224 DESIGN AND ANALYSIS

describe in a model with a single intervening unambiguously causally prior to the dependevariable such as the model shown in Figure variable, and, assuming random assignment:10.1. Assuming the model corresponds to a condition, there is no concern that the modetheoretical account in which tp.e intervening atOr variable could be caused by the indepeJvariable explains the association between the dent variable, ruling out the possibility thatindependent variable and the dependent vari- mediates rather than moderates the effeCt (able, the paths of interest are aI, bl, and c1. If the independent variable on the dependerthe effect of the independent variable on the variable.dependent variable is fully mediated by the Although moderated effects can be evaltintervening variable, then paths aI and bl wiU ated fuUy in a single experiment, such is not th

be nonzero in magnitude and path c1 will, case with mediated effects. Tests of mediate,within sampling error, be zero. A key concern effects require an evaluation of the effect of th

is too strong an association between the inde- independent variable on the intervening varipendent variable and the intervening variable, able and, if both are manipulated in a sing(,which would be reflected in a large value for experiment, there is, by d~finition, no effeCt 0al. All else being equal, as al increases, bl the independent variable on the inrerveninl

decreases. And as b 1 decreases, c1, which we variable. Nonetheless, the question of causa

would like to equal zero, increases. Among priority is critical in tests of mediation, and theother things, the magnitudes of al and bl are experimental design, when properly applied, i!affected by the spacing between the indepen- unmatched in its abiliry to answer this ques.dent and intervening variables and the inter- tion. The use of experimental designs to evalu.vening and dependent variables, respectively. ate mediated effeCts fully requires a series 01Given thar our goal in teSting for mediation is experiments. The effect of the independentto find c1 = 0 (more on this later), and that c1 variable on the dependent variable is evaluated

is diminished as b 1 increases in strength and in an experiment in which the independentbl is diminished as al increases in strength, it variable is manipulated and the dependentis advantageous to measure an intervening variable measured. The effeCt of the interven-variable closer in time to the dependent vari- ing variable on the dependent variable is eval-able than to the independent variable. In uated in an experiment in which theshort, tests of mediated effects are maximally intervening variable is manipulated and thepowerful when bl is larger than al. dependent variable measured. (Conceivably,

these two effects could be studied in a singleEx . . l D . experiment in which the independent and

pen menta estgns .. . bl h 11 .'IntervenIng vana es are orc ogona y mampu-

Although the dependent variable is mea- lated.) The effeCt of the independent variablesured or observed in all studies of mediated on the intervening variable is evaluated in aand moderated effects, independent, modera- design in which the independent variable istor, and intervening variables can, to consider- manipulated and the intervening variable isable benefit, be manipulated and participants measured. More typically, mediated effects arerandomly assigned to levels of these variables evaluated in individual experiments in whichin such studies. In social psychological studies the independent variable is manipulated anddesigned to test moderated effects, it is not the intervening and dependent v.,riables mea-uncommon for both the independent variable sured. Although this approach has the desir-and the moderator variable to be manipulated. able property that it allows a strong inference

The payoff of this approach is tWofold. Both of causality regarding the effect of the indepen-

rh.. i"rI"'npnrl..n~ ..,nrl ,.,.,rvI..,...,..~,.. "..".;..,1-.1= .."... rI..n.. "..".;..,1-.1.. An ..h", ,.1 ,.1 .,nrl ;n~ tt ;nO't' "n ..."", un", UII "'V"'" ...,.. ~ ...V... v.. ""'y,,:""""" « ""'" Y"""'I:'

h~U~;f~"{;;i~%~~;~i~~?~'{~';~;~~X;(~;~.:i;;\'t;;/>;;£;';i:';1'~k{,(~~il~'l:;~;;/~;;::.~,\~(::i:;;J~~~(;>,:f\::~:~k~:'~k,;,'::I,~>.~'~;~;;::;;"~:,,\;:;',t:.,\:; i";',~;i':;'J..;;',i,;"',,,s ,',::,';, :,),:,: ;'",;,~,:,,:;' .""""";,,,,;(,,:',::,~;:,',,' '" ',',;" ,';,

than the one-shoty for inferring aling variable on the

\.Jri.1bles, it is no better thanon-experimental strategy f

causal effect of me intervening

dependent variable.

ANALYSIS ISSUES

There are tWo major analytic approaches toresting mediated effects. Common to the twoapproaches is this basic question: Is some por-tion of the effect of an independent variable ona dependent variable attributable to an inter-vening variable? In the serial approach toaddressing t:his question, the data are evaluated .against a sequentiallisc of criteria that must bemet in order for this question to be answered

affirmatively (Baron & Kenny, 1986).

