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。     

Perceiving a calling and well-being: Motivation and access to opportunity as moderators

The current study examined moderator variables that may accentuate the effect of perceiving a calling on well-being amongst a large and diverse sample of working adults (N = 746). Drawing from Self Determination Theory (SDT; Deci & Ryan, 2000) and the Psychology of Working Theory (PWT: Duffy, Blustein, Diemer, & Autin, 2016), perceiving a calling was hypothesized to have greater effects on wellbeing for individuals with greater calling motivation and access to vocational opportunity, as assessed by income and work volition. Three moderated, multiple mediator models using structural equation modeling were run to test these hypotheses. Specifically, life meaning and living a calling were positioned as mediator variables in the relation of perceiving a calling to life satisfaction and the paths from perceiving a calling to the mediators were proposed to be significantly moderated. Calling motivation was found to be a significant moderator for both paths, supporting propositions of SDT. As the motivation to pursue one's calling increased, the direct effects on life meaning and living a calling and the indirect effects on life satisfaction were stronger. Income was also found to be a significant moderator, supporting propositions of the PWT, but only in the relation of perceiving a calling to living a calling. It was proposed that work volition—a variable related to the perception of vocational opportunity—may be better positioned as correlate of calling variables versus a moderator variable affecting the impact of having a calling. Practical implications are discussed.     

基于结构方程模型的有调节的中介效应分析

有调节的中介模型是中介过程受到调节变量影响的模型。指出了目前有调节的中介效应分析普遍存在的问题：当前有调节的中介效应检验大多使用多元线性回归分析,忽略了测量误差;而基于结构方程模型(SEM)的有调节的中介效应分析需要产生乘积指标,又会面临乘积指标生成和乘积项非正态分布的问题。在简介潜调节结构方程(LMS)方法后,建议使用LMS方法得到偏差校正的bootstrap置信区间来进行基于SEM的有调节的中介效应分析。总结出一个有调节的中介SEM分析流程,并有示例和相应的Mplus程序。文末展望了LMS和有调节的中介模型的发展方向。     

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.     

Methods for integrating moderation and mediation: a general analytical framework using moderated path analysis

Studies that combine moderation and mediation are prevalent in basic and applied psychology research. Typically, these studies are framed in terms of moderated mediation or mediated moderation, both of which involve similar analytical approaches. Unfortunately, these approaches have important shortcomings that conceal the nature of the moderated and the mediated effects under investigation. This article presents a general analytical framework for combining moderation and mediation that integrates moderated regression analysis and path analysis. This framework clarifies how moderator variables influence the paths that constitute the direct, indirect, and total effects of mediated models. The authors empirically illustrate this framework and give step-by-step instructions for estimation and interpretation. They summarize the advantages of their framework over current approaches, explain how it subsumes moderated mediation and mediated moderation, and describe how it can accommodate additional moderator and mediator variables, curvilinear relationships, and structural equation models with latent variables.     

THE INTERACTION OF ABILITY AND MOTIVATION IN PERFORMANCE: AN EXPLORATION OF THE MEANING OF MODERATORS1

It was hypothesized that one possible explanation of moderator effects is that they are due to different degrees of homogeneity with respect to a causal variable among different subgroups. This hypothesis was tested in a laboratory experiment in which performance was predicted from ability using motivation as the moderator. Ability was measured with a work sample and motivation was varied by assigning goals with different degrees of difficulty and specificity. It was found that ability predicted performance better in groups which were homogeneous with respect to motivation that in those which were motivationally heterogeneous. A moderated regression analysis showed that most of the differential validity was reducible to main effects, but significant interaction effects were found. One of them was caused by the fact that in one low motivation condition the variance in performance was reduced, thus decreasing the slope of the regression line.     

Trait-Specific Versus Person-Specific Moderators of Cross-Situational Consistency

ABSTRACT Moderator variables for cross-situational consistency can be tested m two different ways (a) a trait-specific manner which examines differences in cross-situational consistency among traits, or (b) a person-specific manner which examines differences in cross-situational consistency among people The present study examined moderator effects–both trait- and person-specific–of the discrepancy between private self-ratings on trait dimensions (“How do you see yourself?”) and the corresponding public self-ratings (“How do others see you?”) Agreement between self- and peer ratings served as the dependent variable The results showed that public-private discrepancy moderated self-peer agreement when operationalized in a trait-specific manner, i e, for each trait, higher discrepancy was associated with lower self-peer agreement On the other hand, the results showed only minimal moderator effects when public-private discrepancy was operationalized in a person-specific manner, i e, when mean discrepancy across all traits served as the moderator Implications of the distinction between trait- and person-specific approaches to moderator effects are discussed     

A standard for test reliability in group research

Many authors adhere to the rule that test reliabilities should be at least .70 or .80 in group research. This article introduces a new standard according to which reliabilities can be evaluated. This standard is based on the costs or time of the experiment and of administering the test. For example, if test administration costs are 7 % of the total experimental costs, the efficient value of the reliability is .93. If the actual reliability of a test is equal to this efficient reliability, the test size maximizes the statistical power of the experiment, given the costs. As a standard in experimental research, it is proposed that the reliability of the dependent variable be close to the efficient reliability. Adhering to this standard will enhance the statistical power and reduce the costs of experiments.     

