Interaction Moderating Effect

8/4/2019 Interaction Moderating Effect

http://slidepdf.com/reader/full/interaction-moderating-effect 1/43

Yeşim Kaya

Marmara University

Research Metodology Course

15 June 2010



Introduction

Model of Interaction Effect

Differences Between Mediator and Moderator Effect

Categorical Moderator Variable

Continous Moderator Variable

Importance and Scope of Interaction ModeratingEffect

Types of Moderating Effect



Different Moderation Patterns

Testing the Significance of the Moderator Effect.

Statistical Tests of Moderating Effects

Examples of Interaction Moderating Effect fromliterature

Advantages of including an interaction that isrelevant to a model

Conclusion

References



Many interesting findings in the social sciencesinvolve “interaction” or “moderator” effects .

Two independent variables have an interaction

effect on a dependent variable if the relationshipof an independent variable with the dependentvariable changes across values of the other independent variable (Hargens, 2006).

For example, in an early study of radio listenership,

Lazersfeld found that age was positively related tolistening to classical music programs among thehighly educated, but negatively related to itamong the less educated (Zeisel 1968, pp.123-25).



A moderator variable modifies the form or stregthof the relation between an independent anddependent variable.

Moderator effects are also called interactions tosignify that the third variable interacts with therelation between two other variable.

X Y

Z



The interest in moderated relationships hasincreased dramatically over the past 20

years,social sciences have noted theexistence of moderator variables for almosthalf a century . (Aguinis, 2004)

The label „‟moderator variable‟‟ seems tohave been used first by Saunders in 1955,butaccording to Zedeck (1971),the concept hadbeen discussed previously. For example,Court(1930) used „‟ joint causation’’.

Other tems that were used Population controlvariable (Gaylord & Carroll, 1948);Subgrouping variable (Frederiksen & Melville,

1954); Predictability variable (Ghiselli, 1956);Referent variable (Toops, 1959); Modifier variable (Grooms & Endler, 1960); Homologizer variable (Johnson, 1966).



The interaction effect model is shown below;Y=i1+c1X+c2Z+c3XZ+e1

where Y is the dependent variable,X is the independentvarible,Z is the moderator variable and XZ is the interaction

of the moderator. The independent variable which is called product

variable; e1 is a residual and c1 represent the relation between the

dependent variable and the independent varible,c2 represent the relation between moderator variable and

the dependent variable,c3 represent the relation betweenmoderator by independent variableinteraction,respectively.

The interaction variable XZ is formed by the product of Xand Z. Often X and Z are centered.



Independentvariable (X)(Predictor variable)

Dependentvariable (Y)

(Outcome variable)

Moderator variable

(Z)



Sometimes it is difficult to distinguish mediators andmoderators when forming hypotheses aboutvariables .

The definitional difference, that a mediator ispredicted by the independent variable and amoderator is a separate independent variable, isimportant but not always obvious.





Mediating Effect• A mediator is the mechanism through which a

predictor influences an outcome variable

• X causes M and M then causes Y

• Mediating effects explain how or why such effectsoccur (Baron and Kenney 1986)

•

One typically looks for mediators if there already isa strong relation between a predictor and anoutcome and one wishes to explore themechanisms behind that relation.



Predictor Mediator Outcome

Variable (X) Variable (M) Variable (Y)

Moderating Effect;Predictor Outcome

Variable (X) Variable(Y)

Moderator

Variable (Z)



Moderators are often are introduced when theyare unexpectedly weak or inconsistent relationsbetween a predictor (independent) and an

outcome (dependent) across studies. Decisions about potential moderators and

mediators should be based on previous researchand theory and are best made a priori in the

design stage rather than post hoc. Also,a given variable may function as either a

moderator or a mediator, depending on the theorybeing tested.



One also can examine mediators and moderatorswithin the same model.

Moderated mediation refers to instances in which themediated relation varies across levels of a

moderator. Mediated moderation refers to instances in which a

mediator variable explains the relation between aninteraction term in a moderator model and anoutcome.

These more complex models have been described inmore detail elsewhere (e.g., Baron & Kenny,1986;Hoyle & Robinson, in press; James & Brett, 1984;Wegener & Fabrigar, 2000).



Moderators can be:› Continuous (e.g., age,rumination) or

› Categorical (e.g., gender, country, etc.)



