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The question

Examine the literature in your topic area and identify five articles published within the past five years that investigate mediating, moderating, or independent variables in an attempt to contribute to theory in the topic area. Write a paper in which for each article, you:

1.Describes the theory the researchers explore. What are the key constructs in the theory? How are they related? Identify which ones are cause, effect, mediating, or moderating constructs. How are the constructs operationalized?

2.Briefly describe the study, including the number of participants and research methods.

3.Briefly describe the statistical analyses used

4.Briefly described the findings and how the researchers interpreted them and their contribution to theory.

Using some or all of the five articles, argue for a gap in the knowledge in the topic area and briefly describe a study involving mediator and or moderator variables that can contribute to theory.

Support your paper with a minimum of 5 resources. In addition to these specified resources, other appropriate scholarly resources, including older articles, may be included.

Length: 5-7 pages not including title and reference pages
References: Minimum of 5 scholarly resources.


Creswell, J. W. (2013) Research design: Qualitative, quantitative, and mixed methods approaches.

Read Pages 49-61

Trochim, W. M. K., & Donnelly, J. P. (2008) The research methods knowledge base.

Read Pages 61-62

Prev Sci (2009) 10:87?99


DOI 10.1007/s11121-008-0109-6 A General Model for Testing Mediation


and Moderation Effects


Amanda J. Fairchild & David P. MacKinnon Published online: 12 November 2008


# Society for Prevention Research 2008 Abstract This paper describes methods for testing mediation and moderation effects in a dataset, both together and


separately. Investigations of this kind are especially


valuable in prevention research to obtain information on


the process by which a program achieves its effects and


whether the program is effective for subgroups of individuals. A general model that simultaneously estimates


mediation and moderation effects is presented, and the


utility of combining the effects into a single model is


described. Possible effects of interest in the model are


explained, as are statistical methods to assess these effects.


The methods are further illustrated in a hypothetical


prevention program example.


Keywords Mediation . Indirect effect . Moderation .


Mediated moderation . Moderated mediation


Relations between variables are often more complex than


simple bivariate relations between a predictor and a criterion.


Rather these relations may be modified by, or informed by,


the addition of a third variable in the research design.


Examples of third variables include suppressors, confounders, covariates, mediators, and moderators (MacKinnon et al.


2000). Many of these third variable effects have been


investigated in the research literature, and more recent


A. J. Fairchild (*)


Department of Psychology, University of South Carolina,


Barnwell College,


1512 Pendleton St.,


Columbia, SC 29208, USA




D. P. MacKinnon


Research in Prevention Lab, Department of Psychology,


Arizona State University,


P.O. Box 871104, Tempe, AZ 85287-1104, USA research has examined the influences of more than one third


variable effect in an analysis. The importance of investigating mediation and moderation effects together has been


recognized for some time in prevention science, but


statistical methods to conduct these analyses are only now


being developed. Investigations of this kind are especially


valuable in prevention research where data may present


several mediation and moderation relations.


Previous research has described the differences between


mediation and moderation and has provided methods to


analyze them separately (e.g., Dearing and Hamilton 2006;


Frazier et al. 2004; Gogineni et al. 1995; Rose et al. 2004).


More recent research has presented models to simultaneously estimate mediation and moderation to investigate


how the effects work together (e.g., Edwards and Lambert


2007; MacKinnon 2008; Muller et al. 2005; Preacher et al.


2007). A review of the substantive literature illustrates that


few applied research examples have used these models,


however. Although analyzing mediation and moderation


separately for the same data may be useful, as described


later in this paper, simultaneous examination of the effects


is often relevant and allows for the investigation of more


varied, complex research hypotheses. What Type of Research Questions Can Be Addressed


with the Simultaneous Analysis of Mediation


and Moderation Effects?


?Is the Process By Which a Program Has an Effect


the Same Across Different Types of Participants??


In prevention and intervention research, the mediation model


has been used to understand the mechanism(s) by which


program effects occur. To determine the generalizability 88 Prev Sci (2009) 10:87?99 of these mechanisms or to explain an unexpectedly small


mediated effect it may be of interest to investigate


whether the mediation relation, or the indirect effect,


holds across different subgroups (e.g., men vs. women or


low-risk vs. high-risk). To investigate these hypotheses, a


researcher asks whether the indirect effect is moderated, or


whether the mediated effect depends on levels of another


variable. For example, suppose that a business implements


a worksite-wellness program (the independent variable, X)


to reduce obesity-related health risks in its employees.


