(solution) Question Please free grammar errors and free plagiarism Read the

(solution) Question Please free grammar errors and free plagiarism Read the

Question

  • Please free grammar errors and free plagiarism
  • Read the requirements of the question deeply and answer each one
  • Attached four resources, two books indicated the chapter of each to be read, and two articles
  • Your answer must be from the materials of the four resources in addition to your resources

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.

References

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
e-mail: [email protected]
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
Obesityrelated
Illness WorksiteWellness
Program Hours
worked
(full time
vs. part
time) Norm for
consuming
fruit &
vegetables WorksiteWellness
Program Fruits &
Vegetables
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 &
Vegetable
Benefits Family
History of
Obesityrelated
Illness Fruits &
Vegetables
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:
r???????????????????????
s^ ^ ¼
ab ^ 2
2a
s^ b2 þ s^ ^ 2
a b ð4Þ 2
2
^
Where sa is the variance of the a coefficient and S ^ is the
^
b
^
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
Program
Theory Conduct
Pilot Work
and Collect
Empirical
Feedback Refine
Program
Theory (Repeat link until satisfied) Implement
& Evaluate
Full
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
model:
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
XZ XMZ j
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…