We‟ll consider the categorical MV case first.

If either the predictor or moderator variable iscategorical, we need to dummy code the

moderator and the predictor variable. Jose (2008) tested that the relationship between

anxiety and depression is the same or differentbetween males and females.

The gender as a moderator must be coded asmales=0, females=1.



Moderation Model

Anxiety Depression

Gender



Hierarchical regression with three steps:1. Anxiety;2. Gender (0 = males; 1 = females); and3. Anxiety X Gender (product term: just multiply these two

variables in SPSS, but note that the IV must be centered)

(Note that gender is dummy coded (not 1 = males; 2 = females),and NOT centered.)

What are we looking for?1. Does anxiety predict depression?2. Does gender predict depression, i.e., is there a gender

difference in depression?3. Does the product term predict depression? If so, then

one has obtained a significant moderation effect.



Two significant results: one main effect and the interaction.

Can interpret the main effect from its beta, but not the interaction.

Coefficientsa

9.530 .279 34.149 .000

.259 .024 .430 10.958 .000

9.055 .492 18.397 .000

.254 .024 .421 10.536 .000

.708 .605 .047 1.170 .242

8.700 .508 17.136 .000

.141 .049 .233 2.854 .004

1.005 .612 .066 1.641 .101

.148 .056 .212 2.632 .009

(Constant)

anxiety t1 centered

(Constant)

anxiety t1 centered

Are you male or female?

(Constant)

anxiety t1 centered

Are you male or female?

anxiety X gender

Model

1

2

3

B Std. Error

Unstandardized

Coefficients

Beta

Standardized

Coefficients

t Sig.

Dependent Variable: dept1a.





We found that anxiety significantly and positivelypredicted depression, b = .43, R 2 = .19, p < .001.

No main effect for gender, b = .05, R 2 = .00, p = .24.

Depression was not higher among female thanmale adolescents (after anxiety was entered).

The most important finding is the third term, whichwas a significant predictor, b = .21, R 2 = .01, p < .01.It is important to find that this is a sig. predictor

above and beyond the two main effects. Cannotenter this in isolation.

What the significant interaction term tells us is thatthe association between anxiety and depression is

significantly different between the two groups.



There are many situations in which the moderator variable is continuous.

Aiken and West stated that one should center

one‟s main effects before computing theinteraction term because of multicollinearity (highcorrelations among the predictor variables).

Centering reduces problems associated with

multicollinearity (i.e., high correlations) among thevariables in the regression equation (for further explanation, see Cohen et al., 2003; Cronbach,1987; Jaccard et al., 1990; West et al., 1996).



Let‟s consider the case of a continuous moderator.

In the same dataset, Jose (2008) investigated howrumination moderates the stress to depression

relationship. (Note that rumination have examinedas both a moderator and a mediator.).

Obtain the means for your two IVs: stress andrumination. Remove the means from the variablesto create new centered variables.

Multiply Stressc X Ruminc to obtain your newinteraction term.

Enter these variables in the hierarchical regression.

Obtain the results on the following page.



Stress and rumination both worsen depressive symptoms bythemselves, and we also obtained a significant interaction. Enter the following numbers into ModGraph under “continuousmoderator

Coefficientsa

5.409 .251 21.552 .000

1.454 .213 .449 6.824 .000

5.407 .240 22.569 .000

.932 .236 .288 3.950 .000

.069 .016 .317 4.348 .000

5.067 .264 19.220 .000

.679 .248 .210 2.735 .007

.072 .016 .331 4.606 .000

.033 .011 .190 2.845 .005

(Constant)

stressc

(Constant)

stressc

ruminc

(Constant)

stressc

ruminc

strxrum

Model1

2

3

B Std. Error

UnstandardizedCoefficients

Beta

StandardizedCoefficients

t Sig.

Dependent Variable : depression totala.





Notice that the Low group is practically flat (non-significant).

Simple Slope T-Value SignificanceLevel (p)

High .10 2.73 .007

Medium .68 2.18 .03

Low 1.25 0.16 .87



Going beyond main effects

We typically say “it depends”

More complex models

There are many instances in which researchersare interested in whether relations betweenpredictor and outcome variables are stronger for some people than for others

Identification of important moderators ofrelations between predictors and out comes isat the heart of theory in social science.(Cohen,2003).



