Can we disregard the whole model? Omnibus non-inferiority testing for R2 in multi-variable linear regression and in ANOVA

Determining a lack of association between an outcome variable and a number of different explanatory variables is frequently necessary in order to disregard a proposed model (i.e., to confirm the lack of a meaningful association between an outcome and predictors). Despite this, the literature rarely offers information about, or technical recommendations concerning, the appropriate statistical methodology to be used to accomplish this task. This paper introduces non-inferiority tests for ANOVA and linear regression analyses, which correspond to the standard widely used F test for and R², respectively. A simulation study is conducted to examine the Type I error rates and statistical power of the tests, and a comparison is made with an alternative Bayesian testing approach. The results indicate that the proposed non-inferiority test is a potentially useful tool for ‘testing the null’.     

A Comparative Investigation of Confidence Intervals for IndependentVariables in Linear Regression

In linear regression, the most appropriate standardized effect size for individual independent variables having an arbitrary metric remains open to debate, despite researchers typically reporting a standardized regression coefficient. Alternative standardized measures include the semipartial correlation, the improvement in the squared multiple correlation, and the squared partial correlation. No arguments based on either theoretical or statistical grounds for preferring one of these standardized measures have been mounted in the literature. Using a Monte Carlo simulation, the performance of interval estimators for these effect-size measures was compared in a 5-way factorial design. Formal statistical design methods assessed both the accuracy and robustness of the four interval estimators. The coverage probability of a large-sample confidence interval for the semipartial correlation coefficient derived from Aloe and Becker was highly accurate and robust in 98% of instances. It was better in small samples than the Yuan-Chan large-sample confidence interval for a standardized regression coefficient. It was also consistently better than both a bootstrap confidence interval for the improvement in the squared multiple correlation and a noncentral interval for the squared partial correlation.     

The stress of food allergy issues in daily life

Objective: Food allergies are a growing health concern, but their implications for daily psychological functioning are unknown. This micro-longitudinal study investigated the daily frequency of food allergy issues and how this related to experiences of stress, mood and physical energy.

Design: One hundred and eight adults with physician-diagnosed food allergies completed an initial Internet survey followed by a 2-week Internet daily diary survey.

Main outcome measures: The initial survey collected socio-demographic and food allergy information. The daily survey collected information about the participants’ experiences of stress, mood, physical energy and food allergy issues during that day.

Results: Commonly experienced allergy issues included negative physical symptoms, higher food prices, anxiety about safety of food, trouble maintaining a healthy diet and anxiety/stress at social occasions. Furthermore, multilevel modelling analyses showed that stress and negative mood were significantly higher on days with more allergy issues. Older adults experienced lower positive mood and physical energy on days with more issues.

Conclusion: This is the first study to incorporate near to real-time tracking to examine the frequency of food allergy issues and the implications for daily psychological functioning. Targeting the issues we identified could reduce stress in patients with food allergies and improve their overall quality of life.     

基于阶层线性理论的多层级中介效应

本文介绍了三种常见的多层级中介效应模型, 并根据阶层线性理论和依次检验回归系数的方法, 详述了多层级中介效应的检验步骤以及中介效应量的估计方法, 在2-1-1和1-1-1中介效应模型中, 推荐采用对层1自变量按组均值中心化, 同时将组均值置于层2截距方程式的中心化方法, 以实现组间和组内中介效应的有效分离。本文还展望了多层级中介效应模型的拓展方向, 即多层级调节性中介模型和多层级结构方程模型; 以及检验方法的拓展, 即Sobel检验和置信区间检验。     

Fourier‐Motzkin elimination method in MOLP problems

This paper introduces a method for finding the non‐dominated set in criterion space of an MOLP problem based on Fourier–Motzkin Elimination. The method incorporates a procedure that eliminates decision variables from constraints and transforms a feasible region from decision space to criterion space. While avoiding characterization of the efficient set in decision space, it finds the non‐dominated set in criterion space. After the decision maker's most preferred criterion vector has been identified, the corresponding efficient solutions can be found by backward substitution. The method was implemented in MATLAB using a tabular form and computational experiments were conducted. The results indicate that although the method performs well for relatively small problems, it can be computationally intensive for larger problems. Nonetheless, the method is intuitively appealing and it provides useful insights into the geometry and theory of MOLP. As such it makes it a valuable educational tool for students of multi‐criteria decision analysis. Copyright © 2003 John Wiley & Sons, Ltd.     

An interactive fuzzy satisficing method for multiobjective stochastic linear programming problems using chance constrained conditions

Two major approaches to deal with randomness or ambiguity involved in mathematical programming problems have been developed. They are stochastic programming approaches and fuzzy programming approaches. In this paper, we focus on multiobjective linear programming problems with random variable coefficients in objective functions and/or constraints. Using chance constrained programming techniques, the stochastic programming problems are transformed into deterministic ones. As a fusion of stochastic approaches and fuzzy ones, after determining the fuzzy goals of the decision maker, interactive fuzzy satisficing methods to derive a satisficing solution for the decision maker by updating the reference membership levels is presented. Copyright © 2003 John Wiley & Sons, Ltd.     

A caveat on the Savage–Dickey density ratio: The case of computing Bayes factors for regression parameters

The Savage–Dickey density ratio is a simple method for computing the Bayes factor for an equality constraint on one or more parameters of a statistical model. In regression analysis, this includes the important scenario of testing whether one or more of the covariates have an effect on the dependent variable. However, the Savage–Dickey ratio only provides the correct Bayes factor if the prior distribution of the nuisance parameters under the nested model is identical to the conditional prior under the full model given the equality constraint. This condition is violated for multiple regression models with a Jeffreys–Zellner–Siow prior, which is often used as a default prior in psychology. Besides linear regression models, the limitation of the Savage–Dickey ratio is especially relevant when analytical solutions for the Bayes factor are not available. This is the case for generalized linear models, non-linear models, or cognitive process models with regression extensions. As a remedy, the correct Bayes factor can be computed using a generalized version of the Savage–Dickey density ratio.     

Attachment Change in Emotionally Focused Couple Therapy and Sexual Satisfaction Outcomes in a Two-year Follow-up Study

Emotionally focused couple therapy (EFT) is an empirically validated attachment based approach to couple therapy. From an EFT perspective, sexual functioning is viewed within the context of an attachment bond, but sexual satisfaction in EFT has not been empirically tested. We examined self-reported sexual satisfaction across 24?months in a sample of 32 couples who received an average of 21 EFT sessions. We found that sexual satisfaction increased across six time points from pre to post therapy and across follow-up (6, 12, 18, and 24?months), and that decreases in attachment avoidance from pre to post therapy predicted increases in sexual satisfaction across time. These findings provide evidence that EFT may help couples improve their sexual satisfaction by reducing attachment avoidance in therapy.