[R] negative variances

[Dimitris Rizopoulos]

In fact this implies that random-effects might not be the way to go 
for your data. When you're using random-effects the marginal 
covariance matrix is of the form:

V = Z D Z^t + Sigma,

where Z is the design matrix for the random-effects, D their 
covariance matrix and Sigma is the covariance matrix for the error 
terms. If the correlation between the repeated measurements of your 
sample units could be explain by a set of random-effects, then D 
should be a positive definite matrix. However, note that V might be 
positive definite even if D it is not, as in your case, which implies 
that the assumption of some common random-effects that the sample 
units share might not be valid.

Alternatively, you could model directly the marginal covariance matrix 
V using the 'correlation' and 'weights' arguments of gls().

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/(0)16/336899
Fax: +32/(0)16/337015
Web: http://med.kuleuven.be/biostat/
     http://www.student.kuleuven.be/~m0390867/dimitris.htm



----- Original Message ----- 
From: "Tu Yu-Kang" <yukangtu at hotmail.com>
To: <r-help at stat.math.ethz.ch>
Sent: Wednesday, April 11, 2007 12:34 PM
Subject: [R] negative variances


> Dear R experts,
>
> I had a question which may not be directly relevant to R but I will 
> be
> grateful if you can give me some advices.
>
> I ran a two-level multilevel model for data with repeated 
> measurements over
> time, i.e. level-1 the repeated measures and level-2 subjects. I 
> could not
> get convergence using lme(), so I tried MLwiN, which eventually 
> showed the
> level-2 variances (random effects for the intercept and slope) were
> negative values. I know this is known as Heywood cases in the 
> structural
> equation modeling literature, but the only discussion on this 
> problem in
> the literature of multilevel models and random effects models I can 
> find is
> in the book by Prescott and Brown.
>
> Any suggestion on how to solve this problem will be highly 
> appreciated.
>
> Many thanks.
>
> With best regards,
>
> Yu-Kang
>
>


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