R help - Apr 2007 - 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

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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> PLEASE do read the posting guide 
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> 

Disclaimer: http://www.kuleuven.be/cwis/email_disclaimer.htm

On 4/11/07, Tu Yu-Kang <yukangtu at hotmail.com>
wrote:
> 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.
It is possible that the ML or REML estimates for a variance component
can be zero.  The algorithm used in lme doesn't perform well in this
situation which is one reason that the lmer and lmer2 functions in the
lme4 package were created.  Could you try fitting the model with those
or provide us with the data so we can check it out?

I recommend moving this discussion to the R-SIG-mixed-models mailing
list which I am copying on this reply.