Graphical Models with R by Søren Højsgaard David Edwards & Steffen Lauritzen

Author:Søren Højsgaard, David Edwards & Steffen Lauritzen
Language: eng
Format: epub
Publisher: Springer US, Boston, MA

(4.15)

where is the MLE for K A∪C under the marginal model and likewise for . The determinant of appears in the expression for the deviance in (4.8) and this determinant can be factorized in a way similar to (4.15),

(4.16)

As an illustration, consider the model displayed in Fig. 4.2 and let A={Fat13,LeanMeat}, B={Meat12,Meat13} and C={Fat11,Fat12,Meat11}. Then the triple (A,B,C) is a decomposition of its dependence graph. Secondly, the marginal models and are both saturated models so for these and . Therefore the MLE of K can be found using (4.15) as follows:

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