二次响应面回归方法及其在个体-环境匹配研究中的使用

二次响应面回归分析是指二次多项式回归与响应面分析相结合的一种研究方法, 该方法在工业与组织心理学领域起源于个体−环境(P-E)匹配研究。它使用对个体−环境进行间接匹配测量的策略, 考察二者间的最佳匹配以及与结果变量的复杂关系, 并在三维空间对其进行检验和解释。该文在分析以往P-E匹配研究方法(例如差异分数)缺陷性的基础上, 阐述了二次响应面回归方法的产生与发展, 逻辑思想, 统计分析方法, 并以实例演示其操作步骤与结果解释, 以及相对于其他方法的优势与不足。     

Robust Methods for Moderation Analysis with a Two-Level Regression Model

Moderation analysis has many applications in social sciences. Most widely used estimation methods for moderation analysis assume that errors are normally distributed and homoscedastic. When these assumptions are not met, the results from a classical moderation analysis can be misleading. For more reliable moderation analysis, this article proposes two robust methods with a two-level regression model when the predictors do not contain measurement error. One method is based on maximum likelihood with Student's t distribution and the other is based on M-estimators with Huber-type weights. An algorithm for obtaining the robust estimators is developed. Consistent estimates of standard errors of the robust estimators are provided. The robust approaches are compared against normal-distribution-based maximum likelihood (NML) with respect to power and accuracy of parameter estimates through a simulation study. Results show that the robust approaches outperform NML under various distributional conditions. Application of the robust methods is illustrated through a real data example. An R program is developed and documented to facilitate the application of the robust methods.     

Justice Beliefs,Personal Well-Being and Harsh Social Attitudes: Initial Demonstration of a Polynomial Regression and Response Surface Methodology

Tendencies to believe in justice are multidimensional and include beliefs that the world is fair to one’s self (personal justice beliefs) as well as to others (general justice beliefs). Previous research suggests that personal and general justice beliefs are divergently linked to well-being and harsh social attitudes, respectively. However, whether and how these justice tendencies conjointly affect well-being and harsh social attitudes is less well known. Guided by equity theory, the current study used polynomial regression and surface response methodology to demonstrate how specific discrepancies between justice beliefs for self and others predict personal well-being and harsh social attitudes. Participants (N?=?1079) completed measures of tendencies to believe in personal and general justice, as well as measures of physical symptoms associated with illness and attitudes towards the poor. Results suggested that discrepancy between personal and general justice beliefs had detrimental effects on these outcomes (i.e., higher number of illness symptoms and harsher attitudes towards the poor). Moreover, discrepancy resulting from a strong belief in general justice and a weak belief in personal justice (i.e., other-favorable discrepancy) was more strongly negatively associated with well-being and positively associated with harsh attitudes towards the poor than discrepancy resulting from a strong personal justice belief and a weak general justice belief (i.e., self-favorable discrepancy). The current research highlights the potential for personal and general justice beliefs to conjointly predict well-being and social attitudes, while simultaneously demonstrating the capacity to better understand these interactive relationships through the use of surface response methodology.     

Testing Informant Discrepancies as Predictors of Early Adolescent Psychopathology: Why Difference Scores Cannot Tell You What You Want to Know and How Polynomial Regression May

Multiple informants commonly disagree when reporting child and family behavior. In many studies of informant discrepancies, researchers take the difference between two informants’ reports and seek to examine the link between this difference score and external constructs (e.g., child maladjustment). In this paper, we review two reasons why difference scores cannot serve as unambiguous predictors of outcomes. Further, we use polynomial regression analyses to both test the validity of difference scores and provide a more direct test of the hypothesis that discrepancies in parent and child reports predict child psychopathology. Data from 218 parent-adolescent dyads (M adolescent age?=?11.5 years, 51 % female; 49 % European American, 47 % African American) were used to predict adolescent-reported antisocial behavior and depression from parent and adolescent reports of parent-adolescent conflict, parental knowledge, parental acceptance, adolescent rule-breaking behavior, and adolescent pubertal development. Results demonstrate that analyses using difference scores do not provide valid tests of the utility of informant discrepancies in predicting adolescent psychosocial maladjustment. However, interaction terms in polynomial regression analyses provide evidence that informant discrepancies predict child psychopathology. Parent-adolescent informant discrepancies predict adolescent psychopathology but researchers should avoid using difference scores to measure informant discrepancies. Polynomial regression analyses provide more comprehensive and accurate tests of whether informant discrepancies predict child and adolescent psychopathology.     