Program developers hypothesize that by increasing employee knowledge about the benefits of eating fruits and


vegetables (the mediator variable, M), employee consumption of fruits and vegetables will increase (the dependent


variable, Y), thus reducing health risk. An estimate of the


indirect effect of the program on employee fruit and


vegetable consumption through employee knowledge of the


benefits of eating fruits and vegetables is unexpectedly low.


Through talks with employees, it becomes apparent that


participants were more or less motivated to gain and use


knowledge from the program to improve their diet based on


whether they had a family history of obesity-related illness


such as diabetes or cardiovascular disease. Program developers hypothesize that participants? family history of obesityrelated illness may moderate the mediation relation in the


data, affecting the influence of the program on employee


knowledge of fruits and vegetables and its subsequent impact


on fruit and vegetable consumption (See Fig. 1).


?Can a Mediation Relation Explain an Interaction Effect


in My Data??


Suppose a similar worksite-wellness program was implemented in a larger sister company and program effects had


been dependent on whether the participant was a full or


part-time employee at the company. To investigate the


underlying reasons for this unexpected interaction, or


moderation relation, program analysts could investigate a


mediation hypothesis where the interaction effect predicts a Fig. 1 Conceptual diagram for


the moderation of an indirect


effect example Family


History of




Illness WorksiteWellness


Program Hours




(full time


vs. part


time) Norm for




fruit &


vegetables WorksiteWellness


Program Fruits &




Consumed Fig. 2 Conceptual diagram for the mediation of a moderator effect


example mediator variable which predicts the outcome, defined here


as the mediation of a moderator effect. For example,


perhaps in addition to increasing employee knowledge of


fruit and vegetable benefits with the wellness curriculum,


the program (X) also introduced a work culture, or a social


norm (M), of healthy eating which contributed to employee


fruit and vegetable consumption (Y; See Fig. 2). Program


developers hypothesize that the more hours an employee


worked in a week determined how much they were


subjected to the social norm which ultimately influenced


their fruit and vegetable consumption. Current Research


The purpose of this article is to provide a straightforward,


methodological resource on models to simultaneously test


mediation and moderation effects for the substantive


researcher. To that end, we organize methods for simultaneously testing mediation and moderation into a single


framework that allows for point estimation and construction of confidence intervals. Interpretation and effect


computation are provided, and the model is applied to a


substantive dataset to illustrate the methods. To ensure


common ground for this discussion, basic mediation and


moderation effects from which the model is formed are


first reviewed. Knowledge


of Fruit &




Benefits Family


History of




Illness Fruits &




Consumed Prev Sci (2009) 10:87?99 89 Review of the Mediation Model


The mediation model offers an explanation for how, or why,


two variables are related, where an intervening or mediating


variable, M, is hypothesized to be intermediate in the


relation between an independent variable, X, and an


outcome, Y (See Fig. 3). Early presentations of mediation


in prevention research (e.g., Baron and Kenny 1986; Judd


and Kenny 1981a; 1981b) illustrated causal step methods to


test for mediation, but more recent research has supported


tests for statistical mediation based on coefficients from two


or more of the following regression equations (MacKinnon


and Dwyer 1993):


Y ¼ i1 þ cX þ e1 ð1Þ Y ¼ i2 þ c'X þ bM þ e2 ð2Þ M ¼ i3 þ aX þ e3 ð3Þ Where c is the overall effect of the independent variable


on Y; c? is the effect of the independent variable on Y


controlling for M; b is the effect of the mediating variable


on Y; a is the effect of the independent variable on the


mediator; i1, i2 , and i3 are the intercepts for each equation;


and e1, e2, and e3 are the corresponding residuals in each


equation (see Fig. 3). X Y


c Although there are alternative ways to estimate mediation, the product of coefficients is most easily applied to


complex models and is used in this paper. The product of


coefficients test computes the mediated effect as the product






of the a and b coefficients from Eq. 2 and 3. Sobel (1982,




1986) derived the variance of ab product based on the


multivariate delta method. This formula has been widely




used to estimate the normal theory standard error of ab:




s^ ^ ¼


ab ^ 2




s^ b2 þ s^ ^ 2


a b ð4Þ 2






Where sa is the variance of the a coefficient and S ^ is the








variance of the b coefficient.


MacKinnon et al. (1998) and MacKinnon and Lockwood


(2001) showed that tests for the mediated effect based on


normal theory can yield inaccurate confidence limits and


significance tests, however, as the product of two normally


distributed variables is not itself normally distributed.


