[R] lme RE variance computation

[Spencer Graves]

      It may help to explicitly distinguish between parameter estimates 
and the true but unknown and unknowable "reality" that is assumed to 
have generated the data.  In that "reality", all variance components are 
nonnegative.  Generally inferior algorithms can compute negative 
variance components.  These were quite useful prior to the advent of 
modern computers and software like the nlme package. 

      I suggest you think very carefully about the problem you want to 
solve.  I have found Pinheiro and Bates (2000) Mixed-Effects Models in S 
and S-Plus (Springer) quite helpful both in theory and in how to 
implement it.  Bates is the primary architect of lme, nlme, etc., and 
this book provides basic documentation for that package.  In particular, 
I would expect that "simulate.lme" could be quite useful if you have any 
doubts about any issue. 

      hope this helps.  spencer graves

Dimitris Rizopoulos wrote:

> Hi Steve,
>
> Estimation problems for the variance components in linear mixed models 
> are usually occur for two reasons:
>
> 1. Due to model misspecification, i.e., using years instead of decades 
> may show no variability in the slopes
>
> 2. Because the data do not support the assumptions of the linear mixed 
> model (i.e., positive definite covariance matrix for the 
> random-effects => increasing variance with time).
>
> These may cause zero or even negative variance components. For more 
> info you could take a look at Verbeke and Molenberghs (2000, Section 
> 5.6) and Searle, Casella and McCullogh (1992, Section 3.5).
>
> I don't know the exact formulation you are using, but maybe you could 
> consider an analogue of you model using "gls", i.e.,
>
> lme(..., random=~1|id)
> gls(..., corr=corCompSymm(form=~1|id))
>
>
> The references mentioned above are:
>
> @Book{verbeke.molenberghs:00,
>  author    = {G. Verbeke and G. Molenberghs},
>  title     = {Linear Mixed Models for Longitudinal Data},
>  year      = {2000},
>  address   = {New York},
>  publisher = {Springer-Verlag}
> }
>
> @Book{searle.et.al:92,
>  author    = {S. Searle and G. Cassela and C. McCulloch},
>  title     = {Variance Components},
>  year      = {1992},
>  address   = {New York},
>  publisher = {Wiley}
> }
>
> I hope it helps.
>
> Best,
> Dimitris
>
> ----
> Dimitris Rizopoulos
> Ph.D. Student
> Biostatistical Centre
> School of Public Health
> Catholic University of Leuven
>
> Address: Kapucijnenvoer 35, Leuven, Belgium
> Tel: +32/16/396887
> Fax: +32/16/337015
> Web: http://www.med.kuleuven.ac.be/biostat/
>     http://www.student.kuleuven.ac.be/~m0390867/dimitris.htm
>
>
> ----- Original Message ----- From: "Steve Roberts" 
> <steve.roberts at man.ac.uk>
> To: <r-help at stat.math.ethz.ch>
> Sent: Tuesday, September 21, 2004 1:38 PM
> Subject: [R] lme RE variance computation
>
>
>> As I understand it lme (in R v1.9.x) estimates random effect variances
>> on a log scale, constraining them to be positive. Whilst this seems
>> sensible, it does lead to apparently biased estimates if the variance is
>> actually  zero - which makes our simulation results look strange. Whilst
>> we need to think a bit deeper about it - I still haven't got my head
>> around what a negative variance could mean - does anyone know a
>> way to take away the contraint and allowing zero or negative
>> variances?
>>
>> Steve.  Dr Steve Roberts
>>  steve.roberts at man.ac.uk
>>
>> Senior Lecturer in Medical Statistics,
>> CMMCH NHS Trust and University of Manchester Biostatistics Group,
>> 0161 275 5192 / 0161 276 5785
>>
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-- 
Spencer Graves, PhD, Senior Development Engineer
O:  (408)938-4420;  mobile:  (408)655-4567