Solving Mixed Models with EM-Algorithm

Frank Simon · science forum beginner Joined: 18 Aug 2005 Posts: 2

Hi !

I am a student of applied mathematics and I am searching a good
book/reference/explanation/(or anything else) for the following problem.

Many statistical programms SPS/SAS can handle, so called MIXED Models.
This is

$y=X\beta+Z\gamma+\varespilon$

Where gamma contains the normal distributed random effects and
varespilon is also normal distributed both with mean zero. The
covariance between epsilon and gamma should vanish.

In my work I have to solve such a mixed model. (But the variance
matrices are unknown ! They have to be parametrized by some set of
variables. In my case it something like a autoregressive process of
first order for the varepsilon case. A Toeplitz Matrix.)

I hope I described exactly the thing I have to solve.

All statistical programms SPS/SAS can solve such MIXED Models with the
very good Expectation-Maximization Algorithm, which is really
straightforward, if you have understand it. (Which is also not my
problem anymore). EM-Algorithm doesn't use Least Squares. It uses
Maximum-Likelihood principle.

The EM-Algorithms fills up the given dataset with "Latent Data". Which
is a neat trick to get a known distribution. In my case I don't really
know what latent data I have to choose to get a known distribution.

The book I alread have "Statistical Analysis of Missing Data" by Rubin
doesn't seem to deal this topic exactly. Maybe one of the people here
know's what is going behind the Blackboxes SAS and SPS.

Thank you

Frank Simon

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