With strong support from the users of SmartPLS in Malaysia, the 1st edition was sold out quickly. This is the updated 2nd edition of the manual, specifically with the addition of chapters pertaining to mediation and moderation analyses. SmartPLS has become a popular choice to perform PLS-SEM among researchers and students today.
This post intends to introduce the basics of mediation analysis and does not explain statistical details. For details, please refer to the articles at the end of this post.
What is mediation?
Let’s say previous studies have suggested that higher grades predict higher happiness: X (grades) → Y (happiness). (This research example is made up for illustration purposes. Please don’t consider it a scientific statement.)
I think, however, grades are not the real reason that happiness increases. I hypothesize that good grades boost one’s self-esteem and then high self-esteem boosts one’s happiness: X (grades) → M (self-esteem) → Y (happiness).
This is a typical case of mediation analysis. Self-esteem is a mediator that explains the underlying mechanism of the relationship between grades (IV) and happiness (DV).
How to analyze mediation effects?
Before we start, please keep in mind that, as any other regression analysis, mediation analysis does not imply causal relationships unless it is based on experimental design.
To analyze mediation:
1. Follow Baron & Kenny’s steps 2. Use either the Sobel test or bootstrapping for significance testing.
The following shows the basic steps for mediation analysis suggested by Baron & Kenny (1986). A mediation analysis is comprised of three sets of regression: X → Y, X → M, and X + M → Y. This post will show examples using R, but you can use any statistical software. They are just three regression analyses!
Step 1.
$$Y = b_{0} + b_{1}X + e$$
Is (b_{1}) significant? We want X to affect Y. If there is no relationship between X and Y, there is nothing to mediate.
Although this is what Baron and Kenny originally suggested, this step is controversial. Even if we don’t find a significant association between X and Y, we could move forward to the next step if we have a good theoretical background about their relationship. See Shrout & Bolger (2002) for details.
Step 2.
$$M = b_{0} + b_{2}X + e$$
Is (b_{2}) significant? We want X to affect M. If X and M have no relationship, M is just a third variable that may or may not be associated with Y. A mediation makes sense only if X affects M.
Step 3.
$$Y = b_{0} + b_{4}X + b_{3}M + e$$
Is (b_{4}) non-significant or smaller than before? We want M to affect Y, but X to no longer affect Y (or X to still affect Y but in a smaller magnitude). If a mediation effect exists, the effect of X on Y will disappear (or at least weaken) when M is included in the regression. The effect of X on Y goes through M.
If the effect of X on Y completely disappears, M fully mediates between X and Y (full mediation). If the effect of X on Y still exists, but in a smaller magnitude, M partially mediates between X and Y (partial mediation). The example shows a full mediation, yet a full mediation rarely happens in practice.
Once we find these relationships, we want to see if this mediation effect is statistically significant (different from zero or not). To do so, there are two main approaches: the Sobel test (Sobel, 1982) and bootstrapping (Preacher & Hayes, 2004). In R, you can use
sobel() in ‘multilevel’ package for the Sobel test and mediate() in ‘mediation’ package for bootstrapping. Because bootstrapping is strongly recommended in recent years (although Sobel test was widely used before), I’ll show only the bootstrapping method in this example.
mediate() takes two model objects as input (X → M and X + M → Y) and we need to specify which variable is an IV (treatment) and a mediator (mediator). For bootstrapping, set boot = TRUE and sims to at least 500 . After running it, look for ACME (Average Causal Mediation Effects) in the results and see if it’s different from zero. For details of mediate() , please refer to Tingley, Yamamoto, Hirose, Keele, & Imai (2014).
Note that the Total Effect in the summary (
0.3961 ) is (b_{1}) in the first step: a total effect of X on Y (without M). The direct effect (ADE, 0.0396 ) is (b_{4}) in the third step: a direct effect of X on Y after taking into account a mediation (indirect) effect of M. Finally, the mediation effect (ACME) is the total effect minus the direct effect ((b_{1} – b_{4}), or 0.3961 - 0.0396 = 0.3565 ), which equals to a product of a coefficient of X in the second step and a coefficient of M in the last step ((b_{2} times b_{3}), or 0.56102 * 0.6355 = 0.3565 ). The goal of mediation analysis is to obtain this indirect effect and see if it’s statistically significant.
