When one of the level - models performs significantly much better than the rest—like in the Euthyroid and Vowel datasets  MLR performs either as good as BestCV by selecting the best performing level model or better than BestCV
MLR has an advantage over the other three level   generalizers in that its model can easily be interpreted  Examples of the combination weights it derives  for the probability based model M ′ appear in Table - for the Horse Credit Splice Abalone Waveform Led and Vowel datasets The weights indicate the relative importance of the level generalizers for each prediction class  For example  in the Splice dataset  in Table NB is the b dominant generalizer for predicting class    NB and IB  are both good at predicting class and all three generalizers make a worthwhile contribution to the prediction of class In contrast in the Abalone dataset all three generalizers contribute substantially to the prediction of all three classes Note that the weights for each class do not sum to one because no such constraint is imposed on MLR

## 3.2 Are Non-Negativity Constraints Necessary?

a and LeBlanc Tibshirani use the stacked generalization Both Breiman method in a regression setting and report that it is necessary to constrain the regression cccefficients to be non negative in order to guarantee that stacked regression improves pre dictive accuracy Here we investigate this finding in the domain of classification tasks To assess the effect of the non negativity constraint on performance three versions of MLR are employed to derive the level - model M ′
i each linear regression in MLR is calculated with an intercept constant that is

I
weights for the I classes but without any constraints ii each linear regression is derived with neither an intercept constant I weights for I classes  nor constraints iii  each linear regression is derived without an intercept constant  but with non negativity constraints I non negative weights for I classes
The third version is the one used for the results presented earlier  Table   shows the results of all three versions They all have almost indistinguishable error rates We conclude that in classification tasks  non negativity constraints are not necessary to guarantee that stacked generalization improves predictive accuracy However there is another reason why it is a good idea to employ non negativity con straints Table shows an example of the weights derived by these three versions of MLR on dataset The third version shown in column iii supports a more perspicuous the Led interpretation of each level   generalizer s contribution to the class predictions than do the other two In this dataset IB is the dominant generalizer in predicting classes and and both NB and IB  make a worthwhile contribution in predicting class as evidenced by their high weights However the negative weights used in predicting these classes render the interpretation of the other two versions much less clear