1. The independent variable is associated withthe dependent variable.

2. The independent variable is associated withthe intervening variable.

3. The intervening variable is associated with.the dependent variable, controlling for theindependent variable. At this step, an addi-tional evaluation is made regarding the

magnitude of the association betWeen theindependent and dependent variables, con-trolling for the intervening variable. If theeffect is, within sampling error, zero, thenthe correct inference is that the interveningvariable fully explains the effect of theindependent variable on the dependentvariable. If, controlling for the interveningvariable, the effect remains significantlydifferent from zero, then the correCt infer-ence is partial mediation.

There are two primary statistical proce-dures for implementing rhe serial approach totesting mediated effects. If the independentvariable is manipulated or measured on anominal scale, thereby defining levels of afactor, the effect of the independent variable onthe dependent and intervening variables typi-cally is evaluated using analysis of variance.

~~!~il~*~t:~"i'Y'~~~~~:i':i' \;~})'~~~)t~Yh'tv!~t~~~~~;i;~ii~~j;?~:t {{~f~;;~"f);~!.~~i/J.,~~:'i£I.~ ~~:\ \ ~;{;~:;;~~~~'.;;f;~ ~.:~;~",;,>.~,~~::!,~;:;.~~; l~;f.~"J'::.,"..j:;;~'/~'~';~'",;;::,~~:;;,;"ji,\.., ,},:;;,'i;~:~:~~;;:~'1::':;i;;;" ~;.;:.. .~.~: ,; ;::~, :.:,.','

Mediation and Moderation I 225

(Note that the intervening variable is treatedas a dependent variable at this stage of theanalysis.) If these effects are statistically sig-

dependent variables controlling for the inde-pendent variable. If the effect of the covariateis significant in this analysis, then there is sta-tistical evidence of a mediated effect. If theeffect of the independent variable also is sig-nificant, then the correct inference is partial

mediation. H the effect of the independent

variable is nonsignificant, then the findingswarrant an inference of full mediation.

If the independent variable is oPerationallydefined in such a way that it is not properlyviewed as defminga faCtor typical of faCtorialdesigns, then all three steps can be evaluatedmore effectively using regression analysis.(Regression, of which analysis of varianceand covariance are special cases, could beused for manipulated or nominally scaledindependent variables as well.) In the three-variable case, Steps 1 and 2 require simpleregression runs in which the dependent andintervcnillg variables, in turn, are regressedon the independent variable. Assuming statis-tical support at Steps 1 and 2, Step 3 requiresregressing the dependent variable simultane-ously on the intervening and independentvariables and evaluating first the coefficientfor the intervening variable, then the coeffi-cient for the independent variable. If the coef-ficient for the intervening variable isstatistically significant, then there is evidenceof a mediated effect. If the coefficient for theindependent variable is nonsignificant, thenthere is evidence of fun mediation. Otherwise~the correct inference is partial mediation.

An alternative strategy is the integrated

approach, in which all relevant effects areeva(uated within a single model. The modelincludes both the direct effect of the indepen-dent variable on the dependent variableand the indirect effeCt of the independent

DESIGN AND ANAL YSIS226

Figure 10.5

variable on the dependent variable through anintervening variable. The basic model for the

three-variable case is shown in Figure 10.5.

The coefficientS in such models typically areestimated using maximum likelihood proce-dures (as opposed to ordinary least squarestypical of regression) using structural equation

modeling. The test of primary interest in these

models is the indirect, or ab, effect. This test is

available in most software packages for esti-

mating srructuralequarion models, althoughnew tests that are not yet available in these

packages promise greater power and precision

(MacKinnon, Lockwood, Hoffman, West, &

SheetS, 2002).

There are two approaches to evaluatingmoderated effects as welL In the interaction

approach, the interaction effect is evaluatedin the context of a single model that alsoincludes the unqualified effectS of the inde-'pendent and moderator variables on the

dependent variable. As with tests of media-

tion, when the independent variable and/ormoderator variable are manipulated or mea-sured on a nominal scale, the evaluationtypically is accomplished with analysis ofvariance. As implemented in most statisticalsoftware packages) the interactions among allvariables in fa<.loria[ design are evaluatedautomatically. Multiple regression is prefer-able when either the independent or the mod-erator variable is operationaHy defined todefine a continuum. Evaluation of interaction

Path Diagram Depicting a Model in Which the Attitude~Behavior Association IsMediated by Perceptions of the Object

effects in multiple regression models requiresthe creation of interaction terms "after center~

ing scores on the independent and moderatorvariables.