Alternative tests based on the asymmetric distribution of


the product of two normally distributed variables are


available and have been shown to outperform traditional


methods (MacKinnon et al. 2002; MacKinnon et al. 2004).


A new program called ?PRODCLIN? (MacKinnon et al.


2007) has automated computation of the distribution of the


product test for mediation so that it is widely accessible.


^ ^


The researcher need only specify values of a, b, the




^ the standard error of b, and the


standard error of a,


statistical significance level desired.


Assumptions of the mediation model include the usual


OLS estimation assumptions (e.g., correct specification of


the model?s functional form, no omitted variables, no


measurement error; Cohen et al. 2003). Mediation analysis


also assumes correct causal ordering of the variables, no


reverse causality effects, and no XM interaction. (Total Effect of X on Y) Review of the Moderation Model M


a b X Y


c' Fig. 3 Path diagram for the single-mediator model. Note. X= the


independent variable, Y= the dependent variable, and M= the


mediating variable. The mediation model decomposes the total effect


of X on Y (c), into two parts: the indirect effect of X on Y, quantified


by ab (the product of a and b), and the direct effect of X on Y with the


effect of the mediator removed, quantified by c?. c=ab+c? The moderation model tests whether the prediction of a


dependent variable, Y, from an independent variable, X,


differs across levels of a third variable, Z (See Fig. 4).


Moderator variables affect the strength and/or direction of


the relation between a predictor and an outcome: enhancing, reducing, or changing the influence of the predictor.


Moderation effects are typically discussed as an interaction


between factors or variables, where the effects of one


variable depend on levels of the other variable in analysis.


Detailed descriptions of moderator effects and a framework


for their estimation and interpretation were presented in


Aiken and West (1991).


Moderation effects are tested with multiple regression


analysis, where all predictor variables and their interaction 90 Prev Sci (2009) 10:87?99 the residual variance in the outcome that remains after


predicting Y from X is equivalent across values of the


moderator variable. Z Combining Mediation and Moderation Analyses


Analyzing the Models Separately


X X Y ?1 ?2


Z Y ?3


XZ Fig. 4 Alternate path diagram representations of the moderation


model. Note. X= the independent variable, Y= the dependent variable,


Z= the moderator variable, XZ= the product of X and the moderator


variable, ?1 = the effect of X on Y, ?2 = the effect of Z on Y, and ?3 =


the effect of XZ on Y term are centered prior to model estimation to improve


interpretation of regression coefficients. A single regression


equation forms the basic moderation model:


Y ¼ i5 þ b1 X þ b2 Z þ b3 XZ þ e5 ð5Þ Where ?1 is the coefficient relating the independent


variable, X, to the outcome, Y, when Z = 0, ?2 is the


coefficient relating the moderator variable, Z, to the


outcome when X = 0, i5 the intercept in the equation, and


e5 is the residual in the equation.


The regression coefficient for the interaction term, ?3,


provides an estimate of the moderation effect. If ?3 is


statistically different from zero, there is significant moderation of the X-Y relation in the data. Plotting interaction


effects aids in the interpretation of moderation to show how


the slope of Y on X is dependent on the value of the


moderator variable. Regression slopes that correspond to


the prediction of Y from X at a single value of Z are termed


simple slopes.


Assumptions of the moderation model include OLS


regression assumptions, as described earlier, and homogeneity of error variance. The latter assumption requires that Much of the work combining mediation and moderation


analyses has been presented in the context of prevention


program design and development, where examining mediation and moderation effects together aims to improve


program implementation by combining theory-driven ideas


and empirical evidence. For example, Donaldson (2001)


indicates that multivariate relations between variables in a


treatment program tend to be one of three types: (a) direct


effects, (b) mediated effects, and (c) moderated effects. By


combining the examination of these effects in a single


analysis, the researcher may not only identify mediating


processes through which the program achieves its effects


but may also identify effective program components and/or


particular characteristics of the participants or the environment that moderate the effectiveness of the program. If the


theoretical underpinnings of a treatment or prevention


program serve as a starting point for its curriculum, separate


analyses of mediation and moderation may be used to


iteratively refine program theory. These analyses may be


used to collect empirical feedback and to conduct pilot


work of the program before large-scale implementation of


the curriculum (See Fig. 5). Specifically, by examining


mediation one is able to investigate how effective a


program curriculum was in changing target behaviors, and


whether the program aimed to alter appropriate mediators


of desired outcomes. Analyzing moderation effects in this


context allows the researcher to identify variables that may


improve or reduce the program?s ability to alter mediating


variables, as well as to examine the external validity, or Construct




Theory Conduct


Pilot Work


and Collect




Feedback Refine




Theory (Repeat link until satisfied) Implement


& Evaluate




Program (Use Program Implementation and Evaluation to Inform Original Theory) Fig. 5 Refining program theory: an empirical-theoretical exchange.


