[R] lme RE variance computation

[Dimitris Rizopoulos]

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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