Alternatively, moderated effects can beevaluated using the multi group approach.This approach is particularly attractive whenthe moderator variable is manipulated ornominally scaled and the independent vari-able is operationally defined in such a waythat it could be modeled as a latent variable.In the .ffiultigroup approach, a single predic-tive equation is estimated separately forgroups that vary on the moderator variable.Corresponding coefficients are statisticallycompared and, to the extent that they differfrom one group to another, the grouping vari-able moderates the effect of that variable onthe dependent variable. Most statistical sofr-ware packages do not provide an option tocompare coefficientS when the equations areestimated for the groups using ordinary leasesquares regression; hence, hand calculationsometimes is required. When the equations

are estimated as structural equation models,

or

way

ware

sometimes

the tenability of between-groups equality con-straints imposed on the relevant coefficientScan be evaluated without hand calculation. Ifequality constraints on the coefficients repre-senting the effect of the independent vari"bleare not tenable across levels of the moderatOrvari;'1ble, then there is statistical support for amoderated effect. If the model includes an

intervening variable and indirect effect, thisstrategy can be used to test for moderatedmediatioll, variability in the degree of media-tion across the groups representing differentlevels of the moderator variable.

Analysis Issues Specific to Mediation

In our discussion of considerationsregarding when to measure, we highlighted

the interdependence of effectS. involved in

testS of mediation. The relevant effects areillustrated in Figure 10.5, which displays inpath diagram form a simplified version of the

attinIde-to-behavior process model that hasprovided context for our discussion. Thedirect effect of attitude on behavior is repre-sented by c, and the alb combination cap-tures the indirect effect of attitude onbehavior through perceptions. If the theoreti-cal account that inspired this model specifiesthat perceptions fully mediate the attitude-behavior association, then we would hope to

find c == 0 in this model. As noted earlier,

the c path is influenced by the strength of b,the influence of perceptions on behavior,and the strength of b is influenced by theand the srrength of b is influenced by thestrength of a, the influence of attitude on per-

ceptions. As such, it is critical that we not

underestimate b lest we overestimate c and infer

partial or no mediation through perceptions.

We already noted that it is advantageous to

position measurement of the intervening vari-

able-perceptions, in our example-closer in

time to the dependent variable than to the

independent variable to avoid the situation in

which b is diminished because so much vari-

ability in the intervening variable is accounted

for by the independent variable (via path a)

that little is left to explain variability in the

Outcome. Another means by which b can be

underestimated and c overestimated involves

measurement error. To illustrate this point,

assume that we had population daro. on error-

free measures, and we knew that c ;;; 0, a ;;; .3,and b = .4. Now assume thar we have data

;.ni;;{.~\:~i~j):')?~~~1";f~~~Y;~"~~Y~!.Mi~~~~:i'-:h~\:~~:~;~;,.~~-t~("~',j.",t;.£I;.~i;,~;~~'~~:j:\":,,,-~,.~~:...~.!..,';.1' ;';W,(;},.'>:J:";'~.\\~'~'~"~~~:~,>,:~; ;:-~.;;..;.:.,~ .,:~:; :,..;.;.;';..::.,;.: ~~.:<;::; :;;;';":~'::_::'~:< .:. .::.':~ .

~

Mediation and Moderation I 227

from a sample and our measure of perceptions

of the object, the intervening variable, is noterror free. We can show the ill effects of mea-

suremenr error in the intervening variable by

substituting hypothetical values in the follow-

ing equation (Hoyle & Kenny, 1999):

C"b. ::: (1 - ru) ab + c.

In this equation, r u is an estimate of thereliability (e.g., coefficient alpha, test-retest r)of our measure of perceptions of the object.

The resultant value, 'obI' is the value of , we

would observe given certain values of a and b(.3 and .4, respectively, in this case) andcertain levels of reliability of the measure of

perceptions of the object. Recall that we know

that c = 0 in the population, a value that indi-

cates full mediation of the attitude-behaviorassociation by perceptions of the object. If ourmeasure of perceptions were perfecclyretiable,

indicated by a value of 1.0, we would expect

to observe the population value of zero for '0/>$because (1-1) (.3)(.4) + 0 = O. If'a = .9, then

we would expect to observe c = .012. If r u =

.8, a value more typical of measures in social

psychological research, we would expect to

observe c = .024. It is not uncommon for the

reliability of measures in social psychologicalresearch to hover closer to .7. Were this the

case, we would expect to observe c ::::: .036

despite the faCt that c = 0 in the population.With a relatively modest sample size, thiscoefficient would be significantly greater thanzero, leading to the erroneous inference thatperceptions do not fully mediate the attitude-behavior association. In practice, this erroris more pronounced because, in the strongestcases of mediation, the value of c is trivialbut greater than zero. For instance, if c = .07in the population, a value that might be

viewed as trivial, the estimate of c when r u =

.7 will be .11, an effect size that cannot be

ignored.

