Some further aspects of the löwner-ordering antitonicity of the moore-penrose inverse

A survey is given of known proofs of the antitonicity of the inverse matrix function for positive definite matrices w.r.t. the Lowner partial ordering, and of the corresponding result for the Moore-Penrose inverse of nonnegative definite matrices [the theorem of Milliken and Akdeniz (1977)]. A short new proof of the latter result is obtained by employing an extremal representation of a nonnegative definite quadratic form. Another proof of this result involving Schur complements is also given, and is seen to be extendable to the case of symmetric (not necessarily nonnegative definite) matrices. A geometrical interpretation of Milliken and Akdeniz's theorem is presented. As an application, the relationship between the concepts of greater (maximum) concentration and smaller (minimum) dispersion is considered for a pair (class) of vector-valued statistics with possibly degenerate distributions.     

Computation of exact probability values for multi-response permutation procedures (MRPP)

An algorithm is presented for computing the exact probability value associated with a recently–developed class of statistical inference techniques termed multi–response permutation procedures (MRPP).     

Statistical Computing Software Reviews

This section is similar in organization to a Book Review section in other journals; however, software of interest to statisticians is the subject of review here. Emphasis is on software for microcomputers. Programs that operate only in larger mainframe computers will seldom receive review. Normally, producers of programs make a copy of their product available to the Section Editor, who then selects one or more persons to test the product and prepare a review.

Producers of computer software who wish to have their product reviewed are invited to contact the Section Editor, Professor Kenneth Berk, Department of Mathematics, 313 Stevenson Hall, Illinois State University, Normal, IL 61761.

Findings and opinions expressed in every review are solely those of the author. They should not be construed as reflecting endorsement of the product, or opinions held, by the American Statistical Association, nor is any warranty implied about any product reviewed.

STAN, Version II.0. David M. Allen. Available from Statistical Consultants, Inc., 462 E. High Street, Lexington, KY 40508. $300. Reviewed by Peter A. Lachenbruch     

360 Video: A prototyping process for developing virtual reality interventions

Abstract

Virtual reality (VR) has emerged as a promising technological intervention for anxiety disorders. However, there are no existing standards and best practices to evaluate the effectiveness of environments to achieve their intervention goals. The purpose of this study was to develop a VR intervention for student veterans with social anxiety disorder and test feasibility utilizing a three-stage development model. The development of a therapeutic VR environment may benefit from an interdisciplinary collaboration of researchers from various fields of study. Utilizing three stages of prototyping with two virtual reality platforms, fully immersive video (n?=?6) and three-dimensional (3-D) immersive virtual reality (n?=?8), the research team designed an intervention for student veterans with social anxiety disorder, testing bio-reactivity of participants. Results of prototyping include user feedback validating increased stress levels and increased bio-reactivity specifically in galvanic skin response and heart rate elevation. Implications include the use of 360° video for prototyping 3-D virtual reality interventions.     

The Changing Nature and Patterns of Traditional Marriage Practices among the Owerre-Igbo,a Subgroup of the Igbo of Southeast Nigeria

This research investigates the changing nature and patterns as well as the social construct of traditional marriage and practices among the Owerre-Igbo of Southeast Nigeria. In particular, it investigates the practice of heterosexual marriage, woman-to-woman marriage, child marriage, and the dynamics of bride price. It also analyses the eclectics that has come to characterise Igbo traditional marriages especially the plethora of cultural borrowings that have become features of Igbo traditional marriage practices in recent times. The research investigates how this acculturation has shaped the contemporary social construct of marriage as well as how it articulates with continuities and changes in Owerre-Igbo social organization. The research found out that these changes were brought about by three major factors; (1) the extensive contacts which the Owerre-Igbo have had with other ethnic groups, (2) the influence of Christianity and Western education, and (3) occupational influence.     

Customer Behavior in an Online Ordering Application: A Decision Scoring Model*

This research presents the development of behavioral scoring models to predict future customer purchases in an online ordering application. Internet retailing lowers many barriers for customers switching between retailers for repeat purchases; thus, retaining existing customers is a key challenge for achieving profitability. Survey data were collected from 1,089 online customers of two companies. The subjective survey data were then used to predict purchases over the ensuing 12 months based on data from the company databases. The analysis illustrates the general applicability of predictive models of future customer purchases while also demonstrating the need to develop specific models tailored for an individual company's operating and marketing environment. The models provide insight on how companies can target marketing dollars more effectively and allocate investment across multiple operational areas for maximum return. The research answers a call for rigorous research in the area of predictive marketing, an area in which many companies are excelling but where there is a scarcity of detailed knowledge regarding application of such models.