Note. Figure is based on Donaldson (2001) diagram that occurs on


p. 472 of that text Prev Sci (2009) 10:87?99 91 generalizability, of the model across different groups or


settings (Hoyle and Robinson 2003). Hypothesized moderator variables may be more or less amenable to program


tailoring, however. Although program subgroups may be


formed on moderators such as age or gender with little


difficulty, forming program subgroups based on other


moderator variables such as ethnicity or family risk may


be impractical and/or unethical. Nonetheless, the identification of subgroups for which a program is most effective


is useful, and the examination of moderation and mediation


effects in this context increases the scientific understanding


of behaviors and improves program efficacy. West and


Aiken (1997) have argued that these analyses are especially


useful after the successful implementation and evaluation of


a treatment program. This allows for the continual


development and improvement of a program, but after an


effective first evaluation.


Analyzing the Models Simultaneously


By simultaneously investigating mediation and moderation,


the effects may not only be disentangled and analyzed


separately but can also be evaluated together. There have


been two primary effects analyzed in the literature: (a) the


mediation of a moderator effect, and (b) the moderation of


an indirect effect. The mediation of a moderator effect


involves exploring mediating mechanisms to explain an


overall interaction of XZ in predicting Y, whereas the


moderation of an indirect effect involves investigating


whether a mediated relation holds across levels of a fourth,


moderating variable. These effects have previously been


referred to as mediated-moderation and moderated-mediation in the literature, respectively. These alternative


descriptions may enhance the distinction between the two.


Previous models to simultaneously test mediation and


moderation effects have been presented with varying


notation (e.g., Edwards and Lambert 2007; James and Brett


1984; Muller et al. 2005; Preacher et al. 2007) or without


testable equations (e.g., Baron and Kenny 1986; Wegener


and Fabrigar 2000), making it difficult to understand


similarities and differences among the methods. Moreover


the criteria for testing the effects have varied across sources,


making it hard to extrapolate recommendations for use. It is


possible to create a general model to test these effects,


however, that subsumes several previous frameworks by


including all possible interactions between variables in the


mediation and moderation models (MacKinnon 2008).


Such a model unifies the methods into a single presentation


where different models are represented as special cases of


the larger framework. Three regression equations form the




Y ¼ i6 þ c1 X þ c2 Z þ c3 XZ þ e6 ð6Þ M ¼ i7 þ a1 X þ a2 Z þ a3 XZ þ e7


Y ¼ i8 þ c01 X þ c02 Z þ c03 XZ þ b1 M þ b2 MZ


þ hXM þ jXMZ þ e8 ð7Þ ð8Þ where all predictors in the model are centered at zero to


improve interpretation of the lower order coefficients. In


Eq. 6, c1 is the effect of the independent variable on the


outcome when Z = 0 (also the average effect of X on Y


because the mean of Z = 0), c2 is the effect of the moderator


variable on the outcome when X = 0 (also the average effect


of Z on Y because the mean of X = 0), c3 is the effect of the


interaction between the independent variable and the


moderator on the outcome, and i6 and e6 are the intercept


and the residual in the equation, respectively. In Eq. 7, a1 is


the effect of the independent variable on the mediator when


Z = 0 (also the average effect of X on M because the mean


of Z = 0), a2 is the effect of the moderator variable on the


mediator (also the average effect of Z on M because the


mean of X = 0), a3 is the effect of the interaction between


the independent and moderator variables on the mediator,


and i7 and e7 are the intercept and the residual in the


equation, respectively. In Eq. 8, c' 1 is the effect of the


independent variable on the outcome when M = 0 and Z = 0


(the average effect of X on Y), c' 2 is the effect of the


moderator on the outcome when X = 0 and M = 0 (the


average effect of Z on Y), c' 3 is the effect of the interaction


between the independent and moderator variables on the


outcome when M = 0 (the average effect of XZ on Y), b1 is


the effect of the mediator on the outcome when X = 0 and


Z = 0 (the average effect of M on Y), b2 is the effect of the


interaction between the moderator and mediator variables


on the outcome when X = 0 (the average effect of MZ on


Y), h is the effect of the interaction between the


independent and mediator variables on the outcome when


Z = 0 (the average effect of XM on Y), and j is the effect of


the three-way interaction of the mediating, moderating, and


independent variables on the outcome. The intercept and


residual in Eq. 8 are coded i8 and e8, respectively. A path


diagram for the model is presented in Fig. 6.