By the way, we don’t have to follow all three steps as Baron and Kenny suggested. We could simply run two regressions (X → M and X + M → Y) and test its significance using the two models. However, the suggested steps help you understand how it works!
Mediation analysis is not limited to linear regression; we can use logistic regression or polynomial regression and more. Also, we can add more variables and relationships, for example, moderated mediation or mediated moderation. However, if your model is very complex and cannot be expressed as a small set of regressions, you might want to consider structural equation modeling instead.
To sum up, here’s a flowchart for mediation analysis!
For more information:
Bommae Kim Statistical Consulting Associate University of Virginia Library April 18, 2016 (published) July 12, 2016 (typos in flowchart corrected)
For questions or clarifications regarding this article, contact the UVa Library StatLab: [email protected]
June 04-07, 2019
Established in 1980, Institute of Management Technology, Ghaziabad (IMTG) is India’s premier AACSB accredited management school with a distinct focus on grooming leadership through Innovation, Execution and Social Responsibility. An autonomous, not–for–profit institute, offering highly sought after postgraduate programmes over the past more than three–and–a–half decades. IMTG has been consistently ranked among the top management institutes of the country. Publication has been a focus area of IMT Ghaziabad and we are among the top business school for research and publication in India. This workshop aims to extent the expertise of IMT Ghaziabad in research to other management institute to facilitate career development of the faculties and research scholars in the other management institution.
Structural Equation Modelling (SEM) is a statistical methodology that is widely used in social sciences research (especially marketing, organizational behavior, human resource management, psychology, behavioral finance and behavioral economics). SEM models are so general that they encompass most of the statistical methods that are currently used in the social and behavioral sciences. SEM allows a researcher to test complex models with multiple pathways, model latent variables with multiple indicators, investigate mediation and moderation in a systematic way and adjust for measurement error in predictor variables. This workshop shall provide the participants a descriptive theoretical and practical knowledge to SEM, moderation and mediation. AMOS, PLS, and Process macro will be use to learn all the statistical technique, which is uniqueness of the workshop.
Research scholars, Faculty members who aspire to publish and professional from industry engaged in research and data analysis
Participants are requested to register by filling the online registration form after the payment has been successfully completed. Please mail screenshot of Payment made to email id: [email protected]
*The registration fee includes Participation, course materials, certificate, lunch for each day and tea/coffee during the program and post program support for analyzing your data. 10% group member discount (3 or more from same institute). Accommodation will be provided on payment basis in the Institute for outstation participants depending on the availability.
Bank details for NEFT:
Beneficiary Name: Institute of Management Technology
Pan No: AAATL1391H Address : Hapur Road, Raj Nagar, Ghaziabad, UP -201001, INDIA Beneficiary Bank Name : ORIENTAL BANK OF COMMERCE Beneficiary Bank Address : Raj Kunj, Raj Nagar, Ghaziabad Beneficiary Bank A/c No.: 09202010010580 Type of Account.: Saving Account IFSC Code: ORBC0100920 Beneficiary Email ID: [email protected] [email protected] Contact No.: 0120-3002278, 0120-3002205
Registration form for participants :
Registration will close on May 25, 2019 or when the seats of the workshop are filled (whichever is earlier). The seats of the workshop are limited (20 in number). The registration will be purely on first-come-first-serve basis. IMT Ghaziabad reserves the right to deny registration once the seats are full.
Amit Shankar
Assistant Professor (Marketing)
Prof. Amit Shankar is Assistant Professor at IMT Ghaziabad in the area of Marketing Management. He is PhD from Vinod Gupta School of Management, IIT Kharagpur. He has Academic experience of 3 years working with renowned Institutes. He has published in leading journals (ABDC journal classification). He has conducted workshops on SPSS, Amos, SmartPLS, Advanced Excel, and Process Macro in premier institutes of India.
Bikramjit Rishi
Associate Professor (Marketing)
Prof. Bikramjit Rishi is Associate Professor at IMT Ghaziabad in the area of Marketing Management. He is PhD from Punjabi University, Patiala and holds Post-Doctoral Fellowship of the European Union.. He has published in leading journals (ABDC journal classification). He has conducted several workshops on research methodology in premier institutes of India.
Advanced Structural Equation Modeling, Moderation and Mediation Analysis using AMOS, SmartPLS, & Process Macro ultima modifica: 2019-02-27T09:58:22+05:30 da
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