It is clear that error in measures of inter-vening variables poses significant problems

228 DESIGN AND ANALYSIS

for tests of mediated effects. As such, it is

crucial that researchers deal with measure-

ment error in such models. One approach isto select a measure with well-documentedhigh reliability, at least .9. S~ch measures are

not always available. An alternative is to

model the intervening variable as a latent

variable, as illustrated for attitude inFigure 10.3) thereby removing uniquenessfrom the variable before estimating associa-

tions between variables. Depending on theamount of information available on theintervening variable) it can be modeled in oneof four ways. The best approach is to obtainmultiple measures representing differentmeasurement strategies. This approach hasthe additional benefit of allowing theremoval of variability attributable to mea-surement strategy. Typically) investigatOrsmight have only one measure of a mediator,but the measure is a multi-item scale. Whenthis is the case) the individual items can betreated as indicators of the latent variable, astrategy that provides no information about

method variance but nonetheless segregatescommonality across items from uniqueness

associated with individual items or subsets of

items. Sometimes the number of items in

such scales is too large to effectively model alatem variable of which each item is an indi-

cator (see Marsh & Hau, 1999). In such

cases, a compromise solution is to sort items

into four or more composites, referred to asparcels. Parcels may correspond to subseales,subsets of items that emerge from factor

analysis, or arbitrary groupings of items.A final strategy for dealing with measure-

ment error in an intervening variable con-

cerns the situation in which there is only a

single indicator. Assuming there exists

enough prior research on the indicator toprovide a good estimate of its reliability, theindicator can be modeled with a fixed error

term equal to (1 - r;~) 51, where r a is the reli-

ability estimate and 52 is the variance ofscores on the indicator.

,~:i?:-:'>~<""W.\ ,\').'j.;~{{$'{:~:;~?~~)~'(~;i.:i>.;;~(~!;!;!;)!~,~:;~:')'r>('t.';t~~i~'i~~~i.i$.~i~;~~.;~;!;<f.~;"J~.iN~ii.(;;~,~;j".,~,~~; ;;~~'j ::t..\kl).:~.'j;;,.ji(ii;j~I);,}(,:!:~:;l,;.}/.~,i;;,;(; /;/ i:,\,ii,; ;,0,;;;:" J,;,.; r,,;~,(';:; ,,; ,;J';\'~.i;.Li, :t:::;.";,,,;,\:i ;;:;" ; ,'"

Analysis IssuesSpeciftc to Moderation

Measurement error also is detrimental

statistical tests of moderation. Unlike in ttof mediation, in which the primary conCI

is measurement error in one variable (

intervening variable), in tests of moderatJthe concern involves two variables (the in.pendent variable and the moderator v~

able). In the same way that the modera!

effect is represented as a product of the inependent and moderator variables, errorthe variable that representS the moderateffect, the interaction term, is a productthe error in the independent variable and tmoderator variable (Busemeyer & Jon!

1983). Specifically, the reliability of the innaction term can be computed as

rji r""" + r;",

1 + r.1""

where r;; and r """ are reliabilities of the indpendent and moderator variables, respeCtiveland r in< is the correlation between the tWo

When the independent and moderator VaJ

abIes are uncorrelared, the reliability of dproduct term is the product of the two reliab!

ities. Thus, if we assume typical values 6f relic

bility, say .8, the reliability of the product tenwill vary between .64, when the independerand moderator variables are uncorrelared, an.7, when they are strongly correlated. Th;diminished reliability is especially problematibecause the detection of moderated effectunder typical research conditions is a ch,lllengfor reasons other than measurement erro(McCieUand & Judd, 1993).

