基于多元回归的调节效应分析

在心理学和其他社科研究领域,大量实证研究建立调节模型,以分析自变量对因变量关系的影响机制,但在基于多元回归的调节效应分析实践中仍存在不足。我们回顾了均值中心化在基于多元回归的调节效应分析中的作用,均值中心化不影响乘积项(即调节效应)的检验,仅对一阶项(即主效应)的检验有影响。讨论了简单斜率的检验方法,建议在调节变量为连续变量时,使用Johnson-Neyman法进行简单斜率检验;在调节变量为类别变量或研究者对某个调节变量值感兴趣时,使用选点法。并用一个实际例子演示如何进行调节效应分析。随后展望了调节效应检验的拓展方向。     

Probing three-way interactions in moderated multiple regression: development and application of a slope difference test

Researchers often use 3-way interactions in moderated multiple regression analysis to test the joint effect of 3 independent variables on a dependent variable. However, further probing of significant interaction terms varies considerably and is sometimes error prone. The authors developed a significance test for slope differences in 3-way interactions and illustrate its importance for testing psychological hypotheses. Monte Carlo simulations revealed that sample size, magnitude of the slope difference, and data reliability affected test power. Application of the test to published data yielded detection of some slope differences that were undetected by alternative probing techniques and led to changes of results and conclusions. The authors conclude by discussing the test's applicability for psychological research.     

两类常见的类别变量调节效应分析

类别变量在心理学和其他社科研究领域经常遇到,当自变量或调节变量为类别变量时,应当如何分析调节效应呢？详述了多类别变量的被试间设计和两水平被试内设计（因变量重复测量2次）的调节效应分析方法,并给出了分析流程。先进行调节效应的显著性检验,后用选点法或Johnson-Neyman法进行简单斜率检验。多类别变量被试间设计的简单斜率检验是先进行整体检验,后进行配对检验。用两个实际例子演示如何进行类别变量的调节效应分析,最后展望了两类设计的类别变量调节研究的拓展方向,例如更复杂的类别变量的调节模型等。     

Extensions of the Johnson-Neyman Technique to Linear Models With Curvilinear Effects: Derivations and Analytical Tools

The past decade has witnessed renewed interest in the use of the Johnson-Neyman (J-N) technique for calculating the regions of significance for the simple slope of a focal predictor on an outcome variable across the range of a second, continuous independent variable. Although tools have been developed to apply this technique to probe 2- and 3-way interactions in several types of linear models, this method has not been extended to include quadratic terms or more complicated models involving quadratic terms and interactions. Curvilinear relations of this type are incorporated in several theories in the social sciences. This article extends the J-N method to such linear models along with presenting freely available online tools that implement this technique as well as the traditional pick-a-point approach. Algebraic and graphical representations of the proposed J-N extension are provided. An example is presented to illustrate the use of these tools and the interpretation of findings. Issues of reliability as well as “spurious moderator” effects are discussed along with recommendations for future research.     

Buy three but get only two: The smallest effect in a 2 × 2 ANOVA is always uninterpretable

Loftus (Memory & Cognition 6:312–319, 1978) distinguished between interpretable and uninterpretable interactions. Uninterpretable interactions are ambiguous, because they may be due to two additive main effects (no interaction) and a nonlinear relationship between the (latent) outcome variable and its indicator. Interpretable interactions can only be due to the presence of a true interactive effect in the outcome variable, regardless of the relationship that it establishes with its indicator. In the present article, we first show that same problem can arise when an unmeasured mediator has a nonlinear effect on the measured outcome variable. Then we integrate Loftus’s arguments with a seemingly contradictory approach to interactions suggested by Rosnow and Rosenthal (Psychological Bulletin 105:143–146, 1989). We show that entire data patterns, not just interaction effects alone, produce interpretable or noninterpretable interactions. Next, we show that the same problem of interpretability can apply to main effects. Lastly, we give concrete advice on what researchers can do to generate data patterns that provide unambiguous evidence for hypothesized interactions.     