Estimating Optimal Weights for Compound Scores: A Multidimensional IRT Approach

A method is proposed for constructing indices as linear functions of variables such that the reliability of the compound score is maximized. Reliability is defined in the framework of latent variable modeling [i.e., item response theory (IRT)] and optimal weights of the components of the index are found by maximizing the posterior variance relative to the total latent variable variance. Three methods for estimating the weights are proposed. The first is a likelihood-based approach, that is, marginal maximum likelihood (MML). The other two are Bayesian approaches based on Markov chain Monte Carlo (MCMC) computational methods. One is based on an augmented Gibbs sampler specifically targeted at IRT, and the other is based on a general purpose Gibbs sampler such as implemented in OpenBugs and Jags. Simulation studies are presented to demonstrate the procedure and to compare the three methods. Results are very similar, so practitioners may be suggested the use of the easily accessible latter method. A real-data set pertaining to the 28-joint Disease Activity Score is used to show how the methods can be applied in a complex measurement situation with multiple time points and mixed data formats.     

多项式回归与一致性研究：应用及分析

本文介绍了多项式回归的分析方法, 讨论并验证了它相比传统的差异分数分析法在检验一致性假设中的优势。针对目前该方法在国内应用方面的缺失状况, 本文从分析基准、理论推导、分析步骤和假设检验等方面完善了多项式回归与响应面分析相结合的应用分析框架。最后, 本文以个人-组织价值观一致性对员工情感性变革承诺的影响研究为例, 对分析框架的具体应用进行了说明。结果表明, 被传统差异分数很好支持的一致性效应并不一定完美, 新的分析框架能够揭示更多的有用信息并给管理实践带来更具体而准确的引导。     

Bayesian Extended Redundancy Analysis: A Bayesian Approach to Component-based Regression with Dimension Reduction

Abstract

Extended redundancy analysis (ERA) combines linear regression with dimension reduction to explore the directional relationships between multiple sets of predictors and outcome variables in a parsimonious manner. It aims to extract a component from each set of predictors in such a way that it accounts for the maximum variance of outcome variables. In this article, we extend ERA into the Bayesian framework, called Bayesian ERA (BERA). The advantages of BERA are threefold. First, BERA enables to make statistical inferences based on samples drawn from the joint posterior distribution of parameters obtained from a Markov chain Monte Carlo algorithm. As such, it does not necessitate any resampling method, which is on the other hand required for (frequentist’s) ordinary ERA to test the statistical significance of parameter estimates. Second, it formally incorporates relevant information obtained from previous research into analyses by specifying informative power prior distributions. Third, BERA handles missing data by implementing multiple imputation using a Markov Chain Monte Carlo algorithm, avoiding the potential bias of parameter estimates due to missing data. We assess the performance of BERA through simulation studies and apply BERA to real data regarding academic achievement.     

Low Self-control and Deviance: Examining the Moderation of Social Support from Parents

Drawing on self-report survey data from a sample of 425 college students in 2001, this study examines whether parental support can moderate the link between low self-control and deviance. Using multiple measures of low self-control and parental support and item parcels of deviance, structural equation models are developed to arrive at the results. Results reveal that parental support does not completely moderate the link between low self-control and deviance. Importantly, we find that parental support can reduce the link that low self-control has with deviance, suggesting that this is a measure that may be manipulated to reduce instances of deviance.     

Further Insight and Additional Inference Methods for Polynomial Regression Applied to the Analysis of Congruence

In their seminal paper, Edwards and Parry (1993) presented the polynomial regression as a better alternative to applying difference score in the study of congruence. While this method is increasingly applied in congruence research, its complexity relative to other methods for assessing congruence (e.g., difference score methods) was one of the main claims against its use. The objective of this work is to gain additional insight into the use of polynomial regression in the area of social and behavioral sciences. First, we elaborate on the meaning and the inference based on the coefficients obtained by applying polynomial regression and explain the mathematical terms that are used to describe response surfaces. Then, we introduce additional inference methods and illustrate their application on a real life example from the area of supportive exchanges, using data collected by the Smithers Institute at Cornell University (supported by the National Institute on Alcohol Abuse and Alcoholism). Our work is aimed to provide a guide to researchers who apply polynomial regression in order to assess the effect of congruence between two constructs and enable better understanding and interpretation of the results obtained.     

