Complete designs with blocks of maximal multiplicity

The set of distinct blocks of a block design is known as its support. We construct complete designs with parameters v(?7), k=3, λ=v ? 2 which contain a block of maximal multiplicity and with support size $\text{b}{}^1\text{= (}{}^{\mathrm{v}}{}_3\text{) ? 4(v ? 2)}$. Any complete design which contains such a block, and has parameters v, k, λ as above, must be supported on at most (^v₃) ? 4(v ? 2) blocks. Attention is given to complete designs because of their direct relationship to simple random sampling.     

Interpersonal Behaviour in Families: Research on the Theoretical Relationship of Two Models*

An integration of theories of family process under a recently formulated unified theory is proposed. Research was conducted testing hypothesized interrelationships between two models subsumed under the unified theory: Satir's model of defended communication and Kantor and Lehr's psychopolitical model of family process. Behavioural ratings from an Australian sample and self-report ratings from an American sample both show the two models to be significantly correlated and structurally consistent with the unified theory.     

A Descriptive Study of Home Modifications for People with Dementia and Barriers to Implementation

This study describes home environmental features, safety issues, and health-related modifications in a community dwelling sample of 82 elderly people with dementia. Main barriers to the accessibility of the homes were steps both inside and outside the home. The majority of the caregivers had made home modifications that pertained mainly to physical limitations. Home modifications to support cognitive deficits were made to a lesser extent. The main barrier to the implementation of home modifications to accommodate the care recipient's memory loss was skepticism about their usefulness. Regarding the removal of physical barriers, financial constraints were most frequently mentioned.     

Gauss–Christoffel quadrature for inverse regression: applications to computer experiments

Sufficient dimension reduction (SDR) provides a framework for reducing the predictor space dimension in statistical regression problems. We consider SDR in the context of dimension reduction for deterministic functions of several variables such as those arising in computer experiments. In this context, SDR can reveal low-dimensional ridge structure in functions. Two algorithms for SDR—sliced inverse regression (SIR) and sliced average variance estimation (SAVE)—approximate matrices of integrals using a sliced mapping of the response. We interpret this sliced approach as a Riemann sum approximation of the particular integrals arising in each algorithm. We employ the well-known tools from numerical analysis—namely, multivariate numerical integration and orthogonal polynomials—to produce new algorithms that improve upon the Riemann sum-based numerical integration in SIR and SAVE. We call the new algorithms Lanczos–Stieltjes inverse regression (LSIR) and Lanczos–Stieltjes average variance estimation (LSAVE) due to their connection with Stieltjes’ method—and Lanczos’ related discretization—for generating a sequence of polynomials that are orthogonal with respect to a given measure. We show that this approach approximates the desired integrals, and we study the behavior of LSIR and LSAVE with two numerical examples. The quadrature-based LSIR and LSAVE eliminate the first-order algebraic convergence rate bottleneck resulting from the Riemann sum approximation, thus enabling high-order numerical approximations of the integrals when appropriate. Moreover, LSIR and LSAVE perform as well as the best-case SIR and SAVE implementations (e.g., adaptive partitioning of the response space) when low-order numerical integration methods (e.g., simple Monte Carlo) are used.

     

Circular balanced repeated measurements designs

The concept of a circular design is defined and when proper balance for various effects is assumed, its universal optimality is proved over the class of all designs with the same set of parameters, Such designs are shown to minimize the variance of the best linear unbiased estimators of contrasts of residual and direct effects over the class of equireplicated designs. All models assume first order residual effects and are of a circular nature. The proofs are presented in a unified manner for several models at a time. They are based on certain matrix domination which occurs when parameters are eliminated from a linear modelj this latter fact is proved for a general linear model.     

Development and Assessment of Measures of Adolescents' Attitudes about Sexual Relationship Rights

Objective: Develop and validate measures of adolescents' attitudes about sexual relationship rights. Methods: Items were completed by students in a large U.S. city (N = 655). The authors conducted an exploratory factor analysis, evaluated internal consistency, and assessed construct validity, including ability to predict sexual behavior at 1-year follow-up. Results: Factor analysis identified 2 distinct factors, comprising attitudes about rights to refuse unwanted sexual activity (5 items) and express sexual engagement needs (5 items) in a sexual relationship. The measures showed sound evidence of reliability and construct validity. Conclusions: The psychometric evidence supports the use of these measures in adolescent sexual health research.     

Editor's note

Journal of Family and Economic Issues -