HLTH 653 Lecture 4: Mediator Variables

Raul Cruz-CanoSpring 2013

Mediators

• A mediator is an explanatory link in the relationship between two other. • Often a mediator variable is conceptualized as the mechanism through which one

variable (i.e., the predictor) influences another variable (i.e., the criterion).• mediators represent properties of the person that transform the predictor or input

variables in some way

X

M

YMediated relationship among variables:•X = predictor•M = mediator• Y = criterion/outcome

Mediators– Example: Suppose, hypothetically, that a researcher finds that parental intrusive

behavior is negatively associated with child adherence to a medical regimen.– This finding does not tell us very much about processes that underlie the relationship

between intrusiveness and adherence. – By testing for mediational effects, a researcher can explore whether a third variable(e.g.,

child independence) might account for or explain the relationship between these variables.

X YMediated relationship among variables:•X = intrusive parenting •M = child independence • Y = less medical adherence

MParental intrusiveness impacts negatively on level of child independence, which in turn contributes to poor medical

Where…

• Mediational processes can be proposed in correlational and regression-oriented predictive utility studies, group differences research, longitudinal investigations, complex model testing (with structural equation modeling), studies of interventions including randomized clinical trials, and temporal relationship models in which ‘‘What precedes what?’’ questions are of interest

Mediation Conditions• To establish mediation, the following criteria must hold:

1. The independent variable must affect the mediator2. The independent variable must be shown to affect the dependent

variable 3. The mediator must affect the dependent variable (adjusting for the

Independent Variable).

• If these conditions all hold in the predicted direction, then the effect of the independent variable on the dependent variable must be less in the #3 than in #2.

• Perfect mediation holds if the independent variable has no effect when the mediator is controlled.

Mediation Conditions• Many different tests, this is just one of the most common• To test for mediation one should estimate the three following

regression equations:1. Regressing the mediator on the independent variable;

M=β1+aX+ε1

2. Regressing the dependent variable on the independent variable;Y= β2+cX+ε2

3. Regressing the dependent variable on both the independent variable and on the mediator.

Y= β3+c’X+bM+ε3

Mediation ConditionsTo test the existence of the 3 criteria, the following four conditions must be met :1. the predictor, X, must be significantly associated with the hypothesized mediator,

M=>term a is significant in Eq. 12. the predictor, X, must be significantly associated with the dependent measure, Y =>

term c is significant in Eq. 23. the mediator, M, must be significantly associated with the dependent variable, Y,

and => term b is significant in Eq. 34. the impact of the predictor, X, on the dependent measure, Y, is less after controlling

for the mediator, M => term c’ in Eq. 3 is significantly smaller than term c in Eq. 2

• A corollary of the second condition is that there first has to be a significant relationship between the predictor and the dependent variable for a mediator to serve its mediating role.

• In other words, if X and Y are not significantly associated, there is no significant effect to mediate.

Mediator vs. Moderator

• Moderator variables are typically introduced when there is an unexpectedly weak or inconsistent relation between a predictor and a criterion variable (e.g., a relation holds in one setting but not in another, or for one subpopulation but not for another).

• Mediation, on the other hand, is best done in the case of a strong relation between the predictor and the criterion variable.

Mediator vs. Moderator• A moderator variable is one that affects the relationship

between two variables, so that the nature of the impact of the predictor on the criterion varies according to the level or value of the moderator.

• A moderator interacts with a predictor variable in such a way as to have an impact on the level of a dependent variable.

• A mediator, on the other hand, specifies how (or the mechanism by which) a given effect occurs

• The independent variable causes the mediator which then causes the outcome

Mediator vs. Moderator Example

• Feldman and Weinberger (1994), for example, examined whether child self-restraint was a mediator of associations between parenting behaviors and child delinquent behavior.

Mediator vs. Moderator Example• Study the role of social support in the relationship between

parenting-related stress and psychological distress in parents of children with hearing impairment and seizure disorder.

• Social support is a moderator: Parenting stress is more likely to have adverse effects on adjustment when parents have low levels of social support

• Social support is a mediator: it could also be that parenting stress undermines one’s ability to garner social support, which in turn impacts on parental adjustment

Mediator vs. Moderator Example• The relationship between parental stress and psychological distress did not vary as a function of level of

social support, i.e. social support did not moderate or alter the strength or direction of the relationship between parental stress and psychological distress.

• Parenting stress (the predictor) was significantly associated with psychological distress (the outcome).

