Mediation Analysis using SMART-PLS

What is Mediating Variable?

A mediator variable is the variable that causes mediation in the dependent and the independent variables. In other words, it explains the relationship between the dependent variable and the independent variable.
The variable that explains the mechanism of impact of IV on DV is referred to as a mediator.
When we say that the impact of IV on DV is not direct, and it is through another variable(s), that third variable is the mediator.
Simply mean the IV affect the MV and that leads to the DV. What we are in simple term saying is that IV does not affect the DV directly, but it is actually the IV affecting the MV and that in turn affect the DV.

Mediation

Indirect or mediated effects constitute a type of relationship between constructs that often occurs in Social Sciences Research.
The methods for testing mediation have become more sophisticated. However, many researchers continue to use outdated methods, which can lead to wrong results.
Researchers focus only on direct relationships and ignore mediating effects completely. This can heavily bias the interpretation of the results when a variable has no direct effect because its effect is mediated by another variable.
Mediation model has become ‘almost mandatory’ in the contemporary literature and research endeavours.
To understand the relevance of testing mediating effects, it is first necessary to understand what mediating effects are.
The core of mediation analysis is that it assumes a sequence of relationships in which an antecedent variable affects a mediating variable, which then affects a dependent variable.
In this way, “mediation is one way that a researcher can explain the process or mechanism by which one variable affects another” (MacKinnon et al., 2007).

Preparation for Mediation Analysis

Using multiple mediators to make a model complex and introducing a mediator to see how it works are neither a good advice nor practice. Focusing solely on statistical issues and data analysis tools is also not sufficient to justify a mediation study.

The significance of a mediation model mainly depends on the design decisions that should be considered before any analysis and even before the research is conducted. Simply stating that M will mediate the relationship between X and Y neither justifies the role of mediator nor contributes to the advancement of theory building.

The need of a mediator in a model must be explicitly raised and justified up front by responding to two key questions:

Why a mediator is needed and
Which variable should be considered the mediator, and why?

The conceptualisation of a mediation relationship needs forethought about the relationships between the variables of interest and the theoretical meaning behind those relationships.

Among other issues, reliability and validity of the instrument, and sample size are the key issues one must be aware of before conducting a mediation analysis.

Effects

When Testing for Mediation

Total Effect refers to the effect of Independent Variable on the Dependent Variable without the presence of Mediating Variable (Fig 1 (a)). Represented by C

Direct Effect refers to the effect of Independent Variable on the Dependent Variable in the presence of Mediating Variable in the Model (See Fig 1 (b)). Represented by C’

Indirect Effect refers to the effect of Independent variable on dependent variable through the mediator variable.

No. of Hypothesis

This is one of the most frequently asked questions about mediation. Rungtusanatham et al. (2014) clarified the issue of how formal hypotheses for mediation effects are developed and articulated and recommended two major approaches: segmentation and transmittal approaches.

The mediating effect and Baron and Kenny’s procedure and beyond

The core characteristic of a mediating effect (i.e. indirect effect or mediation) is that it involves a third variable that plays an intermediate role in the relationship between the independent and dependent variables.

Technically speaking, the effect of the independent variable X on the dependent variable Y is mediated by a third variable, M, called the mediating variable or mediator (see Figure Above).

Figure (a) shows the total effect c of the causal relationship between variables X and Y, and Figure (b) shows a mediated effect in which X exerts an indirect effect a × b through M on Y.

Thus, when we formulate mediation hypotheses, we focus on how an independent variable (X) affects a dependent variable (Y) by an intervening variable (M) (Baron and Kenny, 1986).

Scholars have followed a procedure similar to that proposed by Baron and Kenny (1986) for multiple regression analysis.

Preacher and Hayes (2008) summarized this approach as follows:

Variable M has a mediating effect

If X has a significant impact on Y

If X has a significant impact on M,

M significantly accounts for variability in Y, and

The effect of X on Y decreases substantially when M is entered simultaneously with X as a predictor of Y.”

However, in recent years, Baron and Kenny’s (1986) causal-step approach for determining mediating effects has been challenged considerably. For example, it is argued that Baron and Kenny’s (1986) first condition, that X needs to show a significant effect (c) on Y in the first step means an effect c should exist at all.

