On Partial Versus Full Mediation and the Importance of Effect Sizes

PurposeThis study aims to more deeply examine the various types of testing mediations and use the comparison test by using test-based mediation Sobel models and Bayesian approach. The purpose of this study are to apply the traditional (using indirect effect) and Sobel test, extend Yuan and MacKinnon (2009) work on Bayesian mediation analysis. Both analysis methods of mediation (Traditional, Sobel Test and Bayesian estimation) should apply in the research of management, by using structural equation modeling (SEM) in a structural model, with one mediation, one exogenous (independent) and one endogenous variable. The meta-analysis approximation has been used to investigate the job satisfaction as a mediation in the relationship between employee competence and performance (endogenous).Design/methodology/approachData were collected from ten dissertations of students of the Management Doctoral Program at the Brawijaya University from 2009 until 2013; data were analyzed for the mediation variable of job satisfaction (M) in the relationship between employee competence (X) and employee performance (Y) (Muindi and Obonyo, 2015; Olcer, 2015; Sattar et al., 2015; Khan and Ahmed, 2015). A researcher can determine the mediating variable and whether it is complete or partial or if mediation exists in several ways.FindingsThe results of the above findings using meta-analysis showed that 60% of previous research states that job satisfaction is a partial mediation on relationship competence of the performance, 10% of previous research states that job satisfaction is a full mediation on relationship competence of the performance and 30% stated that job satisfaction is not pemediasi (pemediasi means Mediation variable) on the relationship between competence and performance. This research found that all three approaches provide similar conclusions for ten previous research.Research limitations/implicationsThe findings showed that the Sobel approach and the Bayesian approach provide results that are more sensitive than the traditional approach.Practical implicationsIn my opinion, the rule to investigate the mediation variable should be completed with the conditions (1) q (theta) is not statistically significant, (2) α (alpha) and β (beta) are significant, and (3) q’ (theta) is significant, and increase when M is include as an additional predictor. This condition called partial mediation.Social implicationsThe traditional method is simpler and easy. The method is less sensitive and is not sufficient for investigating the mediating variables. In general, the method results in a mediation variable, but it cannot be used to determine either partial or complete mediation variables. So, investigation by Baron and Kenny Methods (in Hair et al., 2010), the rule or testing called Sobel Test and another approach such as Bayesian to determine the mediation variable is necessary.Originality/valueVarious methods for detecting mediating/intervening have been widely used in previous research as a method of measurement using indirect effect (Hair et al., 2010), and calculations have been performed using Sobel test (Baron and Kenny, 1986) and Bayesian approach (Enders, 2013). In this study, I wanted to more deeply examine the various types of testing mediations, and use the comparison test by using the test-based mediation Sobel models and Bayesian approach (Baron and Kenny, 1986; Enders, 2013). The statistical application should not be complicated and difficult, it but must rather be simple and easy, so that it is user-friendly. The traditional method is simpler and easier than the other methods, but how sensitive is it? This research is conducted to investigate this problem. The evaluation of mediating mechanisms has become a critical element of behavioral science research (Enders, 2013), especially in the field of management, not only to assess whether (and how) interventions achieve their effects but also, more, broadly, to understand the cause of behavioral change. Methodologists have developed mediation analysis techniques for a broad range of substantive applications. However, methods for estimating mediation mechanisms with various methods have been understudied. The purpose of this study is to apply the traditional (using indirect effect) and Sobel tests and extend Yuan and MacKinnon’s (2009) work on the Bayesian mediation analysis. Both analyses methods of mediation (traditional and Sobel test and Bayesian estimation) should apply in the research of management, by using structural equation modeling (SEM) in a structural model, with one mediation, one exogenous (independent) and one endogenous variable. The meta-analysis approximation has been used to investigate job satisfaction as the mediation in the relationship between employee competence and performance (endogenous). This study uses software R to complete the mediating effect (Enders, 2013). R is a language and environment for statistical computing and graphics. It is a GNU project which is similar to the S language and environment which was developed at Bell Laboratories (formerly AT&T, now Lucent Technologies) by John Chambers et al. R provides a wide variety of statistical analyses such as SEM and Mediation test. R provides an open source route for participation in that activity. The Bayesian estimation approach provides an R function and a macro that applies the method of mediation analysis.