• Parenting stress was also a significant predictor of social support (mediator). Specifically, those parents who experienced more stress tended to have fewer social contacts and perceive their selves as less supported.

• Found a significant relationship between social support (the mediator) and psychological distress (the outcome), such that less social support was associated with higher distress ratings.

• When she tested the relationship between parental stress and psychological distress in the presence of this mediator, the strength of this previously significant relationship dropped significantly.

• Conclusion: the relationship between stress and psychological functioning is mediated by social support (parenting stress -> social support -> psychological distress), and that reduced social support may be one mechanism by which parental stress is linked with parental psychological distress.

SAS Example 1: Rural Women HIV Study

• The cross-sectional data were collected in the first of three interviews of a longitudinal study designed to test the efficacy of a peer counseling intervention designed for rural women with HIV disease.

• Tested a peer-based social support intervention designed for a population of rural women with HIV disease

• The 280 study participants were recruited from 10 community-based HIV/AIDS service organization serving rural areas of the southeastern United States.

• Study participants were randomly assigned to intervention and control groups.• Intervention group participants received a total of 12 face-to-face peer-

counseling sessions over a period of six months, while the control group received the usual care provided by the agency by which they were recruited.

• Peer counselors were recruited at each local study site to implement the intervention.

SAS Example1: Rural Women HIV Study

• Tavakoli, A., Jackson, K., & Moneyham, L. (2009)

• The mediator effect was examined. • The regression models included – Reason Missing of Medication (Outcome Variable)– available social support (Predictor=X) – spiritual activities (Mediator=M)

SAS Example1: Rural Women HIV Study• Variables:

– X=Available Social Support (TSSQAV) – M=Spiritual Activities (TCOPESA) – Y=Reason Missing of Medication (TREAS)

SAS Syntax for Mediator Effect:

proc reg data=two; model treas = tssqav / stb pcorr2 scorr2; run; proc reg data=two;

model tcopesa = tssqav / stb pcorr2 scorr2; run; proc reg data=two;

model treas = tssqav tcopesa / stb pcorr2 scorr2;run;

STB: displays standardized parameter estimates

PCORR2: displays squared partial correlation coefficients computed using Type II sums of squares

SCORR2 : displays squared semipartial correlation coefficients computed using Type II sums of squares

Equation (2)

Equation (1)

Equation (3)

SAS Example1: Rural Women HIV Study-Results

Three regression equations were run: 1. The mediator (Spiritual Activities) was regressed on the predictor variable

(Social Support). The result indicated that there was significant relationship between mediator and predictor variable (a =.143 (p=.003)).

2. The outcome (Reason Missing of Medication) was regressed on the predictor variable (Available Social Support).This relationship were significant (c =-.98 (p=.02)).

Regressing the outcome (Reason Missing of Medication) variable simultaneously on the predictor (Available Social Support) and mediator variable (Spiritual Activities):

3. The relationship between mediator variable (Spiritual Activities) and outcome (Reason Missing of Medication) was significant (b =-.44 (p=.02)).

4. The result indicated that the previously significant relationship between predictor (Available Social Support) and the outcome (Reason Missing of Medication) becomes non significant (c’ =-.79 (p=.055)).

SAS Example 2: Mediator Effect for Social Support of Mothers of Mentally Ill Children

• Tavakoli, Scharer & Hussey, L. (2011)• This study examines the role of perceived stress in the relationship

between social support and mood, and tested if moderator effects influenced the relationship.

• The role of coping in the relationship between perceived stress and mood was also examined for potential mediator and moderator effects.

• The cross-sectional data reported here were collected in an experimental design with repeated measures with mothers of children who had been hospitalized on a child psychiatric unit.

• A convenience sample of mothers was randomly assigned into three groups: A web-based intervention group, a telephone social support intervention group, and a usual care group.

• Two different mediator effects were tested

SAS Example 2: Moderator Effect for Social Support of Mothers of Mentally Ill Children

• Perceived stress (M=TPSS) as mediator of social support (X=TSS) to mood (Y=POMSMOD)

proc reg data=two; model pomsmod = tss / stb pcorr2 scorr2; title ' Regression model / step1 y=x' ; run; proc reg data=two; model tpss = tss / stb pcorr2 scorr2; title ' Regression model / step2 m=x' ; run; proc reg data=two; model pomsmod = tpss tss / stb pcorr2 scorr2; title ' Regression model / step3 y=m x' ; run;

Equation (2)

Equation (1)

Equation (3)

SAS Example 2: Moderator Effect for Social Support of Mothers of Mentally Ill Children

Equation (1)Equation (2)

Equation (3)

SAS Example 2: Moderator Effect for Social Support of Mothers of Mentally Ill Children -Results

1. The mediator (perceived stress) was regressed on the predictor variable (social support). The result indicated that there was significant relationship between mediator and predictor variable (a =-.17 (p=.0001)).

