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" <[EMAIL PROTECTED]>
To: <[email protected]>
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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