Both instrumental variable (IV) estimation and mediation analysis are tools for causal inference. However, IV estimation has mostly developed in economics for causal inference from observational data. In contrast, mediation analysis has mostly developed in psychology, as a tool to empirically establish the process by which an experimental manipulation brings about its effect on the dependent variable of interest. As a consequence, many researchers well versed in IV estimation are not familiar with mediation analysis, and vice versa. In this paper, we discuss the communalities and differences between IV estimation and mediation analysis. We highlight that IV estimation leverages an a priori assumption of full mediation for causal inference. In contrast, modern practice in mediation analysis focusses on testing the statistical significance of the indirect effect without too much regard for the specification of the estimated model. A drawback of this approach is that inferring mediation from the statistical significance of a (putative) indirect effect through the hypothesized mediator may be spurious altogether. We discuss specification issues and how they relate to inference about mediation, and specifically the distinction between full and partial mediation. Based on this discussion we argue in favor of further developing tests that are more diagnostic about the underlying causal structure, motivated by the implication that full mediation could be more common than currently believed.

Causal Inference Using Mediation Analysis or Instrumental Variables - Full Mediation in the Absence of Conditional Independence

Maxwell and Cole (2007) showed that cross-sectional approaches to mediation typically generate substantially biased estimates of longitudinal parameters in the special case of complete mediation. However, their results did not apply to the more typical case of partial mediation. We extend their previous work by showing that substantial bias can also occur with partial mediation. In particular, cross-sectional analyses can imply the existence of a substantial indirect effect even when the true longitudinal indirect effect is zero. Thus, a variable that is found to be a strong mediator in a cross-sectional analysis may not be a mediator at all in a longitudinal analysis. In addition, we show that very different combinations of longitudinal parameter values can lead to essentially identical cross-sectional correlations, raising serious questions about the interpretability of cross-sectional mediation data. More generally, researchers are encouraged to consider a wide variety of possible mediation models beyond simple cross-sectional models, including but not restricted to autoregressive models of change.

Social support and motivation to transfer are important components in conceptual models on transfer of training. Previous research indicates that both support and motivation influence transfer. To date, however, it is not yet clear if social support influences transfer of training directly, or if this influence is mediated by motivation to transfer. Conceptually, some models assume that motivation to transfer fully mediates the influence of social support on transfer (full mediation models), whereas other models also include direct relationships between social support and transfer of training (partial mediation models). In addition, some models specify finer sub‐dimensions of social support, such as supervisor support, peer support, supervisor sanctions and feedback/coaching. What is the relative influence of these dimensions on the transfer of training? To what extent does motivation to transfer mediate the influence of different support dimensions and transfer? Aimed at answering these questions, the present meta‐analysis (k = 32 studies, N = 5487 participants) examined the relationships between social support, motivation to transfer and transfer of training. Social support was conceptualized in four dimensions: supervisor support, peer support, supervisor sanctions and feedback/coaching. Meta‐analytic structural equation modelling was used to test a partial mediation model and a full mediation model. Full mediation resulted in a better model fit. Peer support was the strongest predictor of motivation to transfer, and feedback/coaching was the strongest predictor of transfer of training. Theoretical and practical implications of the findings for developing conceptual models, measurement instruments and training interventions are discussed.

The study explored the total, direct and indirect effects of emotion knowledge on adjustment in preschoolers and examined whether emotion regulation mediated the relationships between emotion knowledge and adjustment (social competence, and behavioral difficulties, such as anxiety–withdrawal and anger–aggression). Two hundred forty children (118 boys and 122 girls) from 3 to 5 years of age (mean age = 4.23, SD = .80) were administered a vocabulary test to check their verbal ability and a measure of emotion knowledge. Teachers filled out two questionnaires about children’s regulation and adjustment variables. A mediation model was tested combined with an assessment of the indirect effects to evaluate whether emotion knowledge may exert an influence on adjustment through the intervention of emotion regulation. Results showed that all conditions for full mediation were met for social competence and anxiety–withdrawal, confirming the mediation role of emotion regulation in the relationship between emotion knowledge and these variables. Moreover, results indicated that emotion knowledge and anger–aggression were not directly associated as they would be in case of full or partial mediation, but they were however indirectly related through a significant linking with emotion regulation. Findings may have potential implications for prevention and intervention programs in family and school contexts, suggesting how early childhood programs targeting emotion knowledge may be especially beneficial to promote social competence and prevent behavioral problems, above all if they include other emotion-related competences, such as emotion regulation, that may be considered the linking mechanism through which emotion knowledge exerts an influence on adjustment.

Commentary: Mediation Analyses in the Real World.