As with tests of mediation, tests of modera

tion are strengthened when measurement erro

is extracted from variables prior to esri.marin!

associations. This extraction for independenand moderatOr variables can be accomplishe<using one of the strategies described earlielfor modeling intervening variables; however

r

e~tracting measurement error from the

interaction term is significantly more compli-

~lred. One approach to this problem would be

the specification of a latent variable represent-

ing the interaction term. This specification iscomplicated by the faCt that the loadings anduniqueness terms associated with this latentvariable are nonlinear transformations of theircounterparts in the latent variables for theindependent and moderator variables

(Kenny & Judd, 1984). Although this nonlin-

earity can be incorporated into the specifica-

tion of the latent variable representing the

term, if the number of indicators of the inde-

pendent and moderator variables exceedsthree, the specification becomes prohibitively

complex.One solution to this problem would be to

limit the number of indicators of the indepen-

dent and moderator variables to two or three,

either by limiting the number of measures ofeach or, in the case of multi-item scales, creat-

ing item parcels. An alternative approach is to

use the mulrigroup approach described earlier.For instance, we might divide a sample of 100

participants into two groups of 50 corre-

sponding to those highest and lowest in atti-

tude accessibility. We could then fit a model to

data from the tWo groups, a model. in which

attitude toward the object is modeled as a

latent variable and specified as a cause ofbehavior. Using equality constraints, we could

compare the strength of the. influence of atti-tude on behavior for high and low accessibil-

ity groups. If the strength of this associariol),reflected in the path coefficient, differs across

groups, then we infer that accessibility moder-

ates the attitude-behavior association. Thereare two drawbacks to this compromise strat-

egy. First, we have taken a measure of accessi-bility that differentiates among respondents in

terms of milliseconds and reduced it to a

coarsely categorized variable with only two

values. Second, although we have effectively

modeled measurement error our of the atti-

tude measures, we have not addressed the

~;~~~{:,;\i~~-{;~l~;(>',I;;j;}b~,t't;~i,¥:(ii~W~!i~.:vi&:(.'~.;ii;!\.\'~~\~~~~i~,l.t;.~):;i~d (;~i:~:&::~)N~;~ijiJj/!(\.{~ii;i;: ~'~):,~;;~~,X~;~j,,(~~~~;.;~;;.;~;Y\i;; };;:i,~ i:;~:;,,;;:;{:<; ~:;;.:;::.:};:,:~.;. ;,,;:;;J ;i;~:;~: '~'~(i k:!.:: '~;'..::.;:;. ::: ';':

Mediation and Moderation 229

from the issue of measurement error in the measure of

attitude accessibility. The first drawback is

not a concern if the moderator variable iscategorical and can take on relatively few

values (e.g., male vs. female, Hispanic vs. African

American vs. White). The second drawback

can be addressed by choosing or developingmeasures of the moderator variable that arehighly reliable (i.e., r mnt > .90). In short, testS ofmoderation are significantly compromised bymeasurement error in the independent andmoderator variables; hence, effective tests ofmoderated effects require careful attention tomeasurement error at both the measurement

and analytic phases. ,

As with tests of mediated effects (but fordifferent reasons), multicollinearity can posea problem for tests of moderated effects. Ifraw scores on a single indicator of the inde-pendent variable and a single indicator of themoderator variable are multiplied to form

the interaction term, the latter will be highly

correlated with one or both of the original

variables (Aiken & West, 1991). The magni-

tude of these correlations (e.g., r2 and r3 inFigure 10.1) can be substantial (> .80) andgive rise to the problem typically associatedwith multicollinearity in prediction equa-tions-inflated standard errors. Fortunately,there is a rather simple fix for this form ofmulticollinearity, which is an artifact of scal-ing rather than a substantively meaningfulinstance of correlation. If the distributions ofthe variables are normal, then subtractingscores on each variable from the mean onthat variable (i.e., centering) prior to creatingthe interaction term will result in a zero cor-relation between the interaction term and theindependent and moderator variables.

The magnitude of the correlation betweenthe independent variable and the moderatorvariable (e.g., r1 in Figure 10.1) and the cor-relation between each and the dependent vari-able (e.g., reflected in c1 and c2 in Figure 10. t)influ~nce cl1e likelihood of deteCting a signifi-cant moderated effect in the presence of

230 I DESIGN AND ANALYSIS

me-asurement error. To iUustrate this point,

assume that we have measures of attitude and

attitude accessibility that, when multiplied,

yield an interaction term with reliability of

.70. Moreover, assume that we wish to

achieve statistical power of .80 for detecting amedium effect of Attitude x Accessibility onbehavior. How large must our sample be? If

attitude and attitude accessibility were not

correlated with each orher but were stronglycorrelated with behavior, then we would need

a sample size exceeding 250 in order to realizestatistical power of .80. If, 00 the other hand,attitude and attitude accessibility were moder-ately correlated with each other but neither

was correlated with behavior, then we would

need a sample of about 140 to achieve the

same level of statistical power. The basic prin-

ciple is that tests of moderated effects are mostpowerful when the independent and modera-tor variables are correlated with each otherbut unrelated to the dependent variable.