Parenting and Conduct Problems: Moderation by Child Empathy

Child empathy was examined as a moderator of the relations between positive and negative parenting behavior and child conduct problems. Participants were 56 mother-child dyads (child age M?=?10.8 years; 64 % male) and children were recruited with a range of Attention-Deficit/Hyperactivity Disorder (ADHD) symptoms. Parenting was assessed by direct observations of mothers’ praise and criticism during parent–child interactions and child empathy was measured with mother report. Child conduct problems were assessed via observation and mother-report measures, and a composite variable was created. In regression analyses, child ADHD symptoms were uniquely related to child conduct problems. Second, as hypothesized, child empathy moderated the relations between parenting and conduct problems. Mother praise was negatively related to child conduct problems at lower levels of child empathy, but this relation was not significant at higher levels of child empathy. On the contrary, mother criticism was positively related to child conduct problems at high levels of child empathy, but this relation was not significant at low levels of empathy. The results suggest that different types of parenting behavior may be differentially beneficial to children, depending on their level of empathy.     

青少年自尊与攻击的关系：中介变量和调节变量的作用

以705名初、高中生为被试,采用量表法和同伴提名法收集数据,探讨了自尊与攻击的关系以及对二者关系可能有影响的中介变量和调节变量的作用。结果表明：（1）自尊与攻击的相关系数为-0.21,这说明低自尊与高攻击有关;（2）回归方程纳入自控后,自尊对攻击的预测在统计意义上不明显,表明自尊通过自控对攻击产生影响,自控在自尊与攻击的关系中起着中介的作用;（3）社会地位对自尊与攻击之间的关系具有调节作用,它调节着两者关系的强度;（4）社会影响对自控的中介作用具有调节作用     

基于两水平回归模型的调节效应分析及其效应量

使用多元回归法进行调节效应分析在社科领域已常有应用。简述了目前多元回归法的调节效应分析存在的不足,包括人为变换检验模型、自变量和调节变量区分不足、误差方差齐性的假设难以满足、调节效应量指标ΔR²没有直接测量调节变量对自变量与因变量关系的调节程度。比较好的方法是用两水平回归模型进行调节效应分析并使用相应的效应量指标。在介绍新方法和新效应量后,总结出一套调节效应的分析流程,通过一个例子来演示如何用Mplus软件进行两水平回归模型的调节效应及其效应量分析。最后讨论了两水平回归模型的调节效应分析的发展,包括稳健的调节效应分析、潜变量的调节效应分析、有调节的中介效应分析和有中介的调节效应分析等。     

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。     

Detection of interactions between a dichotomous moderator and a continuous predictor in moderated multiple regression with heterogeneous error variance

Moderated multiple regression (MMR) has been widely used to investigate the interaction or moderating effects of a categorical moderator across a variety of subdisciplines in the behavioral and social sciences. In view of the frequent violation of the homogeneity of error variance assumption in MMR applications, the weighted least squares (WLS) approach has been proposed as one of the alternatives to the ordinary least squares method for the detection of the interaction effect between a dichotomous moderator and a continuous predictor. Although the existing result is informative in assuring the statistical accuracy and computational ease of the WLS-based method, no explicit algebraic formulation and underlying distributional details are available. This article aims to delineate the fundamental properties of the WLS test in connection with the well-known Welch procedure for regression slope homogeneity under error variance heterogeneity. With elaborately systematic derivation and analytic assessment, it is shown that the notion of WLS is implicitly embedded in the Welch approach. More importantly, extensive simulation study is conducted to demonstrate the conditions in which the Welch test will substantially outperform the WLS method; they may yield different conclusions. Welch’s solution to the Behrens-Fisher problem is so entrenched that the use of its direct extension within the linear regression framework can arguably be recommended. In order to facilitate the application of Welch’s procedure, the SAS and R computing algorithms are presented. The study contributes to the understanding of methodological variants for detecting the effect of a dichotomous moderator in the context of moderated multiple regression. Supplemental materials for this article may be downloaded from brm.psychonomic-journals.org/content/supplemental.     

有调节的中介模型检验方法：竞争还是替补?