Further Insight and Additional Inference Methods for Polynomial Regression Applied to the Analysis of Congruence

In their seminal paper, Edwards and Parry (1993) Edwards, J. R. and Parry, M. E. 1993. On the use of polynomial regression equations as an alternative to difference scores in organizational research. Academy of Management Journal, 36: 1577–1613. [Crossref], [Web of Science ®] , [Google Scholar] presented the polynomial regression as a better alternative to applying difference score in the study of congruence. Although this method is increasingly applied in congruence research, its complexity relative to other methods for assessing congruence (e.g., difference score methods) was one of the main claims against its use. The objective of this work is to gain additional insight into the use of polynomial regression in the area of social and behavioral sciences. First, we elaborate on the meaning and the inference based on the coefficients obtained by applying polynomial regression and explain the mathematical terms that are used to describe response surfaces. Then, we introduce additional inference methods and illustrate their application on a real-life example from the area of supportive exchanges using data collected by the Smithers Institute at Cornell University (supported by the National Institute on Alcohol Abuse and Alcoholism). Our work is aimed to provide a guide to researchers who apply polynomial regression in order to assess the effect of congruence between two constructs and enable better understanding and interpretation of the results obtained.     

Analysis of Interactions and Nonlinear Effects with Missing Data: A Factored Regression Modeling Approach Using Maximum Likelihood Estimation

Abstract

When estimating multiple regression models with incomplete predictor variables, it is necessary to specify a joint distribution for the predictor variables. A convenient assumption is that this distribution is a multivariate normal distribution, which is also the default in many statistical software packages. This distribution will in general be misspecified if predictors with missing data have nonlinear effects (e.g., x²) or are included in interaction terms (e.g., x·z). In the present article, we introduce a factored regression modeling approach for estimating regression models with missing data that is based on maximum likelihood estimation. In this approach, the model likelihood is factorized into a part that is due to the model of interest and a part that is due to the model for the incomplete predictors. In three simulation studies, we showed that the factored regression modeling approach produced valid estimates of interaction and nonlinear effects in regression models with missing values on categorical or continuous predictor variables under a broad range of conditions. We developed the R package mdmb, which facilitates a user-friendly application of the factored regression modeling approach, and present a real-data example that illustrates the flexibility of the software.     

Examining the Relationship Between Worry and Sleep: A Daily Process Approach

There is growing evidence suggesting that worry and sleep are intimately linked. However, the relationship between these two phenomena over the course of a day remains largely unstudied. It is possible that (a) worry predicts sleep disturbance that night, (b) sleep disturbance predicts worry the following day, or (c) there is a bidirectional relationship between worry and sleep disturbance. The present study examined the daily relationship between worry (both during the day and immediately prior to sleep onset) and sleep in 50 high trait worriers who were randomly assigned to one of two interventions aimed at reducing worry as part of a larger study. A daily process approach was utilized wherein participants completed daily reports of sleep and worry during a 7-day baseline period followed by a 14-day intervention period. Results of repeated measures multilevel modeling analyses indicated that worry experienced on a particular day predicted increased sleep disturbance that night during both the baseline and intervention weeks. However, there was no evidence of a bidirectional relationship as sleep characteristics did not predict worry the following day. Additionally, the type of intervention that participants engaged in did not affect the daily relationship between worry and sleep. Results of the present study are consistent with the cognitive model of insomnia (Harvey, 2002) and highlight the importance of addressing and treating worry among individuals with high trait worry and sleep disturbance.     