This rather simple principle gives rise to anumber of important considerations. One

concerns the associations between the inde-pendent and moderator variables, attitudeand attitude accessibility in our example, andthe dependent variable, behavior. If power ismaximized when these effects are zero, underwhat conditions might we expect them to be

zero? Focusing first on the independent vari-able, it is well known that when the effect ofan independent variable on a dependent vari-able is moderated but the interaction effect isignored, the independent and dependent vari-able would be related in a curvilinear fashion.In the case of a crossover interaction, inwhich the effect of the independent variableon the dependent variable reverses whenmoving from one extreme to the other. of a

moder;,\tor variable, the linear effect of theindependent variable on the dependent vari-able, ignoring the moderated effect~ willbe near zero. As such, moderated effectsthat involve a change in the direction of theassociution between an independent and

:~~.~;;;.~~ii!~~~~~.~~~:»:~<~.r.~}~i(!~¥.*.~f.i>:~~?;,~;:<;~;,/,.1~~s~:.:<j.i;J.~,;..:.~~i';:ci;,;"i.l(;i~~'~1~~J:'~~;":;>.~;j.~..~~~;.~.:.';';~'~..j,~~i(,i~:;'; <;~;>:i,~' ;'\i.:".,;~j~ ;j;;:;;:;::{;';;~'~':';;i;;; ;:~:",':~~;;~;;".:.f,;;;:,:}:(: ';:~ ,',',:',' ':.. .

dependent variable are, st.'ltistically speaking,easiest to detect.

Considerations regarding the associationbetween moderator and dependent vari-

ables are somewhat more complex. As

noted early in the chapter, the moderatorhypothesis implies norhing about the associ-ation between the moderator and dependentvariables. In fact, the differential status ofthe independent and moderator variables iseasiest to defend when there is no reason tosuspect that the moderator variable couldcause the dependent variable (i.e., when the

two are uncorrelated). To the extent thar

the moderator variable could be construed

as a cause of the dependent variable, then itis bereer viewed as a second independentvariable that operates synergistically withthe other independent variable to producevariability in the dependent variable

(Carver, 1989).We have noted that both the reliability of

the interaction term and the statistical power

of the test of a moderated effect are greaterwhen the independent and moderator vari-ables are associated. If the independent andmoderator variables are associated, a keyconcern is the nature of that association. It isimportant to establish that the independentvariable is not causally associated with the

moderator variable. To draw on our

example, for attitude accessibility ro qualify

as a moderator of the attitude-behaviorassociation, there must not be a causal asso-ciation between attitude and attitude acces-sibility. If an association betWeen attitudeand attitude accessibility could be construedas causal, then it is possible that attitudeaccessibility is a mediator rather than a mod-erator of the attitude-behavior association.

As with the question of whether a potential

moderator variable might better be con-strued as an independent variable, the issuecannot be resolved statistically outside aresean.:h design that allows for a persuasivetest of the directionality of an association.

STUMBLING BLOCKS

A commitment to the principles outlined in

this chapter cannot always be translated into

a research study that gives evidence of thatcommitment. In this final section, we touch

on four impediments to full implementation

of the measurement, design, and analysis

strategies we have proposed.

Ambiguous Theory

The reasoned approach to measurement

presupposes a reasonably detailed theoreticalaccount of the phenomenon under investiga-tion. The attitude-to-behavior process model

we used to illustrate the approach is such an

account. Unfortunately, such models are

somewhat rare, leaving investigators to, atbest, combine the opportunistic and rea-soned approaches to measurement. This stateof affairs is problematic, for the determina-tion of how a variable figures into a socialprocess rarely can be made on purely statisti-cal grounds. If theory is not available anddefinitive statistical tests are not possible,then the placement of variables within amodel is arbitrary and, therefore, inferences

are, at best, suggestive of future research.

Theory can be ambiguous in a differentway. It is possible, for example, that a theoreti-cal account proposes a set of mediating mech-

anisms, bur it is not dear what'variables mightstand in for the constructs in statistical tests ofa model. The most useful theoretical accounts

provide information not only about how con-. strllcrs are associated with each other but also

about how those constructs are associat~d with

variables that might represent them (Edwards

& Bagozzi, 2000). Less useful are theories thataccord a prominent role to constructs tharhave no evident concrete manifestation.