在心理和其他社科研究领域, 经常遇到中介和调节变量。模型的变量多于3个时, 可能同时包含中介和调节变量, 一种常见的模型是有调节的中介模型。本文检视文献上各种检验有调节的中介模型的方法, 理清方法之间是竞争关系(分清优劣)还是替补关系(分清先后), 在此基础上总结出检验有调节的中介模型的步骤, 并用一个实例进行演示。文中也讨论了有调节的中介模型与有中介的调节模型的联系与区别。     

Reliability coefficients as a function of individual differences induced by a learning process assuming identical organisms

In this article we show that a particular mathematical learning model, the Bower-Trabasso (1964) concept identification model taken together with an assumption of independence of replicate measurements, implies the existence of substantial and statistically significant performance differences across individuals. The individual differences in turn imply a sizeable reliability coefficient. These results contradict naive intuition, for this model (like many other mathematical models of learning) assumes that all individuals begin the experiment with identical parameter values for the process under study. Thus at least one such model has the characteristic of implying the generation of individual performance differences among originally identical organisms.Examination of data from an experiment by Cotton shows that the Hoyt reliability coefficient under classical test theory, a lower bound for the (composite) reliability of total scores for a series of trials, increases with the number of trials analyzed and exceeds the corresponding theoretical values implied by the Bower-Trabasso model. An experiment by Levine was also analyzed because its use of blank trials between feedback trials permitted direct calculation of composite reliability (or more properly stated composite consistency). For this experiment, the theoretical development just discussed (Case I) was used together with Restle's hypothesis selection model specialized to include a local consistency assumption, the so-called P₂ model of Gregg and Simon (Case II). Moderate conformity of empirical and theoretical reliabilities was found, with discrepancies between observed and predicted values usually being smaller with Case II. However, the Hoyt reliability coefficient is not a lower bound for composite reliability in Case II, because composite reliability is underestimated when identical stimuli are not used for comparable trials.Despite the Bower-Trabasso assumption of no initial differences, it seems reasonable to attribute the difference between predicted and obtained reliabilities to preexisting individual differences. Implications of the tentative conclusion that individual differences in concept identification performance are attributable to a combination of preexisting differences and differences induced in a current task are discussed briefly.     

Child Personality as Moderator of Outcome in a School‐based Intervention for Preventing Externalising Behaviour

Studying moderators of intervention effects is essential to elucidate what works for whom. The present study investigated whether child personality moderates short‐term and follow‐up effects of an individualised preventive school‐based intervention for children with externalising behaviour. The sample consisted of 48 schools, with 264 fourth‐grade children displaying externalising behaviour (M_age = 10.2 years), randomly assigned to the intervention (n = 191) or no intervention control (n = 73) condition. Teachers and children reported at pretest, posttest and follow‐up test about reactive and proactive aggression. Child personality was assessed by teachers at pretest. Child conscientiousness moderated short‐term intervention effects, indicating that more organised and planful children benefited more from the intervention. Child extraversion moderated both short‐term and follow‐up intervention effects, with low extraverted children showing larger effects. These results affirm the importance of including personality as moderator of intervention effects in future studies, as interventions adapted to specific child traits might yield larger effects. Copyright © 2012 John Wiley & Sons, Ltd.     

An affordable computer-aided method for conducting Morris water maze testing

A relatively inexpensive and reliable computer-aided method for assessing Morris water maze performance is described. The procedure uses SigmaScan digitizing software (Jandel Scientific, San Rafael, CA) to collect distance swum data, while escape latencies are measured with a hand-held stopwatch. Swim paths are videotaped for subsequent viewing and saved on disk as data sets ofx,y coordinates. At a later time,x,y data files are printed and analyzed to obtain additional performance measures (e.g., distance swum in previous reinforced quadrant, heading angle, etc.). Intra- and interrater reliabilities associated with this method are presented. Correlation coefficients in ther = .85?.90 and above range are reported for both reliability types. Given its approximate cost of $1,500 (excluding the price of an IBM-compatible computer), the present procedure potentially can aid in performing instructional and research activities at small colleges which typically lack extensive equipment budgets.     

At what sample size do latent variable correlations stabilize?

We conducted a Monte-Carlo simulation within a latent variable framework by varying the following characteristics: population correlation (ρ = 0.10, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90, and 1.00) and composite score reliability (coefficient omega: ω = 0.40, 0.50, 0.60, 0.70, 0.80, and 0.90). The sample sizes required to estimate stable measurement-error-free correlations were found to approach N = 490 for typical research scenarios (population correlation ρ = 0.20; composite score reliability ω = 0.70) and as high as N = 1000+ for data associated with lower, but still sometimes observed, reliabilities (ω = 0.40–0.50). We encourage researchers to take into consideration reliability, when evaluating the sample sizes required to produce stable measurement-error-free correlations.