Effects of predictor intercorrelations and reliabilities on moderated multiple regression

Results of Monte Carlo simulation suggest that detection of moderator effects in moderated multiple regression is hampered by poor reliability in either the independent variable, x, or the moderator variable, w. This finding was anticipated from the fact that reliability of a product term, xw, is determined in part by the product of the reliabilities of its constituents. An interesting finding was that the probability of detection of a product (interaction) term increases as the correlation between x and w increases; it is known that the reliability of a product term increases similarly. An unexpected finding was the inflated probabilities of Type I errors that occurred for direct effects of x or w when they were not directly related to the criterion in the underlying model. Detection of spurious direct effects was exacerbated by increased correlation between x and w. It is clear that moderated multiple regression is adversely affected by measurement error, but that the impact is complex. It is apparent that researchers in this area must strive to improve the reliabilities of predictor variables if they are to have a reasonable chance of discovering moderator effects.     

Conditional Direction Dependence Analysis: Evaluating the Causal Direction of Effects in Linear Models with Interaction Terms

Abstract

Direction dependence analysis (DDA) makes use of higher than second moment information of variables (x and y) to detect potential confounding and to probe the causal direction of linear variable relations (i.e., whether x?→?y or y?→?x better approximates the underlying causal mechanism). The “true” predictor is assumed to be a continuous nonnormal exogenous variable. Existing methods compatible with DDA, however, are of limited use when the relation of a focal predictor and an outcome is affected by a moderator. This study presents a conditional direction dependence analysis (CDDA) framework which enables researchers to evaluate the causal direction of conditional regression effects. Monte–Carlo simulations were used to evaluate two different moderation scenarios: Study 1 evaluates the performance of CDDA tests when a moderator affects the strength of the causal effect x?→?y. Study 2 evaluates cases in which the causal direction itself (x?→?y vs y?→?x) depends on moderator values. Study 3 evaluates the robustness of DDA tests in the presence of functional model misspecifications. Results suggest that significance tests compatible with CDDA are suitable in both moderation scenarios, i.e., CDDA allows one to discern regions of a moderator in which the causal direction is uniquely identifiable. An empirical example is provided to illustrate the approach.     

Multilevel mediation analysis: The effects of omitted variables in the 1–1–1 model

Multilevel mediation analysis examines the indirect effect of an independent variable on an outcome achieved by targeting and changing an intervening variable in clustered data. We study analytically and through simulation the effects of an omitted variable at level 2 on a 1–1–1 mediation model for a randomized experiment conducted within clusters in which the treatment, mediator, and outcome are all measured at level 1. When the residuals in the equations for the mediator and the outcome variables are fully orthogonal, the two methods of calculating the indirect effect (ab, c – c′) are equivalent at the between‐ and within‐cluster levels. Omitting a variable at level 2 changes the interpretation of the indirect effect and will induce correlations between the random intercepts or random slopes. The equality of within‐cluster ab and c – c′ no longer holds. Correlation between random slopes implies that the within‐cluster indirect effect is conditional, interpretable at the grand mean level of the omitted variable.     

Nonlinear Indicator-Level Moderation in Latent Variable Models

Linear, nonlinear, and nonparametric moderated latent variable models have been developed to investigate possible interaction effects between a latent variable and an external continuous moderator on the observed indicators in the latent variable model. Most moderation models have focused on moderators that vary across persons but not across the indicators (e.g., moderators like age and socioeconomic status). However, in many applications, the values of the moderator may vary both across persons and across indicators (e.g., moderators like response times and confidence ratings). Indicator-level moderation models are available for categorical moderators and linear interaction effects. However, these approaches require respectively categorization of the continuous moderator and the assumption of linearity of the interaction effect. In this article, parametric nonlinear and nonparametric indicator-level moderation methods are developed. In a simulation study, we demonstrate the viability of these methods. In addition, the methods are applied to a real data set pertaining to arithmetic ability.     