One-Shot Data

We have noted that a key consideration

beyond how variables are measured is when

.,,-,,-

-IMediation and Moderation 231

they are measured. Even when a theoreticalaccount is very specific regarding the status ofkey constructs in a model of the process underinvestigation, the placement of variables rep-resenting these constructs in a statistical modelis, with few exceptions, arbitrary when the

variables aU are measured at the same time.

One exception is the randomized experiment,

which clearly distinguishes the independent

variable from all other variables in the model.

It is important to acknowledge, however, that

even in randomized experiments, the fact that

potential intervening and moderator variables

typically are measured at the same time is an

issue. In non-experimental designs, the place-

ment of the independent variable is a concernas well. We noted the considerable inferential

power gained by adding a second measure-

ment occasion, noting the importance of areplicative rather than sequential measure-ment strategy. Apart from a replicative mea-

surement strategy, non-experimental data

cannot be used to develop a definitive test of amodel that includes mediated or moderated

effects.

Limited Sample Size

A concern when using statistical models

that allow modeling of measurement error is

sample size. This is ber;:ause the maximum

likelihood estimation characteristic of statisti-cal approaches involving latent variables is a

large-sample technique. Invariably, this con-cern leads to the question, How large is large

enough? A growing literature suggests that

"large" is not as substantial as once thought;however, it is equally clear that a sample thatis large enough for tests of one model wouldbe inadequate for tests of another. Under idealcircumstances-that is, normally distributedvariables and an approximately correct

model-maximum likelihood performs rea-

sonably well with samples as small as 50

(although stability can be an issue; see Marsh& Hau, 1999). The ideal circumstances

232 DESIGN AND ANALYSIS

are rare in practice, and a more reasonablerecommendation given typical circumstances

would be samples of at least 200 (Hoyle &

Kenny, 1999). When it is not possible toachieve a sample this large, then it is criticalthat all measures are highly reliable (rx.~ > .90)

in order to avoid the ill effects of measurementerror.

Limited Number of Indicators

A more general concern is the number of.

measures, or indicators, of key constructsavailable for most statistical tests. Since the1950s, social psychologists have been awareof the virtues of multiple indicators for teas-ing apart variability attributable to the con-struct of interest and systematic errorintroduced by the method of measurement

(Campbell & Fiske, 1959). Relatively recent

advances in statistical software have broughttechniques that can be used t() model mea-surement error (e.g., structural equation mod-eling) into the mainstream. Yet, the inclusionof multiple measures and, better still, multipleoperational definitions of key constructs insocial psychological research remains theexception rather than the rule. As we. have

discussed in this chapter, if a construct servesas an intervening or moderator variable in amodel, then the issue of error in the opera-tional definition of the construct takes centerstage. In the absence of multiple measures ormulti-item scales whose subscales, individual

items, or arbitrary groups of items (Le.,

parcels) can serve as indicators, tests of medi-ated and moderated effects are significantly

compromised.

REFERENCES

~

CONCLUSION

We have drawn a distinction between two

approaches to measurement in social psycho~

logical research: the opportunistic approach) inwhich all variables are measured on one occa-sion using a single method, and the .reasonedapproach, in which variables are assigned dif-ferent statuses in a model based on theory, andthe strategy by which they are measured andtreated in statistical analyses is governed bytheir status in the model. We focused most of

our attention on intervening and moderatorvariables, demonstrating that these variableswarrant particular scrutiny in light of their sen-sitivity to measurement error and complica-tions that arise from assumptions regarding the

temporal ordering of the variables. 'Substantivetheory is central to the reasoned approach, anda recurring theme in the chapter isthe fact thatthe absence of a detailed theoretical account

introduces a measure of arbitrariness into mea-

surement, design, and analysis. To overcome

these obstacles to high-quality research, we

urge investigators to (a) start with a well-developed theoretical account; (b) use this

account to distinguish among independent,dependent, intervening, and moderator vari-ables; (c) develop a measurement strategy thatis sensitive to the differing status of variables inthe model; and (d) operationally define eachconstruct with multiple indicators, preferablyrepresenting'different modes of measurement.In our view, a single study that meets thesecriteria stands to contribute more to ourunderstanding of the phenomenon, underinvestigation than several studies that take the

oppornmistic approach.

Aiken, L. S., & West, S. G. (1991). Multiple regression: Testing and interpreting

interactions. Thousand Oaks, CA: S,lge.