Initially, it seems unnecessary to further investigate whether there is a mediated effect if there is no effect c; however, this argument holds only when complementary mediation occurs in a research model (Zhao et al., 2010), which is the case only when path c has the same effect direction (i.e. positive or negative) as that of the indirect path a ×b.

In the case of competitive mediation, where the effect of the indirect path a ×b differs from that of path c, this requirement no longer holds. In complex SEMs, this can become critical because different types of mediation can occur in the same model at once. In such a case, it is possible that the direct effect c is not significant even if mediation exists and is therefore misleading as a precondition for mediation analysis.

Based on these shortcomings and the growing array of alternative approaches, state-of-the-art guidelines have to consider the following points for testing mediating effects in PLS (Preacher and Hayes, 2008; Shrout and Bolger, 2002; Zhao et al., 2010):

First, testing the indirect effect a × b provides researchers with all information for testing mediation.

Second, the strength of the indirect effect a × b should determine the size of the mediation.

Third, a bootstrap test should be used to test the significance of the indirect effect a × b.

Mediation Analysis SMART-PLS

Figure shows a decision tree that can used to determine the type of mediation analysis. It includes two steps that reflect the recommendations for mediation analysis.

Mediation Analysis - Steps

Step 1. Determining the significance of indirect effects

In Step 1, the indirect effect is tested for significance. In the simplest form of mediation, the indirect effect is the product a × b of the two paths from the source construct X to the mediator construct M (path a) and from the mediator construct M to the target construct Y (path b).

PLS researchers have often applied the parametric Sobel (1982) test for testing indirect effects. Preacher and Hayes (2004, 2008) show that the Sobel test is not appropriate for analyzing indirect effects because the parametric assumptions (i.e. normality) of paths a and b do not hold for the product term of the two paths (i.e. a × b) if one assumes that a and b are normal distributed.

Alternatively, researchers should apply bootstrap routines to test the significance of the indirect effect a × b. The bootstrapping procedure is a non-parametric inferential technique that randomly draws several subsamples (e.g. 5,000) with replacement from the original data set.

Bootstrapping a data sample of an indirect effect is necessary to obtain information about the population distribution, which is then the basis for hypotheses testing. Hence, bootstrapping routines do not require assumptions about the shape of the variable distribution (cf. Chin, 2010).

Step 2. Determining the type of effect and/or of mediation

Step 2 involves defining the type of effect and/or mediation. A mediating effect always exists when the indirect effect a × b in Step 1 is significant.

The current mediation literature discusses two different types of mediation, full and partial mediation.

Partial mediation can be divided again into complementary and competitive partial mediation.

Full Mediation

A full mediation is indicated in the case where the direct effect c′ is not significant whereas the indirect effect a × b is significant, which means only the indirect effect via the mediator exists.

In other words, full mediations means that the effect of the variable X to Y is completely transmitted with help of another variable M.

It also means the condition Y completely absorbs the positive or negative effect of X. In this way, it can completely pass an effect or it can completely hinder the effect in terms of another effect.

It is import to consider the sample size in mediation. “the smaller the sample, the more likely mediation (when present) is to be labeled full as opposed to partial because c′ is more easily rendered nonsignificant”.

Partial Mediation

All other situations under the condition that both the direct effect c′ and the indirect effect a × b are significant represent partial mediation. Two types of partial mediations can be distinguished:

Complementary Partial Mediation.

In a complementary partial mediation, the direct effect c′ and indirect effect a × b point in the same (positive or negative) direction (Baron and Kenny, 1986). It is an often observed result that a × b and c′ are significant and a × b × c′ is positive, which indicates that a portion of the effect of X on Y is mediated through M, whereas X still explains a portion of Y that is independent of M. Complementary partial mediation is often called a “positive confounding” or a “consistent” model (Zhao et al., 2010).

Competitive Partial Mediation.

In a competitive partial mediation, the direct effect c′ and indirect effect a × b point in a different direction (One is Positive while the other is negative).

As mentioned above, this indicates that a portion of the effect of X on Y is mediated through M, whereas X still explains a portion of Y that is independent of M.

