R help - Aug 2007 - Question about lme and AR(1)

Dear R users,


As far as I know, EM algorithm can be only applied to estimate parameter from a
regular exponential family.
A multivariate normal distribution with an AR(1) matrix as covariance matrix
does not belong to a regular exponential family, it is belong to  a curved
exponential family, so EM algorithm can not be applied to estimate parameters
for this kind of  distribution.
I have used nle function from nlme package to estimate variance components with
correlation=corAr1, this function uses first EM algorithm to refine the initial
estimates of the random effects variance-covariance coefficients and uses them
into a Newton-Raphson algorithm.

Do anyone know what kind of modification of the EM algorithm use lme function to
solve the problem mentioned below?

Thank you in advance for your help

Francisco



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On Sat, 18 Aug 2007, Francisco Redelico wrote:
> Dear R users,
>
>
> As far as I know, EM algorithm can be only applied to estimate parameter 
> from a regular exponential family.
No. The EM algorithm will converge to a stationary point (and except in 
artificial cases, to a local maximum) for any likelihood.

The special case you may be thinking of is that in some problems the 
E-step is equivalent to computing E[missing data | observed data] rather 
than the more general E[loglikelihood|observed data]

 	-thomas

Thomas Lumley			Assoc. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle