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Theoretical and Corresponding Models in Mediation Analysis

Question:

Discuss Mediator Plays Important roles in the Conceptual Model.

Mediation generally means to an intermediation, in which one variable bridge the gap between two variables and tries to find out the relationship between both. In other terms, mediation is a causal model explaining the process of ‘‘why’’ and ‘‘how’’ a cause-and-effect happens (VanderWeele, 2016). Thus, it can be significantly quoted that meditational analysis tries to find out the process that leads an independent variable to the dependent. The independent variable is further perceived as a cause to be a dependent variable on the mediating factor.

The researcher has argued that when to discuss of mediation, it is important to understand two main models that exist, one is theoretical, and on the other hand, one is corresponding (Valeri and VanderWeele, 2013). Both are used to access the relationship between two random variables. However, inferring the true state of mediation from observations is a challenging task for researchers. To simplify the theory and to find the most suitable relation among random variables, a third variable is used which is called as mediating variable (Understanding and Using Mediators and Moderators. 2015).

The conceptual models are designed on the basis of establishing a relationship between the variable, however, sometimes it becomes difficult to make and direct relationship between dependent and independent variable (Preacher, 2015). In such situations, mediating factors of variable become useful and are designed to drag the findings while supporting independent variable. The role of mediating analysis is essential to determine whether or not mediators are useful when to find out a relationship between two variables X and Y. The study attempts to know the role of mediating factor/ variable in the conceptual model. The present study is based on the description of determining roles of mediator in the conceptual model by considering the approach of Baron & Kenny and Preacher & Hayes. It will include practical examples of mediation by considering previous studies of various research scholars.

The main issues of here with study are to find out how important a mediating variable is to establish a conceptual model. A conceptual model contains two main variables one is dependent and second one is independent. For example, colleges authorities use the time put be students of study in a day (independent variable)  to get higher marks in the exams (dependent variables). However, there is a need of putting mediator variable in the framework like as other factors affecting study hours. The example given in the above section represents the need of mediating variable for establishing a conceptual framework on which basis the objectives of an investigation can be attained (Fairchild and McDaniel, 2017). The study attempts to know how a mediator variable of the hypothesis is used to establish an effective relationship between an independent variable and a dependent variable so that relationship can be explained better through a conceptual model. The problem of this study is justified as it is a fact that conceptual framework/ model in a research investigation need to be clear in terms of explaining the relationship between variable. So the question is “how a mediating variable helps research to create an effective conceptual model”. 

The Role of Mediating Factors in the Conceptual Model

A conceptual model is the foremost requirement of academic and professional researchers; however, the role of mediating factors cannot be neglected from research area (Preacher, 2015). This research is going to explain the role of mediating factors in the conceptual model. The significance of the findings of the present investigation will be for students, academicians as well as research scholars as they can gain an understanding of the concept of mediator and different forms of mediating factors. Various techniques of mediating effect are explained in this researcher along with examples so that reader can gain sufficient knowledge of the subject and can apply it in their future studies.

  • To study the concept of mediator and the different forms of mediating effects
  • To extract understanding of various assessment techniques for mediating effect
  • What role does a mediating factor/ variable play in the conceptual model?

Concept of mediator and different forms of mediating effects

In statistics, a model of mediation refers to identification and explanation of the mechanism which triggers  an observed connection between an independent variable and a dependent variable through the addition of a third theoretical variable referred as  a mediator variable. It mainly consists two types of effects that are direct and indirect effect. In accordance with the study of Zhao and Co-authors (2010), mediation and its effect can be understood by the following diagram:

In the above diagram, the indirect effect is the result of path coefficients both "A" and "B". Coefficient ‘’C’’ is the direct effect. The direct effect is calculating the level through which dependable variable vary when the independent variable is making an increase by one unit, leaving no effect on mediator variable (Shrout, and Bolger, 2002). On the other hand, the indirect effect calculates the level by which dependent variable takes changes when the in independent variable seems rigid and variable of mediator changes with the amount it would have altered the increase of independent variable by one unit. In linear systems, the overall effect is equivalent to a total of the direct and indirect effects (C + AB in the model above). But in nonlinear models, the overall effect is not commonly equivalent to the subtotal of the direct and indirect effects, but then again to an adapted arrangement of the two.

Assessment technique of mediating effect based on the Baron & Kenny approach

Baron & Kenny's process shows the description of the analyses which are essential for testing the diverse mediational hypothesis. Study of Kristeller (2003) shows that their model has been based on four primary steps. In the first step of Baron & Kenny's procedures, the researcher should be aware of the fact that the primary variable is considered as correlated with the effect variable.  Putting it differently, the first stage in Baron & Kenny's process is engaged in the establishment of an outcome which might be mediated. In the second step of Baron & Kenny's procedures, the researcher should be made known about the primary variable is considered as correlated with the mediator. More simply, the second stage in Baron & Kenny's process is engaged in treating a variable of the mediator as an effect variable.

Baron & Kenny and Preacher & Hayes Approaches to Mediating Effect

Thirdly in Baron & Kenny's procedures, engages in the establishment concerning the correlation between the outcome variable and the mediator variable.  At this stage of Baron & Kenny's procedures, the existence of a correlation is there between the outcome and the mediator variable it is because both are the result of the initial variable (Lutz and et.al. 2008).  Put in other words, in Baron & Kenny's procedures, controlling of the initial variable must be done during the establishment of  the correlation between the two variables. Fourth, last but not the least in Baron & Kenny's procedures, it engages the establishment of the total mediation all over the variables.  It is the last stage of Baron & Kenny's procedures and can simply be attained if the involvement of the primary variable upon effect variable at the same time control over mediator variable is zero.


In accordance with the view point of Hayes and Preacher (2014), all the above, four steps of Baron & Kenny's procedures are attained. As a result the data will be reliable and relevant along with the mediational hypothesis. In case first three steps of Baron & Kenny's process are fulfilled, then incomplete mediation will be noticed in data.

In this aspect, study of Sinclair and Co-authors (2013) shows that the researcher must always pay attention to the complete satisfaction of all four steps involved in Baron & Kenny's procedures, if it still no inclusive of the fact that mediation has happened as there are other fewer conceivable models which are consistent with the data. Related to this, the study of Wolcott and Co-authors (2016) opined that outcome variable causes the mediator variable within mediation hypothesis. This occurs if the initial variable is a controlled variable, mediator variable cannot be caused whether by the mediator or the outcome variables in the mediational hypothesis. Conversely, as the mediator and the outcome variables are not controlled, they might cause one another in the mediational hypothesis. Research work of () suggests that it is forever reasonable to switch the mediator variable and the outcome variable and cover effect cause in the mediational hypothesis.

A discussion was made by Baron and Kenny that various analyses must be done and the outcome evaluated in context to the criterion. These criteria are evaluated by measuring the following equations: if I am observed as intercept coefficient. Where the outcome of X upon Y declines to zero along with the addition of M, thus perfect mediations occurs, this situation is called as complete mediation (Skiera and et.al. 2017). When the outcome of X upon Y declines by a significant amount, but not decreases to zero, partial mediation occurs. In order to fulfil these requirements, two assumptions should be met in addition to state that mediation has taken place. In accordance with Baron and Kelly, no extent error must be there in M, and Y must not cause to M. these first assumptions are generally violated, as this is not discussed above. Ultimately, the legitimacy of one’s conclusions regarding mediation is determined on the basis of the design of the study as much as by considering the statistical criteria.

Four Primary Steps of Baron & Kenny's Procedures

Example of interpretation of mediation analysis as per Baron & Kenny approach

In the study of Kayser and Co-authors (2016) example has been provided that, to address the issue of gender discrimination, a policy maker might contemplate evaluating the level to which gender discrimination in recruitment could be mitigated by not basing the decisions on gender compared with removing inequality in job qualifications and education. The latter is concerned with indirect impact or the impact mediated through job qualifications while the former is focused on the direct impact of gender on recruitment. This example exhibits two crucial components of modern mediation assessment. Firstly, the indirect impact is not just a modelling artefact created by suggestive blends of parameters, rather an internal property of reality which has material implications. Secondly, the policy decisions mentioned in this example are concerned with allowing and disallowing processes instead of reducing or increasing values of particular variables. Hence, the two considerations result in the assessment of natural direct and indirect impacts.


Research work of Muller and Co-authors (2005) shows that for instance, there could be a situation wherein the cumulative impact is shadowed by the fact that two groups of individuals e.g. men and women vary in their relationships between X and Y. If these two sets are signified in corresponding numbers, and their relationship strength is also of equivalent magnitude (although in opposite directions), they are likely to cancel each other out. Likewise, if a sub-group of individuals that demonstrate non-important relationships between X and Y are represented overtly within a sample, then this is the reason of a non-significant total impact. Though it is proposed by Baron and Kenny that mediator must always forecast dependent variable, one must recognize that a significant relationship between X and Y can result in huge standard errors for the mediator and have a negative effect on such causal step.

Study of Bauman (2002) shows that as the association between hours since dawn and waking up is no longer important when controlling for consumption of coffee, this tells that coffee consumption mediates this relationship. Nonetheless, only this method cannot allow for a formalized test of the indirect impact. Hence, it is not known if any modification in this relationship is actually worthwhile. There are two main techniques to formally test the importance of indirect test: Bootstrapping and the Sobel test. In this situation, it can now be confirmed that the relationship between time since dawn and waking up are mediated significantly by coffee consumption.

Limitations and Conclusion

Assessment technique of mediating effect based on the Preacher & Hayes approach

The approach of Preacher & Hayes regarding mediation process can be understood through the study of Kraemer (2002). As shown in the figure in Panel A shows the outcome of the certain planned cause (X) upon effect (Y). Further, in Panel B shows mediation’s simplest form the in which the form that takes place when (M) one variable mediates the outcome of X upon Y. by considering this, this model has been referred as simple mediation. The possibility of More complex mediation models is there; preference is given simple mediation as it is the most effective and utilized type of mediation model.

The plain relationships between both X and Y are sometimes termed as the total outcome of X upon Y (in Fig1 Panel A) representing the total outcome C to differentiate it as of c¢, the effect of X on Y after manipulating M (panel B). Detection of simple mediation effect is often done by the analysis of formal heuristic; effects are clear-cut and directly follow the term of a mediator offered by Baron and Kenny. Consideration of Variable (M) as a mediator is made if X considerably forecasts Y that is, Figure 1, c 0, or X considerably forecasts M that is, figure 1, a 0, or M considerably forecast Y is manipulating for X that is, figure 1, b 0.

Example of interpretation of mediation analysis as per Preacher & Hayes approach

Study of Kayser and Co-authors (2016) shows example regarding the interpretation of mediation analysis as per Preacher & Hayes approach when z is placed to 3000 after then the bootstraps approx is considered on the basis of 3000 resample. When z is placed to 0 (any of the number minimum to 1000), further the module of bootstrapping is disabled.

This will create productivity to Sobel test, which must be as similar as what obtained if performing the Sobel generally, also the bootstrap result has been provided in indirect effect. Describes the effect s.e., and the confidence intervals are 95%. If is not inclusive of zero then the indirect effect is considered as sig @ p < .05. As recommendation given to small samples, the nonparametric bootstrapping analysis is used to examine the model of mediation of moral outrage as mediator relationship between myth and behaviour with Aboriginal Australians. In these analyses, mediation is considerable when 95% partially corrected and increased intervals of confidence for indirect effect and is not inclusive of 0. Outcomes are based on 10000 samples of bootstrapped and shows the total effect of myth and behaviours with Aboriginal Australians was considerable (TE=-2.68, SE=1.30, p=.041), But the direct effect was not (DE=-.80, SE=1.18, p=.498). 

In accordance with the research work of Muller and Co-authors (2005), in Preacher & Hayes approach bias creates a negative impact on comfort but at the same time, it creates a negative impact through rising identification. However, discrimination improves identification and creates a positive impact on security and comfort. So the total zero-array can be ns, considerably coefficients take place from the fourth if the mediator is manipulated and a considerable indirect effect in opposed way is found when meditational analyses are performed. Proposing such model on theory basis, and examine the importance of indirect effect along with bootstrapping or Sobel. Despite from general mediation analysis individual is not required to present the IV predicts the DV in Block 1 but there is essential to present the IV predicts to the suppressor, as there is a major indirect effect of IV -> DV through the suppressor.


As per the study of Preacher (2015), covlist includes a full listing of  covariate variables, and in the cov list, cov is the numeral of covariate variables, z is the numeral of preferred resamples of bootstraps willing to increase to 1000 (example boot is equal to 2000 yield, and 2000 resamples of bootstrap; put it to zero to disable bootstrapping), ci is the expect level of confidence, setting of p  to 1 in order to issue percentile intervals of confidence, setting of b  to 1 in order to issue discriminatory-corrected and familiar  intervals of confidence, setting of n to 1 to assess printing of general theory tests outcomes and setting of t to 1 to perform all likely identical contrast in indirect effects. In case any of the claims are not supplied, using of default values will be done (the defaults are c = 0, z = 1000, ci = 95, p = 0, b =0, d = 1, n = 0, t = 0).