In the past, researchers often focused only on complementary mediation (Zhao et al., 2010). In the competitive partial mediation hypothesis, it is assumed that the intermediate variable will reduce the magnitude of the relationship between the independent and dependent variables. However, it is possible that the intermediate variable could increase the magnitude of the relationship between the independent and dependent variables.

Competitive partial mediation has often been called a “negative confounding” or an “inconsistent” model.

Only Direct Effect

If the indirect effect a × b is not significant (i.e. the right path in the Figure 2 decision tree) whereas the direct path c′ is, the mediator variable has no impact; this indicates that a direct, non-mediating effect is present.

In this case, the study was perhaps searching for a wrong mediation relationship.

However, it is possible that an unrecognized mediation relationship still exists and another mediation variable is present that mediates an effect between X and Y (Shrout and Bolger, 2002). Thus, a researcher should rethink the model’s theoretical basis if the expected mediation relationship cannot be found (cf. Zhao et al., 2010).

No Effect

There is no effect if neither the indirect effect a×b nor the direct effect c′ is significant.

The total effect can still be significant. First of all, in this case, the researcher should determine whether the sample size has enough power to show an effect when there is an effect (Roldán and Sánchez-Franco, 2012).

Putting the last two cases together – the indirect effect a×b is not significant and the direct path c′ is or is not – frequently indicates a problematic or flawed theoretical framework (Zhao et al., 2010).

In this case, the researcher should thoroughly examine the hypothesized model. When, for example, the total effect c is significant, it can indicate that the mediation variable should be deleted because it brings no further degree of explanation. If the mediation variable M has no real effect, it only dilutes the effect of the direct variable X and should be deleted.

Complete or Full Mediation

Contemporary literature on mediation advocates that complete (also called full) and partial mediation concepts have little value and should be abandoned.

Full mediation implies that a researcher has completely explained the process by which X influences Y and no additional research is needed to search for further mediators.

The reality is that to claim full mediation, one would have to have confidently measured all possible mediators and suppressors without error. Nevertheless, measuring variables without error in social science and business research is practically impossible. Hence, ‘one cannot ever claim to have established complete mediation’.

Moreover, scholars have recently advocated that claiming a complete mediation would likely discourage researchers from examining other theoretically driven mediators, which in turn can unnecessarily constrain theory development.

Researchers should avoid using the terms complete and partial mediation when developing a mediation hypothesis or interpreting mediation effects.

References

Carrión, G. C., Nitzl, C., & Roldán, J. L. (2017). Mediation analyses in partial least squares structural equation modeling: Guidelines and empirical examples. In Partial least squares path modeling (pp. 173-195). Springer, Cham.
Memon, M. A., Cheah, J., Ramayah, T., Ting, H., & Chuah, F. (2018). Mediation analysis issues and recommendations. Journal of Applied Structural Equation Modeling, 2(1), 1-9.
Nitzl, C., Roldan, J. L., & Cepeda, G. (2016). Mediation analysis in partial least squares path modeling. Industrial management & data systems.
Ramayah, T., Cheah, J., Chuah, F., Ting, H., & Memon, M. A. (2018). Partial Least Squares Structural Equation Modeling (PLS-SEM) using SmartPLS 3.0: An Updated Guide and Practical Guide to Statistical Analysis (2nd ed.). Kuala Lumpur, Malaysia: Pearson.
Rungtusanatham, M., Miller, J. W., & Boyer, K. K. (2014). Theorizing, testing, and concluding for mediation in SCM research: Tutorial and procedural recommendations. Journal of Operations Management, 32(3), 99-113.
Sarstedt, M., Hair Jr, J. F., Nitzl, C., Ringle, C. M., & Howard, M. C. (2020). Beyond a tandem analysis of SEM and PROCESS: Use of PLS-SEM for mediation analyses!. International Journal of Market Research, 62(3), 288-299.
Zhao, X., Lynch, J. G. and Chen, Q. (2010), “Reconsidering Baron and Kenny: Myths and Truths about Mediation Analysis”, Journal of Consumer Research, Vol. 37 No. 3, pp. 197-206

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