Categorical variable

Abstract: In many applications, data objects are described by both numeric and categorical features. The k-prototype algorithm is one of the most important algorithms for clustering this type of data. However, this method performs hard partition, which may lead to misclassification for the data objects in the boundaries of regions, and the dissimilarity measure only uses the user-given parameter for adjusting the significance of attribute. In this paper, first, we combine mean and fuzzy centroid to represent the prototype of a cluster, and employ a new measure based on co-occurrence of values to evaluate the dissimilarity between data objects and prototypes of clusters. This measure also takes into account the significance of different attributes towards the clustering process. Then we present our algorithm for clustering mixed data. Finally, the performance of the proposed method is demonstrated by a series of experiments on four real world datasets in comparison with that of traditional clustering algorithms.

Abstract: This article uses meta-analyses published in Psychological Bulletin from 1995 to 2005 to describe meta-analyses in psychology, including examination of statistical power, Type I errors resulting from multiple comparisons, and model choice. Retrospective power estimates indicated that univariate categorical and continuous moderators, individual moderators in multivariate analyses, and tests of residual variability within individual levels of categorical moderators had the lowest and most concerning levels of power. Using methods of calculating power prospectively for significance tests in meta-analysis, we illustrate how power varies as a function of the number of effect sizes, the average sample size per effect size, effect size magnitude, and level of heterogeneity of effect sizes. In most meta-analyses many significance tests were conducted, resulting in a sizable estimated probability of a Type I error, particularly for tests of means within levels of a moderator, univariate categorical moderators, and residual variability within individual levels of a moderator. Across all surveyed studies, the median effect size and the median difference between two levels of study level moderators were smaller than Cohen's (1988) conventions for a medium effect size for a correlation or difference between two correlations. The median Birge's (1932) ratio was larger than the convention of medium heterogeneity proposed by Hedges and Pigott (2001) and indicates that the typical meta-analysis shows variability in underlying effects well beyond that expected by sampling error alone. Fixed-effects models were used with greater frequency than random-effects models; however, random-effects models were used with increased frequency over time. Results related to model selection of this study are carefully compared with those from Schmidt, Oh, and Hayes (2009), who independently designed and produced a study similar to the one reported here. Recommendations for conducting future meta-analyses in light of the findings are provided.

Abstract: We propose a method for selecting variables in latent class analysis, which is the most common model-based clustering method for discrete data. The method assesses a variable’s usefulness for clustering by comparing two models, given the clustering variables already selected. In one model the variable contributes information about cluster allocation beyond that contained in the already selected variables, and in the other model it does not. A headlong search algorithm is used to explore the model space and select clustering variables. In simulated datasets we found that the method selected the correct clustering variables, and also led to improvements in classification performance and in accuracy of the choice of the number of classes. In two real datasets, our method discovered the same group structure with fewer variables. In a dataset from the International HapMap Project consisting of 639 single nucleotide polymorphisms (SNPs) from 210 members of different groups, our method discovered the same group structure with a much smaller number of SNPs.

Abstract: ERP averaging is an extraordinarily successful method, but can only be applied to a limited range of experimental designs. We introduce the regression-based rERP framework, which extends ERP averaging to handle arbitrary combinations of categorical and continuous covariates, partial confounding, nonlinear effects, and overlapping responses to distinct events, all within a single unified system. rERPs enable a richer variety of paradigms (including high-N naturalistic designs) while preserving the advantages of traditional ERPs. This article provides an accessible introduction to what rERPs are, why they are useful, how they are computed, and when we should expect them to be effective, particularly in cases of partial confounding. A companion article discusses how nonlinear effects and overlap correction can be handled within this framework, as well as practical considerations around baselining, filtering, statistical testing, and artifact rejection. Free software implementing these techniques is available.