Mark carefully that when c is set to 0, then it estimated that there would be no listing of variables in cov, and after M all listing of variables “m =” will be considered as possible mediators. If availability of covariates is there, then printing of normal theory results will not be done.  Use the similar approach, but only include a clause regarding covariates:

More briefly,  Mediation analyses are totally based on 3000 sample of bootstraps with the use of discriminatory- corrected and increased at 95% confidence intervals demonstrate that  manipulating for covariate effect, and IV predicts a considerable indirect effect upon DV through the mediator [LL=, UL=].” As described above, LL and UL are a phrase for both the upper and lower level of confidence intervals. The online macro outputs partiality-corrected and increases confidence intervals. By considering the importance of testing is apparently more strong in the face of distribution issues common to small samples. 

Conclusion

In the present study, the researcher aims to determine roles of mediator in the conceptual model by considering the approach of Baron & Kenny and Preacher & Hayes. The study shows that mediational hypotheses are a type of hypotheses by which assumption of the influence of an independent variable upon a dependent variable is mediated by the procedure of a mediating variable, and the independent variable might still influence the independent variable. Especially, in the mediational hypothesis, mediator variable is the prevailing or method variable. It presumes the full mediation in the variables. It means that the independent variable not at all influence the dependable variable once the mediator variable has inhibited it

References

Books and Journals

Bauman, A.E., Sallis, J.F., Dzewaltowski, D.A. and Owen, N., 2002. Toward a better understanding of the influences on physical activity: the role of determinants, correlates, causal variables, mediators, moderators, and confounders. American journal of preventive medicine, 23(2), pp.5-14.

Dearing, E. and Hamilton, L.C., 2006. V. Contemporary advances and classic advice for analyzing mediating and moderating variables. Monographs of the Society for Research in Child Development, 71(3), pp.88-104.

Hayes, A.F. and Preacher, K.J., 2014. Statistical mediation analysis with a multicategorical independent variable. British Journal of Mathematical and Statistical Psychology, 67(3), pp.451-470.

Kayser, D.N., Graupmann, V., Fryer, J.W. and Frey, D., 2016. Threat to Freedom and the Detrimental Effect of Avoidance Goal Frames: Reactance as a Mediating Variable. Frontiers in psychology, 7.

Kraemer, H.C., Wilson, G.T., Fairburn, C.G. and Agras, W.S., 2002. Mediators and moderators of treatment effects in randomized clinical trials. Archives of general psychiatry, 59(10), pp.877-883.

Kristeller, J.L., 2003. Mindfulness, wisdom and eating: Applying a multi-domain model of meditation effects. Journal of constructivism in the human sciences, 8(2), pp.107-118.

Lutz, A., Brefczynski-Lewis, J., Johnstone, T. and Davidson, R.J., 2008. Regulation of the neural circuitry of emotion by compassion meditation: effects of meditative expertise. PloS one, 3(3), p.e1897.

Muller, D., Judd, C.M. and Yzerbyt, V.Y., 2005. When moderation is mediated and mediation is moderated. Journal of personality and social psychology, 89(6), p.852.

Preacher, K.J., 2015. Advances in mediation analysis: A survey and synthesis of new developments. Annual Review of Psychology, 66, pp.825-852.

Shrout, P.E. and Bolger, N., 2002. Mediation in experimental and nonexperimental studies: New procedures and recommendations. Psychological methods, 7(4), pp.422-445.

Sinclair, J., Taylor, P.J. and Hobbs, S.J., 2013. Alpha level adjustments for multiple dependent variable analyses and their applicability–a review. Int J Sports Sci Eng, 7(1), pp.17-20.

Skiera, B., Bayer, E. and Schöler, L., 2017. What should be the dependent variable in marketing-related event studies?. International Journal of Research in Marketing.

Understanding and Using Mediators and Moderators. 2015. Available from: https://www.researchgate.net/publication/225421729_Understanding_and_Using_Mediators_and_Moderators [Accessed Aug 2, 2017].

Valeri, L. and VanderWeele, T.J., 2013. Mediation analysis allowing for exposure–mediator interactions and causal interpretation: Theoretical assumptions and implementation with SAS and SPSS macros. Psychological methods, 18(2), p.137.

VanderWeele, T.J., 2016. Mediation analysis: a practitioner's guide. Annual review of public health, 37, pp.17-32.

Wolcott, H.N., Fouch, M.J., Hsu, E.R., DiJoseph, L.G., Bernaciak, C.A., Corrigan, J.G. and Williams, D.E., 2016. Modeling time-dependent and-independent indicators to facilitate identification of breakthrough research papers. Scientometrics, 107(2), pp.807-817.

Zhao, X., Lynch Jr, J.G. and Chen, Q., 2010. Reconsidering Baron and Kenny: Myths and truths about mediation analysis. Journal of consumer research, 37(2), pp.197-206.

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