Scientific Research and Human Rights: A Response to Kitcher on the Limitations of Inquiry

In his recent work exploring the role of science in democratic societies Kitcher (Science in a democratic society. Prometheus Books, New York, 2011) claims that scientists ought to have a prominent role in setting the agenda for and limits to research. Against the backdrop of the claim that the proper limits of scientific inquiry is John Stuart Mill’s Harm Principle (Kitcher in Science, truth, and democracy. Oxford University Press, New York, 2001), he identifies the limits of inquiry as the point where the outcomes of research could cause harm to already vulnerable populations. Nonetheless, Kitcher argues against explicit limitations on unscrupulous research on the grounds that restrictions would exacerbate underlying social problems. I show that Kitcher’s argument in favor of dissuading inquiry through conventional standards is problematic and falls prey to the same critique he offers in opposition to official bans. I expand the conversation of limiting scientific research by recognizing that the actions that count as ‘science’ are located in the space between ‘thinking’ and ‘doing’. In this space, we often attempt to balance freedom of research, as scientific speech, against the disparate impact citizens might experience in light of such research. I end by exploring if such disparate impact justifies limiting research, within the context of the United States, under Title VII of the Civil Rights Act of 1964 or under international human rights standards more generally.     

A Unified Approach to Power Calculation and Sample Size Determination for Random Regression Models

The underlying statistical models for multiple regression analysis are typically attributed to two types of modeling: fixed and random. The procedures for calculating power and sample size under the fixed regression models are well known. However, the literature on random regression models is limited and has been confined to the case of all variables having a joint multivariate normal distribution. This paper presents a unified approach to determining power and sample size for random regression models with arbitrary distribution configurations for explanatory variables. Numerical examples are provided to illustrate the usefulness of the proposed method and Monte Carlo simulation studies are also conducted to assess the accuracy. The results show that the proposed method performs well for various model specifications and explanatory variable distributions. The author would like to thank the editor, the associate editor, and the referees for drawing attention to pertinent references that led to improved presentation. This research was partially supported by National Science Council grant NSC-94-2118-M-009-004.     

Examination and Measurement of Halo Via Curvilinear Regression: A New Approach to Halo1

Much disagreement and confusion has surrounded the nature of the relationship between halo and performance rating accuracy. Traditionally, the relationship has been assumed to be linear ( Cooper, 1981 ), but Fisicaro (1988 ) proposed that the relationship between halo and performance rating accuracy is, instead, curvilinear. Using the halo index suggested by Balzer & Sulsky (1992 ), the results of the present study provided empirical evidence to support Fisicaro's proposal. Future research examining the relationship between halo and accuracy should consider the use of quadratic models, instead of linear ones. For the practitioner, this result implies that low rating dimension intercorrelations (negative halo) may lead to inaccuracy in ratings in much the same way as do high rating dimension intercorrelations (positive halo).     

Transportation and Need for Affect in Narrative Persuasion: A Mediated Moderation Model

Two experiments investigated the idea that individual differences in need for affect are critical for narrative persuasion. Need for affect, that is, the disposition to approach emotions, was assumed to facilitate the experience of being transported into the mental world of the narrative. An intense experience of transportation, in turn, should enhance the persuasive impact of narrative information on readers' beliefs. A mediated moderation analysis was used to test these assumptions. In both experiments (N = 314), need for affect (approach) and transportation moderated the persuasive effects of a fictional narrative compared to a belief-irrelevant control story (Experiment 1) and the persuasive effects of a story with high emotional content compared to a story with low emotional content (Experiment 2). The moderator effects of need for affect were shown to be mediated by the moderator effects of transportation. In sum, the magnitude of a person's need for affect determines whether and to what extent the person experiences transportation into the story world and is persuaded by the information presented in the narrative.     

A Regression Framework for Causal Mediation Analysis with Applications to Behavioral Science

We introduce and extend the classical regression framework for conducting mediation analysis from the fit of only one model. Using the essential mediation components (EMCs) allows us to estimate causal mediation effects and their analytical variance. This single-equation approach reduces computation time and permits the use of a rich suite of regression tools that are not easily implemented on a system of three equations. Additionally, we extend this framework to non-nested mediation systems, provide a joint measure of mediation for complex mediation hypotheses, propose new visualizations for mediation effects, and explain why estimates of the total effect may differ depending on the approach used. Using data from social science studies, we also provide extensive illustrations of the usefulness of this framework and its advantages over traditional approaches to mediation analysis. The example data are freely available for download online and we include the R code necessary to reproduce our results.