A conditional independence graph is a concise representation of pairwiseconditional independence among many variables. Graphical Random Forests (GRaFo)are a novel method for estimating pairwise conditional independencerelationships among mixed-type, i.e. continuous and discrete, variables. Thenumber of edges is a tuning parameter in any graphical model estimator andthere is no obvious number that constitutes a good choice. Stability Selectionhelps choosing this parameter with respect to a bound on the expected number offalse positives (error control). The performance of GRaFo is evaluated and compared with various other methodsfor p = 50, 100, and 200 possibly mixed-type variables while sample size is n =100 (n = 500 for maximum likelihood). Furthermore, GRaFo is applied to datafrom the Swiss Health Survey in order to evaluate how well it can reproduce theinterconnection of functional health components, personal, and environmentalfactors, as hypothesized by the World Health Organization's InternationalClassification of Functioning, Disability and Health (ICF). Finally, GRaFo isused to identify risk factors which may be associated with adverseneurodevelopment of children who suffer from trisomy 21 and experiencedopen-heart surgery. GRaFo performs well with mixed data and thanks to Stability Selection itprovides an error control mechanism for false positive selection.
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