I use the invocation given in the example
> shown by "?lme":
> 
>   > fm1 <- lme(distance ~ age, data = Orthodont) # random is ~ age
> 
> Despite the Comment ("# random is ~ age"),
> 
>   > summary(fm1)
> 
> says that
> 
>   [...]
>   Random effects:
>    Formula: ~age | Subject
>    Structure: General positive-definite
>   [...]
>   Fixed effects: distance ~ age 
> 
> In view of the statement "Formula: ~age | Subject" above,
> I next try:
> 
>   > fm1<-lme(distance~age,data=Orthodont,random=~age|Subject)
>   > summary(fm1)
>   [...]
>   Random effects:
>    Formula: ~age | Subject
>    Structure: General positive-definite, Log-Cholesky parametrization
>   [...]
>   Fixed effects: distance ~ age 
> 
> So the summaries of the two invocations give identical statements
> of the Random and Fixed Effects models, but the second adds
> "Log-Cholesky parametrization" to the "Structure", and the numerical
> results are very slightly different (though hardly enough to visible
> in this case).
> 
> Finally, if I take the Comment ("# random is ~ age") from the first
> invocation and base an invocation on that:
> 
>   > fm1<-lme(distance~age,data=Orthodont,random=~age)
>   > summary(fm1)
> 
> I get results identical with the second invocation.
> 
> I'm not following how/why the first two different invocations give
> rise to the different results, and am puzzled by their relationship
> with the third (given the Comment).
> 
> Can someone explain?
> 
> With thanks,
> Ted.
> 
> 
> --------------------------------------------------------------------
> E-Mail: (Ted Harding) <Ted.Harding at nessie.mcc.ac.uk>
> Fax-to-email: +44 (0)870 167 1972
> Date: 16-Dec-02                                       Time: 23:28:43
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