有调节的多层中介效应分析

多层中介和多层调节效应分析在社科领域已常有应用,但如果将多层中介和调节整合在一起,可以产生2（多层中介类型）×2（调节变量的层次）×3（调节的中介路径）共12种有调节的多层中介模型。面对有调节的多层中介效应分析,研究者往往束手无策。详述了基于多层线性模型的12种有调节的多层中介的分析方法和基于多层结构方程模型的4类有调节的多层中介分析方法,包括正交分割法,随机系数预测法,潜调节结构方程法和贝叶斯合理值法。这四类方法的核心议题在于如何处理潜调节项。当样本量足够大时,建议选择潜调节结构方程法;当样本量不足时,建议选择贝叶斯合理值法。随后用一个实际例子演示如何进行有调节的多层中介效应分析并有相应的Mplus程序。最后展望了有调节的多层中介效应分析研究的拓展方向。     

Addressing Moderated Mediation Hypotheses: Theory,Methods, and Prescriptions

This article provides researchers with a guide to properly construe and conduct analyses of conditional indirect effects, commonly known as moderated mediation effects. We disentangle conflicting definitions of moderated mediation and describe approaches for estimating and testing a variety of hypotheses involving conditional indirect effects. We introduce standard errors for hypothesis testing and construction of confidence intervals in large samples but advocate that researchers use bootstrapping whenever possible. We also describe methods for probing significant conditional indirect effects by employing direct extensions of the simple slopes method and Johnson-Neyman technique for probing significant interactions. Finally, we provide an SPSS macro to facilitate the implementation of the recommended asymptotic and bootstrapping methods. We illustrate the application of these methods with an example drawn from the Michigan Study of Adolescent Life Transitions, showing that the indirect effect of intrinsic student interest on mathematics performance through teacher perceptions of talent is moderated by student math self-concept.     

Self‐construal and social comparison effects

Background. Social comparison research usually demonstrates that students will have higher self‐evaluation in downward comparison but lower self‐evaluation in upward comparison. However, the existence of this contrast effect may depend on people's self‐construal. The contrast effect may exist only for people with independent self‐construal. For people with interdependent self‐construal, the contrast effect may be attenuated. Aim. The study investigated the role of self‐construal as a moderator of the social comparison effects in authentic classrooms. Sample. The participants were 96 Chinese seventh‐grade students (41 male, 51 female and 4 unreported) from a secondary school in Hong Kong. Method. The experiment employed a 2 × 2 between‐subjects design based on 2 levels of self‐construal (independent, interdependent) and 2 levels of comparison standard (upward comparison, downward comparison). The dependent variable was students' self‐evaluation. Results. A two‐way ANOVA indicated a significant interaction between self‐construal and comparison standard on self‐evaluation. When the students' independent self‐construal was activated, they reported higher self‐evaluation in downward comparison but lower self‐evaluation in upward comparison. However, such a contrast effect was attenuated when the students' interdependent self‐construal was activated. They reported high self‐evaluation in both upward and downward comparisons. Conclusions. The outcome of social comparison depends on whether independent or interdependent self‐construal is salient in the classroom.     

A Monte Carlo study of the effects of correlated method variance in moderated multiple regression analysis

It has been suggested that hierarchical regression analysis provides an unambiguous conclusion with regard to the existence of moderator effects (Arnold & Evans, 1979). This paper examines the impact of correlated error among the dependent and independent variables in order to explore whether or not artificial interaction terms can be generated. A Monte Carlo study was performed to investigate the effects of correlated error on noninteraction and interaction models. The results are clear-cut. Artifactual interaction cannot be created; true interactions can be attentuated. Some practical suggestions are provided for drawing inferences from hierarchical regression analysis.     

Flexible Approaches to Computing Mediated Effects in Generalized Linear Models: Generalized Estimating Equations and Bootstrapping

In behavioral research, interest is often in examining the degree to which the effect of an independent variable X on an outcome Y is mediated by an intermediary or mediator variable M. This article illustrates how generalized estimating equations (GEE) modeling can be used to estimate the indirect or mediated effect, defined as the amount by which the regression coefficient of X on Y changes after adjusting for M. Advantages of this method are: (a) it applies to the class of generalized linear models, including linear, logistic, and Poisson regression as special cases; (b) it allows multiple independent variables and mediators in the same model; and (c) asymptotically valid standard errors and confidence intervals are obtained using standard software. This methodology is compared with the bootstrap, another general methodology that can be applied to the same broad class of models, and is evaluated using simulation in both linear and logistic regression scenarios. The methods are utilized to examine the degree to which the effect of low birthweight status on internalizing symptoms at age 20 is mediated through IQ at age 8.     