Baron, R. M., & Kenny, D. A. (1986). The moderator-medi.Hor variable distim;riol1in social psychological research: Conceptu.ll, strategic, and statistic~11 consider-ations. Journal of Personality and Social Psychology, 51, 1173-1182.

Busemeyer, J. R., & Jones, L. D. (1983). Analysis of multiplicative combinationrules when the causal variables are measured with error. Psychological Bulletin,93, 549-562.

Cacioppo, J. T., Tassinary, L. G., & Berntson, G. G. (Eds.). (2000). Handbook of

psychophysiology (2nd ed.). New York: Cambridge University Press.

Campbell, D. T., & Fiske, D. W. (1959). Convergent and discriminant validation

by the mulritrait-mulrimethod matrix. Psychological Bulletin, 56. 81-105.

Carver, C. S. (1989). How should multifaceted personality constructs be tested?

Issues illustrated by self-monitoring, attributional style, and hardiness. Journalof Personality and Social Psychology, 56, 577-585.

Cohen,]., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied multiple regression/corre-lation analysis for the behavioral sciences (3rd ed.). Mahwah, NJ: Lawrence Erlbaum.

Edwards, J. R., & Bagozzi, R. P. (2000). On the nature and direction of relation-

ships between constructs and measures. Psychological Methods, 3, 155-174.Evans, M. G. (1991). The problem of analyzing multiplicative composites:

Ipnreracrions revisited. American Psychologist, 46, 6-15.Fazio, R: H. (1990). MultipLe processes by which attitudes guide behavior: The MODE

model as an integrative framework. In M. P. Zanna (Ed.), Advances in experi-

mental social psychology (Vol. 23, pp. 75-109). New York: Academic Press.

. Fazio, R. H., Powell, M. c., & Williams, C. J. (1989). The role of attitude accessi-bility in the attitude-to-behavior process. Journal of Consumer Research, 16,280-288.

Fazio, R. H., & Williams, C. J. (1986). Attitude accessibility as a moderator of the

attitude-perception and attitude-behavior relations: An investigation of the 1984

presidential election. Journal of Personality and Social Psychology, 51, 505-514.Greenwald, A. G., & Farnham, S. D. (2000). Using the Implicit Association Test to

measure self-esteem and self-concept. Jo~irnal of Personality and SocialPsychology, 79, 1022-1038. .

Hoyle, R. H., & Kenny, D. A. (1999). Sample size, reliability, and tests of statist i-cat mediation. In R. H. Hoyle (Ed.), Statistical strategies for small sample

research (pp. 195-222). Thousand Oaks, CA: Sage.

Kenny, D. A., & Judd, C. M. (1984). Estimating the nonlinear and interactive

effects of latent variables. Psychological Bulletin, 96,201-210.Kimble, G. A. (1989). Psychology from the standpoint of a generalist. American

Psychologist, 44, 491-499.

Lewin, K. (1951). Field theory in soci'11 science: Selected theoretical papers

(D. Cartwright, Ed.). New York: Harper & Row.MacKinnon, D. P., Lockwood, C. M., Hoffman, J. M., West, S. G., & Sheets, V.

(2002). A comparison of methods to test mediation and other intervening vari-

able effects. Psychological Methods, 7, 83-104.Marsh, H. W., & Hau, K.-T. (1999). Confirmatory factor analysis: Strategies for

small sample. sizes. In R. H. Hoyle (Ed.), Statistical strategies for small sampleresearch (pp. 251-284). Thousand Oaks, CA.: Sage.

McClelland, G.H., & Judd, C. M. (1993). Statistical difficulties of detecting inter-

actions and moderatOr effects. Psychological Bulletin, 114, 376-390.

Pearl, J. (2000). Causality: Models, reasoning, and infermce. New York: CambridgeUniversity Press. .

. Roskos-Ewoldsen, D. R., & Fazio, R. H. (1992). On the orienting vaLue of attitudes:

Attitude accessibility as a determinant of an object's attraction of visual atten-tion. Journal of Personality and Social Psychology, 63, 198-211.

. Salmon, W. C. (1997). Causality and explanation. New York: Oxford UniversityPress.

~

Mediation and Moderation I 233

SAGE

Handbook of Methodsin Social Psychology

~ SAGE Pub " . . ?DOL(~.. International Er'lCationsThou vuGallonal and P,

sand Oaks. London N /olessional Publi"' h \ ~

. ew Deihl '" er

byEdited

Carol SansoneUniversity of Utah

Carolyn C. Morf

and

A.T. PanterUniversity of North Carolina, Chapel Hill