“If we want to know how well we are doing in thebiological, psychological, and social sciences, anindex that will serve us well is how far we haveadvanced in our understanding of the moderator

variables of our field” (Hall & Rosenthal, 1991, p. 447) There are also a lot of application areas such as

economy,marketing,business,medicine andeducation.

Additional research areas: training, turnover,

performance appraisal, return on investment,mentoring, self-efficacy, job satisfaction,organizational commitment, and career development, among others



According to Sharma,Durand and Gur-Arie (1981)there are three types of moderator effects:

• homologizer moderator

• quasi moderator

• pure moderator.



Homologizer Moderator The true relation between the independent variable and

the dependent variable does not change across levels ofthe moderator,but the error variance does change across

the levels of moderator. If an effect is examined by subgroups,the strength of thestandardized relation varies because the error variancevaries across subgroups.

The error variance may vary across subgroups because ofdifferent measurement proporties such as response

reliabilities across the subgroups. Influences the strength of the link between the

independent variable and dependent variable becauseof differences in error variance across groups.



The second and third forms of a moderator variableare consistent with most discussions of moderators.

Quasi-moderator If the moderator variable is also significant predictor

of the dependent. Pure moderator If the moderator variable is not a significant predictor

of the dependent variable is also called a psychometric moderator because the

form of the relation between the independentvariable and the dependent variable changes as afunction of the moderator. (p.275)



Cohen et al. (2003, pp. 285 – 286) described threepatterns of interactions among two continuousvariables:

enhancing interactions (in which both the predictor

and moderator affect the outcome variable in thesame direction and together have a stronger thanadditive effect),

buffering interactions (in which the moderator variable weakens effect of the predictor variable onthe outcome)

antagonistic interactions (in which the predictor andmoderator have the same effect on the outcomebut the interaction is in the opposite direction.). (ascited in Frazier , Tix , Barron, 2004).



To test H0: ψ22- ψ1

2 = 0,and F statistic (distributedwith k 2-k 1 and N-k 2-1 degrees of freedom) iscomputed using the following formula:

Ŷ = a + b1 X + b2 Z ; R12 Ŷ = a + b1 X + b2 Z + b3 X·Z; R 2

2

F= (R22-R1

2)/(k 2-k 1)

(1-R22)/(N-k 2-1)

If the test is significant you can conclude that there isan interaction. (Aguinis ,2004)



Testing significance of a moderator effect,if thepredictor or moderator variables are categorical or continous,researcher can use multiple regression.

Moderated Multiple Regression is the preferred

statistical method for identifying moderator effects(interaction effects) when the predictor and themoderator are continuous variables or when thepredictor is continuous and the moderator iscategorical.

ANOVA can also be used for identifying interactions,but is more appropriately used for the analysis ofplanned experiments than for observational andsurvey data. (Jennifer R. Villa*, Jon P. Howell, Peter W.Dorfman, David L. Daniel, 2002).



Michon,Chebat and Turley (2005) investigate themoderating effects of ambient odors on shoppers‟emotions, perceptions of the retail environment, andperceptions of product quality under various levels of

retail density. The results shows that ambient odors positively

influence shoppers‟ perceptions only under themedium retail density condition.

Shin and Park investigates the moderating effect ofgroup cohesiveness both at the individual and at thegroup level.

In this research collective competency influencedpositively to team performance at high level of groupcohesiveness, but it influenced negatively at lowlevel of group cohesiveness.



Baeza,Lao,Menese and Roma (2009) appraised therole of leader charisma in fostering positive affectiveteam climate and preventing negative affectiveclimate.

The analysis of a longitudinal database of 137 bank branches by means of hierarchical moderatedregression shows that leader charisma has a stronger effect on team optimism than on team tension.

In addition, the leader‟s influence and the frequencyof leader-team interaction moderate the relationshipbetween charisma and affective climate.

Results show that to better understand the impact ofleader‟s charisma on team affective climate it isnecessary to differentiate between positive andnegative affect.



Ismail,Rahma,Wan Ismail (2007) examines themoderating role of procedural justice in the relationshipbetween participation in pay systems and personaloutcomes.

The results of tests moderating model using hierarchicalregression analyses showed that the inclusion ofprocedural justice into analysis had increased the effectof participation in pay systems on job commitment, butprocedural justice had not increased the effect ofparticipation in pay systems on job satisfaction.

