An event is ci logci 0 which is in nite

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Unformatted text preview: nately it is not so. One given of tree-based modeling is that a right-sized model is arrived at by purposely over- tting the data and then pruning back the branches. A program that aborts due to a numeric exception during the rst stage is uninformative to say the least. Of more concern is that this edge e ect does not seem to be limited to the pathologic case detailed above. Any near approach to the boundary value  = 0 leads to large values of the deviance, and the procedure tends to discourage any nal node with a small number of events. An ad hoc solution is to use the revised estimate ^ = max ; P ^k  ti where k is 1 2 or 1 6. That is, pure nodes are given a partial event. This is similar to the starting estimates used in the GLM program for a Poisson regression. This is unsatisfying, however, and we propose instead using a shrinkage estimate. Assume that the true rates j for the leaves of the tree are random values P P from a Gamma;  distribution. Set  to the observed overall event rate ci = ti , and let the user choose as a prior the coe cient of variation k = =. A value of k = 0 represents extreme pessimism  the leaf nodes will all give the same result", whereas k = 1 represents extreme optimism. The Bayes estimate of the event rate for a node works out to be P ^ k = + P ci ;  + ti ^ where = 1=k2 and = =. This estimate is scale invariant, has a simple interpretation, and shrinks least those nodes with a large amount of information. In practice, a value of k = 10 does essentially no shrinkage. For method='poisson', the optional parameters list is the single number k, with a default value of 1. This corresponds to prior coe cient of variation of 1 for the estimated j . We have not nearly enough experience to decide if this is a good value. It does stop the log0 message though. Cross-validation does not work very well. The procedure gives very conservative results, and quite often declares the no-split tree to be the best. This may be another artifact of the edge e ect. 8.3 Example: solder data The solder data frame, as explained in the Splus help le, is a design object with 900 observations, which are the results of an experiment varying 5 factors relevant to the wave-soldering procedure for mounting components on printed circuit boards. The 37 response variable, skips, is a count of how many solder skips appeared to a visual inspection. The other variables are listed below: Opening Solder Mask PadType Panel factor: factor: factor: factor: factor: amount of clearance around the mounting pad S amount of solder used Thin Thick Type of solder mask used 5 possible Mounting pad used 10 possible panel 1, 2 or 3 on board being counted M L In this call, the rpart.control options are modi ed: maxcompete = 2 means that only 2 other competing splits are listed default is 4; cp = .05 means that a smaller tree will be built initially default is .01. The y variable for Poisson partitioning may be a two column matrix con...
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This document was uploaded on 09/26/2013.

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