[R] Large determinant problem

maj at stats.waikato.ac.nz maj at stats.waikato.ac.nz
Mon Dec 10 21:16:26 CET 2007

Ravi Varadhan wrote:
> It is evident that you do not have enough information in the data to
> estimate 9 mixture components.  This is clearly indicated by a positive
> semi-definite information matrix, S, that is less than full rank.  You can
> monitor the rank of the information matrix, as you increase the number of
> components, and stop when you suspect rank-deficiency.
> Ravi.

What you say is likely to be true, but I was interested to see if this was
reflected in some of the traditional model selection criteria (AIC, BIC,
...). In this case numerical problems caused by overfitting prevent the
calculation of a diagnostic measure for overfitting. Incidentally here
other measures of overfitting that I was able to calculate continue to
indicate underfitting. Of course in the mixture model case these measures
are heuristic only as the assumptions behind their asymptotic
justification are not valid.

Dr Murray Jorgensen      http://www.stats.waikato.ac.nz/Staff/maj.html
Department of Statistics, University of Waikato, Hamilton, New Zealand
Email: maj at waikato.ac.nz                                Fax 7 838 4155
Phone  +64 7 838 4773 wk    Home +64 7 825 0441    Mobile 021 1395 862

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