Multiplicatively interacting factors selectively influencing parameters in multiple response class processing and rate trees

Evidence in many experiments indicates that the processes involved in producing responses are arranged in a tree structure. Evidence often indicates further that an experimental factor, such as item similarity, changes a single parameter, leaving others invariant. In typical studies, a few tree structures are hypothesized a priori, and tested by goodness of fit. With the method of Tree Inference, a tree is constructed by examining the data to see if patterns occur that are predicted when two factors selectively influence different processes (Schweickert & Chen, 2008). The patterns can reveal, for example, whether selectively influenced processes are executed in order, and what the order is. If the patterns do not occur, one can conclude that no tree is possible in which the factors selectively influence processes. In earlier work, three restrictions were imposed on the trees considered: There were two classes of responses; parameters were probabilities, bounded above by 1; and factors were assumed to change parameters associated with children of a single vertex. More general results are derived here, removing these restrictions. Results on representation, uniqueness of parameters, uniqueness of tree structure, and mixtures of trees are presented.     

Is it worth generating rules from neural network ensembles?

Although many authors generated comprehensible models from individual networks, much less work has been done in the explanation of ensembles. DIMLP is a special neural network model from which rules are generated at the level of a single network and also at the level of an ensemble of networks. We applied ensembles of 25 DIMLP networks to several datasets of the public domain and a classification problem related to post-translational modifications of proteins. For the classification problems of the public domain, the average predictive accuracy of rulesets extracted from ensembles of neural networks was significantly better than the average predictive accuracy of rulesets generated from ensembles of decision trees. By varying the architectures of DIMLP networks we found that the average predictive accuracy of rules, as well as their complexity were quite stable. The comparison to other rule extraction techniques applied to neural networks showed that rules generated from DIMLP ensembles gave very good results. In the last problem related to bioinformatics, the best result obtained by ensembles of DIMLP networks was also significantly better than the best result obtained by ensembles of decision trees. Thus, although neural networks take much longer to train than decision trees and also rules are generated at a greater computational cost (however, still polynomial), at least for several classification problems it was worth using neural network ensembles, as extracted rules were more accurate, on average. The DIMLP software is available for PC-Linux under http://us.expasy.org/people/Guido.Bologna.html.     

Meta‐CART: A tool to identify interactions between moderators in meta‐analysis

In the framework of meta‐analysis, moderator analysis is usually performed only univariately. When several study characteristics are available that may account for treatment effect, standard meta‐regression has difficulties in identifying interactions between them. To overcome this problem, meta‐CART has been proposed: an approach that applies classification and regression trees (CART) to identify interactions, and then subgroup meta‐analysis to test the significance of moderator effects. The previous version of meta‐CART has its shortcomings: when applying CART, the sample sizes of studies are not taken into account, and the effect sizes are dichotomized around the median value. Therefore, this article proposes new meta‐CART extensions, weighting study effect sizes by their accuracy, and using a regression tree to avoid dichotomization. In addition, new pruning rules are proposed. The performance of all versions of meta‐CART was evaluated via a Monte Carlo simulation study. The simulation results revealed that meta‐regression trees with random‐effects weights and a 0.5‐standard‐error pruning rule perform best. The required sample size for meta‐CART to achieve satisfactory performance depends on the number of study characteristics, the magnitude of the interactions, and the residual heterogeneity.     

The regression trunk approach to discover treatment covariate interaction

The regression trunk approach (RTA) is an integration of regression trees and multiple linear regression analysis. In this paper RTA is used to discover treatment covariate interactions, in the regression of one continuous variable on a treatment variable withmultiple covariates. The performance of RTA is compared to the classical method of forward stepwise regression. The results of two simulation studies, in which the true interactions are modeled as threshold interactions, show that RTA detects the interactions in a higher number of cases (82.3% in the first simulation study, and 52.3% in the second) than stepwise regression (56.5% and 20.5%). In a real data example the final RTA model has a higher cross-validated variance-accounted-for (29.8%) than the stepwise regression model (12.5%). All of these results indicate that RTA is a promising alternative method for demonstrating differential effectiveness of treatments. Supported by The Netherlands Organization for Scientific Research (NWO), grant 030-56403 to Jacqueline Meulman for the Pioneer project “Subject-Oriented Multivariate Analysis,” and grant 451-02-058 to Elise Dusseldorp for the Veni project “Modeling interaction effects as small trees in regression and classification.” We thank Bram Bakker for making the data of his doctoral dissertation available, and David Hand, Jerome Friedman, Bart Jan van Os, Philip Spinhoven, and the anonymous reviewers for their helpful suggestions. Special thanks are due to Lawrence Hubert.