With the rapid implementation of enhanced recovery after surgery, most gynecological patients are discharged without full recovery. Discharge planning is necessary for patients and their families to transition from hospital to home. Discharge teaching and discharge readiness are two core indicators used to evaluate the quality of discharge planning, which impacts the post-discharge outcomes. To improve post-discharge outcomes, the interaction mechanism of the three variables needs to be determined, but few studies have focused on it. Explore the mediating effect of discharge readiness between discharge teaching and post-discharge outcomes of gynecological inpatients. Discharge teaching and discharge readiness were measured by the Quality of Discharge Teaching Scale (QDTS) and Readiness for Hospital Discharge Scale (RHDS). Post-discharge outcomes on postoperative Day 7 (POF-D7) and postoperative Day 28 (POF-D28) were measured by a self-designed tool. Spearman correlations, Kruskal‒Wallis tests and Mann‒Whitney U tests were conducted to explore the correlation between post-discharge outcomes and other variables. Mediation analysis was used to explore the mediating effect of discharge readiness between discharge teaching and post-discharge outcomes. QDTS and RHDS showed strong positive correlations with post-discharge outcomes. The mediation analyses verified that RHDS was a full mediator between QDTS and POF-D7, and the indirect effect accounted for 95.6% of the total direct effect. RHDS was a partial mediator between QDTS and POF-D28, and the indirect effect accounted for 50.0% of the total direct effect. RHDS was a full mediator between QDTS and total scores of post-discharge outcomes, and the indirect effect accounted for 88.9% of the total direct effect. Discharge teaching can improve the post-discharge outcomes of gynecological inpatients through the intermediary role of discharge readiness. Doctors and nurses should value the quality of discharge teaching and the discharge readiness improving of gynecological inpatients. Future studies should note the interaction mechanism of the three variables to explore more efficient ways of improving post-discharge outcomes of gynecological inpatients.

As a theoretical framework for understanding illness self-management, the commonsense model of self-regulation (CSM) has been commonly used to promote health behaviors. However, its application to examining gambling disorder (GD) is still in an exploratory stage. Based on CSM, the current study aimed to address this knowledge gap and test whether illness representations (i.e., perceived consequences, illness coherence, and emotional representations) of GD are associated with gambling behaviors (i.e., responsible gambling [RG] and superstitious gambling). We also aimed to explore the potential mediating role of positive gambling beliefs (i.e., personal responsibility about gambling and gambling literacy) in such associations. An online questionnaire survey with snowballing sampling method was administered to Chinese adult past-year gamblers, and 603 valid responses were collected. The structural equation modeling (SEM) analysis with a bootstrapping approach was utilized to test the associations of illness representations with gambling behaviors and the hypothesized mediation effects of positive gambling beliefs. We found that (a) perceived consequences of GD had significant, positive associations with RG and negative associations with superstitious gambling, with positive gambling beliefs acting as full mediators; (b) emotional representations for GD showed significant, negative correlations with RG and positive ones with superstitious gambling, with positive gambling beliefs acting as full and partial mediators, respectively; (c) the direct effect of illness coherence of GD on superstitious gambling behaviors was unexpectedly positive, and its indirect effects via positive gambling beliefs were nonsignificant. Under the framework of CSM, the current findings provided new insights in understanding both controlled and at-risk gambling patterns from a perspective of illness self-management. We suggest future GD prevention campaigns may adopt psychoeducational programs to help gamblers form a better understanding about GD as an illness, which may promote RG practices and hence lower the risk of developing GD.

The study gives an account of management control practices in Libya during a period of relative political and economic stability that preceded the 2011 war and regime change. Using a two-level contingency model and survey data, stepped mediation regression first ascertains contingency relationships between organisational variables and management control system (MCS)effectiveness. We also explicitly focus on the mediating role of management accounting information (MAI) in MCS effectiveness. We find that centralisation, formalisation, environmental uncertainty and competitive strategy significantly influence MCS effectiveness. Full mediation is observed in relation to centralisation, whereas partial mediation is detected for formalisation, environmental uncertainty, and competitive strategy. Manufacturing process complexity is not present in first level relationships and further tests only yielded an indirect MAI effect, not mediation in this case. The full vs. partial mediation distinction is not evident in most previous MCS interaction research, nor is the isolation of the indirect effect, and future research needs to explore this with larger samples. This is possibly the first study to develop and apply a multi-level contingency model that explicitly focuses on the mediating role of MAI to empirically examine MCS effectiveness and contributes to the nascent literature on management accounting in emerging economies.

Mediation analysis is an important statistical method in prevention research, as it can be used to determine effective intervention components. Traditional mediation analysis defines direct and indirect effects in terms of linear regression coefficients. It is unclear how these traditional effects are estimated in settings with binary variables. An important recent methodological advancement in the mediation analysis literature is the development of the causal mediation analysis framework. Causal mediation analysis defines causal effects as the difference between two potential outcomes. These definitions can be applied to any mediation model to estimate natural direct and indirect effects, including models with binary variables and an exposure–mediator interaction. This paper aims to clarify the similarities and differences between the causal and traditional effect estimates for mediation models with a binary mediator and a binary outcome. Causal and traditional mediation analyses were applied to an empirical example to demonstrate these similarities and differences. Causal and traditional mediation analysis provided similar controlled direct effect estimates, but different estimates of the natural direct effects, natural indirect effects, and total effect. Traditional mediation analysis methods do not generalize well to mediation models with binary variables, while the natural effect definitions can be applied to any mediation model. Causal mediation analysis is therefore the preferred method for the analysis of mediation models with binary variables.