Assumptions of the general model include assumptions


of the mediation and moderation models as described


earlier. Issues of causal inference in non-additive models


may also require additional stipulations for estimation. Note


that the presence of any significant two-way interactions in


the model implies that the main effects of X and M do not


provide a complete interpretation of effects. The presence


of a significant three-way interaction in the model also


implies that lower order two-way interactions do not


provide a complete interpretation of effects. If there are


significant interactions, point estimates can be probed with 92 Prev Sci (2009) 10:87?99 Fig. 6 MacKinnon (2008) General Joint Analysis Mode. Note.


X= the independent variable, Y=


the dependent variable, Z= the


moderator variable, M= the mediating variable, XZ= the interaction of X and Z, MZ=the


interaction of M and Z, XM=


the interaction of X and M, and


XMZ= the three-way interaction


between X, M, and Z X c1


c2 Z Y c3




XM h


MZ b2 c'1 X a1 c'2 Y Z a2


XZ c'3 a3 b1


M plots and tests of simple effects to probe the interaction


effects. Edwards and Lambert (2007), Preacher et al.


(2007), and Tein et al. (2004) provide methods to perform


these analyses.


Testing effects: Criteria for the moderation of an indirect


effect To examine whether an indirect effect is moderated,


it is of interest to investigate whether the mediated effect


(ab) differs across levels of a fourth, moderating variable.


Previous sources have argued that this effect can be defined


by either a moderated a path, a moderated b path, or both


moderated a and b paths in the mediation model (James and


Brett 1984; Muller et al. 2005; Preacher et al. 2007;


Wegener and Fabrigar 2000), such that if there is


moderation in either path of the indirect effect then the


mediated relation depends on the level of a moderator


variable. There are circumstances, however, in which a


heterogeneous a or b path does not imply a heterogeneous


ab product term.


Although significant heterogeneity in either the a or b


path may imply significant heterogeneity in the ab product term in some cases, examining moderation of the product


term or moderation of both paths versus examining


moderation of single paths in the mediation model are not


conceptually identical. Consider the following example


where a moderated a path in the mediation model means


something different from both moderated a and b paths in


the model. Presume that X is calcium intake, M is bone


density, Y is the number of broken bones, and Z is gender.


Calcium intake is known to have an effect on the bone


density of women, and the relation between calcium intake


and bone density is stronger in women than it is in men


(i.e., heterogeneity in the a path in the model). Specifically,


men have greater bone density in general and thus yield


fewer gains from supplemental calcium intake. However,


bone density affects the fragility of bones in a constant way


across males and females, such that low bone density leads


to more broken bones (i.e., no heterogeneity of the b path in


the model). Previous models would deem this scenario as


moderation of the indirect effect, arguing that moderation of


the a path suffices as a test for the effect. There are two


problems with this argument. First, testing the heterogene- Prev Sci (2009) 10:87?99 93 ity of only the a or b path in the mediation model is not a


test of mediation because only a single link in the


mediated effect is tested in each case. Second, a


heterogeneous a path in this model suggests something


different from both heterogeneous a and b paths or a


heterogeneous ab product. Heterogeneity in both paths of


the mediated effect would suggest that gender not only


moderates the effect of calcium intake on bone density, but


that gender also moderates the effect of bone density on


broken bones. Heterogeneity of the product estimate of the


mediated effect would suggest that gender moderates the


mechanism by which calcium intake affects bone loss; this


may or may not be true based on the research literature.


Although the moderation of a single path may imply


moderation of the product term in some cases, it is critical


to differentiate the scenarios as they correspond to


different research hypotheses.


There are also numerical examples that show instances


when heterogeneity in individual paths of the mediation


model does not imply heterogeneity of the product term.


Consider the following mediated effect scenarios in two


moderator-based subgroups: Case 1:


Case 2: Mediated Effect in Group 1


(a = -2)(b = -2)


(a = 1)(b = 2) Mediated Effect in Group 2


(a = 2)(b = 2)


(a = 2)(b = 1) In both scenarios the a and b paths are heterogeneous


across groups thus satisfying criteria for the moderation of a


mediated effect as defined by Edward and Lambert (2007),


James and Brett (1984), Morgan-Lopez and MacKinnon


(2006), Preacher et al. (2007), and Wegener and Fabrigar


(2000). However the ab product is identi...


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