We consider the problem of decomposing the total mutual information conveyed by a pair of predictor random variables about a target random variable into redundant, unique and synergistic contributions. We focus on the relationship between “redundant information” and the more familiar informationtheoretic notions of “common information.” Our main contribution is an impossibility result. We show ...

We consider nonparametric dimension reduction techniques for multivariate regression problems in which the variables constituting the predictor space are strongly nonlinearly related. Specifically, the predictor space is approximated via “local” principal manifolds, based on which a kernel regression is carried out.

A number of potential biases have been identified that may contribute a spurious component to the observed correlation between variables. One such potential bias is the manner in which items are worded. This paper presents a technique and a program of research to estimate the magnitude of method bias arising from item wording. We hypothesize that the greater the level of text similarity between...

When selecting a set of study variables, social work researchers frequently test correlations between the outcome variables (i.e., dependent variables) and theoretically relevant predictor variables (i.e., independent variables). In some instances, one or more of the predictor variables are uncorrelated with the outcome variable. This situation poses the question of whether researchers’ multipl...

The aim of this study was to examine the unique and shared predictive power of psychological variables on reproductive physical health. Three months before fertility treatment, 97 women completed measures of dispositional optimism, trait anxiety, and coping. Information about biological response to treatment (e.g., estradiol level) was collected from medical charts after treatment. Structural e...

The purpose of regression analysis is to expose the relationship between a response variable and predictor variables. In real applications, the response variable cannot be predicted exactly from the predictor variables. Instead, the response for a fixed value of each predictor variable is a random variable. For this reason, we often summarize the behavior of the response for fixed values of the...

Projection pursuit regression is generalized to multivariate responses. By viewing classification as a special case, this generalization serves to extend classification and discriminant analysis via the projection pursuit approach. Submitted to Journal of the American Statistical Association * Work supported by the Department of Energy under contract DEAC03-76SF00515, by the Office of Naval Res...

BACKGROUND AND PURPOSE Five pretreatment variables (P<0.1 univariate analysis), including serum glucose (>300 mg/dL), predicted symptomatic intracerebral hemorrhage (ICH) in the National Institute of Neurological Disorders and Stroke rtPA trial. We retrospectively studied stroke patients treated <3 hours from onset with intravenous rtPA at 2 institutions to evaluate the role of these variables ...

A Matlab based software for logistic regression is developed to enhance the process of teaching quantitative topics and assist researchers with analyzing wide area of applications where categorical data is involved. The software offers an option of performing stepwise logistic regression to select the most significant predictors. The software includes a feature to detect influential observation...

The effect that measurement error of predictor variables has on regression inference is well known in the statistical literature. However, the influence of measurement error on the ability to quantify relationships between chemical stressors and biological responses has received little attention in ecotoxicology. We present a common data-collection scenario and demonstrate that the relationship...