This result shows that procedural justice does act as apartial moderator in the pay system models of the hotelindustry sector.



if an interaction does in fact exist and is notincluded in the estimation, this introduces aspecification error in the form of omitted variable

bias. Estimation of a model that fails to account for the

interaction will not provide an accurate estimationof the true relationship between the dependent

and independent variables. A model that includes the interaction term

provides a better description of the relationshipbetween the independent and dependentvariables.



the inclusion of the product term will offer a moreaccurate estimation of the relationship and explainmore of the variation in the dependent variable.

including a product term according to Friedrich(1982) is a "low-risk strategy" in that if the productterm is significant then keep it in the modelotherwise one can drop the product term out of

the model.



In summary, moderators are variables that affect theassociation between an independent variable andan outcome variable.

If a researcher fails to consider the possibility of a

mediator or moderator effect in the data, a moreexact explanation for an outcome may be missed. we defined the concept of moderator variables

,different types of moderator variable. Then wedescribed difference between mediator andmoderator variables and we discussed theimportance and advantages of moderators. Wegave some examples from literature.

The goal of this paper is that using these tools willallow researchers to make more informed decisionsregarding the operation of moderating effects.



Aguinis H.(2004). Regression Analysis for Categorical Moderators.Retrieved from internet on April 24,2010-04-29

http://books.google.com/books?hl=tr&lr=&id=6sdRuhBTOLQC&oi=fnd&pg=PA1&dq=Regression+Analysis+for+Categorical+Moderators&ots=1bhckcefI2&sig=BG--TiyVhIe_7Px99_qiIuKYCts#v=onepage&q&f=false

Baeza* A. H., Lao A. C., Meneses and V. G., Romá* I. G. (2009). Leader charisma and affective team climate: The moderating role of theleader‟s influence and interaction. Universitat València * e Idocal.

Bennet J.A.(2000). Focus on Research Methods: Mediator andModerator Variables in Nursing Research: Conceptual and StatisticalDifferences. School of Nursing, San Diego State University.

Frazier A., Tix P., Barron E.(2004). Testing Moderator and Mediator Effectsin Counseling Psychology Research. Journal of Counseling Psychology.

http://books.google.com/books?hl=tr&lr=&id=6sdRuhBTOLQC&oi=fnd&pg=PA1&dq=Regression+Analysis+for+Categorical+Moderators&ots=1bhckcefI2&sig=BG--TiyVhIe_7Px99_qiIuKYCts











Jose P. (2008). Statistical Moderation. Victoria University of Wellington.SASP Conference

Hargens L. (2006). Interpreting Product-Variable Models of Interaction

Effects. Center for Statistics and the Social Sciences, University of Washington.

Michon R., Chebat J.C., Turley L. W.(2005). Mall atmospherics: theinteraction effects of the mall environment on shopping behavior.

Journal of Business Research.

Ismail A., Rahma H.A., Wan Ismail W. K. (2007). Moderating effect ofprocedural justice in the relationship between participation in paysystems and personal outcomes. Jurnal Kemanusiaan bil.9, Jun 2007.



MacKinnon D.P.( 2008). Introduction to Statistical Mediation Analysis.Retrieved from internet on April 25,2010 http://www.google.com/books?hl=tr&lr=&id=qg0Eiz1ZmagC&oi=fnd&pg=PR7&dq=interaction+moderating+effect+book+chapter+pdf&ots=hQPjKB_kQY&sig=5ZX8nXux7Uj8-Lyk_bxiwyE9ACc#v=onepage&q&f=false

Shin S. Y., Park W. Moderating Effects of Group Cohesiveness inCompetency-Performance Relationships: A Multi-Level Study. Journal of Behavioral Studies in Business

Villa J. R., Howell J. P., Dorfman P. W., Daniel D. L. ( 2003). Problems with

detecting moderators in leadership research using moderated multipleregression. The Leadership Quarterly 14 (2003) 3 – 23.

Zeisel, Hans. (1968) Say it with Figures (Fifth Edition). New York: Harper and Row.

http://www.google.com/books?hl=tr&lr=&id=qg0Eiz1ZmagC&oi=fnd&pg=PR7&dq=interaction+moderating+effect+book+chapter+pdf&ots=hQPjKB_kQY&sig=5ZX8nXux7Uj8-Lyk_bxiwyE9ACc










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Interaction Moderating Effect