Mediation analysis is important for research in psychology and other social and behavioral sciences. Great progress has been made in testing mediation effects and in constructing their confidence intervals. Mediation effect sizes have also been considered. Preacher and Kelley (2011) proposed and recommended κ² as an effect size measure for a mediation effect. In this article, we argue that κ² is not an appropriate effect size measure for mediation models, because of its lack of the property of rank preservation (e.g., the magnitude of κ² may decrease when the mediation effect that κ² represents increases). Furthermore, κ² can lead to paradoxical results in multiple mediation models. We show that the problem of κ² is due to (a) the improper calculation of the maximum possible value of the indirect effect, and (b) mathematically, the maximum possible indirect effect is infinity, implying that the definition of κ² is mathematically incorrect. At this time, it appears that the traditional mediation effect size measure PM (the ratio of the indirect effect to the total effect), together with some other statistical information, should be preferred for basic mediation models. But for inconsistent mediation models where the indirect effect and the direct effect have opposite signs, the situation is less clear. Other considerations and suggestions for future research are also discussed.

Reports an error in "Monotonicity of Effect Sizes: Questioning Kappa-Squared as Mediation Effect Size Measure" by Zhonglin Wen and Xitao Fan (Psychological Methods, Advanced Online Publication, Feb 9, 2015, np). There were various errors pertaining to the use of variable "R". Under the heading Lack of Monotonicity of k², the second, eleventh, and thirteenth paragraph and under the heading Paradoxical Behaviors of k² Multiple Mediation Models, the third paragraph incorrectly italicized the variable "R." All versions of this article have been corrected. (The following abstract of the original article appeared in record 2015-04977-001.) Mediation analysis is important for research in psychology and other social and behavioral sciences. Great progress has been made in testing mediation effects and in constructing their confidence intervals. Mediation effect sizes have also been considered. Preacher and Kelley (2011) proposed and recommended κ2 as an effect size measure for a mediation effect. In this article, we argue that κ2 is not an appropriate effect size measure for mediation models, because of its lack of the property of rank preservation (e.g., the magnitude of κ2 may decrease when the mediation effect that κ2 represents increases). Furthermore, κ2 can lead to paradoxical results in multiple mediation models. We show that the problem of κ2 is due to (a) the improper calculation of the maximum possible value of the indirect effect, and (b) mathematically, the maximum possible indirect effect is infinity, implying that the definition of κ2 is mathematically incorrect. At this time, it appears that the traditional mediation effect size measure PM (the ratio of the indirect effect to the total effect), together with some other statistical information, should be preferred for basic mediation models. But for inconsistent mediation models where the indirect effect and the direct effect have opposite signs, the situation is less clear. Other considerations and suggestions for future research are also discussed.

Objectives This study aims to establish and verify a structural equation model of the variables related to critical consciousness, multicultural counseling self-efficacy, and multicultural counseling competence. Methods The participants of this study were selected on the basis that they obtained bachelor’s degrees or higher in counseling and psychology and who have worked as counselors in institutions with multicultural education. A total of 233 data was analyzed with SPSS 27 and AMOS 29. Results All variables showed significant positive correlations. Model identification was based on goodness of fit and χ2 difference test criteria. This study compared a partial mediation (research) model with a full mediation (alternative) model, based on theoretical foundations. The partial mediation model was ultimately selected. The mediating effect of multicultural counseling self-efficacy was found to be significant. Conclusions Multicultural counseling self-efficacy demonstrated a partial mediating effect between critical consciousness and multicultural counseling competence. When utilizing critical consciousness to enhance multicultural counseling competence, it would be beneficial to apply it in conjunction with self-efficacy. This study provides a foundation for counselors to incorporate critical consciousness into multicultural counseling competence development training, which is considered to be its significant contribution.

Mediation analysis, or more generally models with direct and indirect effects, are commonly used in the behavioral sciences. As we show in our illustrative example, traditional methods of mediation analysis that omit confounding variables can lead to systematically biased direct and indirect effects, even in the context of a randomized experiment. Therefore, several definitions of causal effects in mediation models have been presented in the literature (Baron & Kenny, 1986; Imai, Keele, & Tingley, 2010; Pearl, 2012). We illustrate the stochastic theory of causal effects as an alternative foundation of causal mediation analysis based on probability theory. In this theory we define total, direct, and indirect effects and show how they can be identified in the context of our illustrative example. A particular strength of the stochastic theory of causal effects are the causality conditions that imply causal unbiasedness of effect estimates. The causality conditions have empirically testable implications and can be used for covariate selection. In the discussion, we highlight some similarities and differences of the stochastic theory of causal effects with other theories of causal effects.