Conjunctive moderator variables in vulnerability and resiliency research: life stress, social support and coping skills, and adolescent sport injuries

In life event research relating to vulnerability and resilience factors, single moderator variables have typically been the focus of study. Little is known about the ways in which moderator variables may interact with one another to increase vulnerability or resilience. We propose a distinction between conjunctive moderation, in which multiple moderators must co-occur in a specific combination or pattern to maximize a relation between a predictor and an outcome variable, and disjunctive moderation, in which any one of a number of moderators maximizes the predictor-criterion relation. Our results indicate that social support and psychological coping skills are statistically independent psychosocial resources and that they operate in a conjunctive manner to influence the relation between life stress and subsequent athletic injury in adolescents. Only athletes low in both coping skills and social support exhibited a significant stress-injury relation, and in that vulnerable subgroup, negative major life events accounted for up to 30% of the injury variance. Methodological considerations in the assessment of conjunctive moderator effects are discussed.     

大学生心理需求与网络社交:认知评估与自我调控的作用

为探讨大学生心理需求、认知评估、自我调控和网络社交的关系,采用大学生心理需求量表、网络利弊权衡问卷、自我调控问卷和网络交往问卷对503名大学生进行调查,结果发现:(1)大学生心理需求可显著正向预测网络社交;对上网的好处和代价认知评估在两者间起部分中介作用。(2)自我调控在心理需求和网络社交间起调节作用。由此得出结论,大学生的心理需求可显著影响网络社交,对上网的好处和代价认知评估在二者间起中介作用,自我调控起调节作用。研究结果进一步揭示了心理需求影响网络社交的内在机制,可为网络时代大学生进行健康网络社交提供有益指导。     

Neurobehavioral deficits,adolescent traumatic brain injury,and transition to college

Outcome following traumatic brain injury (TBI) has been frequently evaluated for adults, although there has been minimal research on adolescents with TBI. It has been argued that TBI sequelae may be more difficult for adolescents to adjust to given developmental changes in physical (puberty), interpersonal (self-concept), and environmental domains (transition to college). In addition, it is commonly acknowledged that moderator variables such as psychiatric history, family functioning, substance use, and sexuality impact functional outcome following TBI, although it is often difficult to objectively evaluate these variables. The current study examined relationships among TBI-related deficits, moderator variables, and academic outcomes for six adolescents transitioning to college. The findings suggest that it may not be appropriate to predict functional outcome based solely on objective neuropsychological results. However, moderator variables appear to have a more direct relationship with outcome, depending on the moderator variable and the individual.     

Moderation in Management Research: What,Why, When,and How

Many theories in management, psychology, and other disciplines rely on moderating variables: those which affect the strength or nature of the relationship between two other variables. Despite the near-ubiquitous nature of such effects, the methods for testing and interpreting them are not always well understood. This article introduces the concept of moderation and describes how moderator effects are tested and interpreted for a series of model types, beginning with straightforward two-way interactions with Normal outcomes, moving to three-way and curvilinear interactions, and then to models with non-Normal outcomes including binary logistic regression and Poisson regression. In particular, methods of interpreting and probing these latter model types, such as simple slope analysis and slope difference tests, are described. It then gives answers to twelve frequently asked questions about testing and interpreting moderator effects.     

纳入式分类分析法在潜在剖面模型的后续多元回归中的应用

纳入式分类分析法能克服传统的分类分析法对后续一元回归模型参数的低估,发挥潜在类别模型的后续分析简化变量间交互作用的功能。本文进一步将纳入式分类分析法拓展至潜在剖面模型后续的多元统计分析中。通过蒙特卡洛模拟实验,比较各种纳入变量的方法思路与后续分析模型在四种常见的多元回归模型中参数估计的表现。结果发现,纳入式分类分析法所需纳入的变量取决于后续分析中与因变量、潜类别变量的关系,且后续分析使用含交互作用的模型更为稳健。