Dear gR-folk! As Steffen previously announced, Michael Perlman and I have been doing some work on model selection in Gaussian graphical models. In a Gaussian graphical model, the conditional independences that define the model hold iff partial correlation coefficients are zero. Thus, for model selection (i.e. determination of a graph from data) we can simply test, for each possible edge, a hypothesis about a zero partial corr. coeff. If the hypothesis is accepted, then we do not include the associated edge in the graph. If it is rejected, then we include the edge. In a paper appearing in September's issue of Biometrika, see http://www.stat.washington.edu/drton/Papers/2004sin.pdf for a preprint, we show, in the setting of undirected graphs, how Fisher's z-transform and Sidak's inequality can be used to test these multiple hypotheses simultaneously. Carrying out the tests simultaneously, we can control the overall error rate of incorrect edge inclusion in our model selection. In a follow-up paper, we show how to apply this model selection procedure (which we named SIN) in the setting of DAGs and chain graphs. This paper is available as Univ. of Washington Tech. Report 457 at http://www.stat.washington.edu/www/research/reports/ In particular, we improve our simultaneous testing procedure using a p-value adjustment due to Holm. The paper also provides a brief overview of Gaussian graphical models, which might be interesting in its own right. I have prepared a version 0.1 of an R package that implements SIN model selection. The package with name 'SIN' can be downloaded from http://cran.r-project.org/ I am planning on revising the package over the next few weeks as I am not happy with how I handled the labelling of the variables (be careful with the chain graph routines). Suggestions are welcome. Best wishes, Mathias (Drton)
[R--gR] SIN model selection
1 message · Mathias Drton