Tree-structured scale effects in binary and ordinal regression

In binary and ordinal regression one can distinguish between a location component and a scaling component. While the former determines the location within the range of the response categories, the scaling indicates variance heterogeneity. In particular since it has been demonstrated that misleading effects can occur if one ignores the presence of a scaling component, it is important to account for potential scaling effects in the regression model, which is not possible in available recursive partitioning methods. The proposed recursive partitioning method yields two trees: one for the location and one for the scaling. They show in a simple interpretable way how variables interact to determine the binary or ordinal response. The developed algorithm controls for the global significance level and automatically selects the variables that have an impact on the response. The modeling approach is illustrated by several real-world applications.

Adaptive Scheme for ANOVA Models

This paper deals with the concept of adaptive scheme and with an application to the Oneway ANOVA model under uncorrelated errors. Oneway ANOVA model is sensitive to nonnormality as well as variance heterogeneity. To overcome these problems, an adaptive scheme is proposed. The adaptive test is a two step procedure. The given data is first examined and classified based on measures of skewness and tailweight. Secondly, a selector statistic is used for selecting a test to be conducted. A 10,000 simulations were conducted to compare the performance of the two models from different continuous distributions. Analysis of real data sets on equal and unequal sample sizes were performed to evaluate the efficiency of the two models. The findings showed that our adaptive scheme outperformed the parametric F-test in symmetric or skewed distributions with varying tailweights except for symmetric and medium-tailed distributions.

Comparing Means under Heteroscedasticity and Nonnormality: Further Exploring Robust Means Modeling

Comparing the means of independent groups is a concern when the assumptions of normality and variance homogeneity are violated. Robust means modeling (RMM) was proposed as an alternative to ANOVA-type procedures when the assumptions of normality and variance homogeneity are violated. The purpose of this study is to compare the Type I error and power rates of RMM to the trimmed Welch procedure. A Monte Carlo study was used to investigate RMM and the trimmed Welch procedure under several conditions of nonnormality and variance heterogeneity. The results suggest that the trimmed Welch provides a better balance of Type I error control and power than RMM.