2. The outcome was regressed on the predictor variable (social support). The result indicated that there was significant relationship between outcome and predictor variable (c =-.38 (p=.0001)).

Regressing the outcome (mood) variable simultaneously on the predictor (social support) and mediator variable (perceived stress). 3. Significant relationship between perceived stress and the outcome (b =2.38 (p=.0001))4. The result indicated that the previously significant relationship between predictor

(social support) and the outcome (mood) becomes non significant (c’ =.009 (p=.919)).

• Therefore, there is almost complete mediator effect for Perceived stress in the relationship between social support and mood.

SAS Example 2: Mediator Effect for Social Support of Mothers of Mentally Ill Children -Results

• Coping (M=TCOPE) as mediator of perceived stress (X=TPSS) to mood (Y=POMSMOD)

proc reg data=two; model pomsmod = tpss / stb pcorr2 scorr2; title ' Regression model / step1 y=x' ; run;

proc reg data=two; model tcope = tpss / stb pcorr2 scorr2; title ' Regression model / step2 m=x' ; run;

proc reg data=two; model pomsmod = tcope tpss / stb pcorr2 scorr2; title ' Regression model / step3 y=m x' ; run;

Equation (2)

Equation (1)

Equation (3)

SAS Example 2: Moderator Effect for Social Support of Mothers of Mentally Ill Children -

Results

Equation (1)Equation (2)

Equation (3)

SAS Example 2: Moderator Effect for Social Support of Mothers of Mentally Ill Children -Results

The result did not reveal that the significant relationship between perceived stress (predictor X) and mood (outcome Y)(c =.822 (p=.0594)) => Condition 2 not met (no need to check anything else)

SAS Practical Example

• See MediationExample.sas and mediation_example.sas7bdat– Independent Variable X= pain– Mediator M = function– Dependent Variable Y= depress

• W. Dudley, University of Utah College of Nursing

SAS Practical Example1. Is a significant? Yes, the F-statistic was 38.46 and the p-value was <.000. We found

that about 21% of the variation in function is explained by pain. In addition, the regression coefficient for pain is statistically significantly different from zero (p=<.000). We can conclude that pain is negatively correlated with function.

2. Is c significant? Yes, the F-statistic was 18.86 and the p-value was <.000. We found that about 11% of the variation in depression is explained by pain. Furthermore, the regression coefficient for pain is statistically significantly different from zero (p=<.000). So far we can conclude that there is an effect that may be mediated.

3. Is b significant? Yes, the regression coefficient for function is statistically significantly different from zero (p=<.000)

4. Finally, the Sobel and Goodman tests are significant (p=.000), indicating that the mediation pathway is statistically significant.

Sobel’s first-order approximation

2 2 2 2a b

a bzb s a s

More accurate test of condition 4

Approximate using standard errors

Wait a minute, I thought that condition #4 used c and c’, not a and b…it’s okay: Iacobucci (2008)

Sobel’s first-order approximation

2 2 2 2 2 2 2 2

.423 1.065 .4505 .4505 1.40156.3214.0024 .101(1.065 .046 ) (.423 .751 )a b

a bzb s a s

More accurate test of condition 4

Coefficient a= .423 with standard error .046

Coefficient b=1.065 with standard error .751

P-value =.16105

How to get P-values in SAS?

data sobel2;set sobel1;testest = (a*b)/sqrt(((b*b)*(sa*sa))+((a*a)*(sb*sb)));abssobel = abs(testest);p_val = 2*(1-CDF('NORMAL',abssobel));

run;

Aroian’s second-order exact solution

2 2 2 2 2 2a b a b

a bzb s a s s s

More accurate test of condition 4

Approximate using standard errors

Aroian’s second-order exact solution

2 2 2 2 2 2 2 2 2 2

.423 1.065 1.3935(1.065 .046 ) (.423 .751 ) (.046 .751 )a b

a bzb s a s

More accurate test of condition 4

Coefficient a= .423 with standard error .046

Coefficient b=1.065 with standard error .751

P-value =.16346

Goodman’s (1960) unbiased solution

2 2 2 2 2 2a b a b

a bzb s a s s s

More accurate test of condition 4

Approximate using standard errors

Goodman’s (1960) unbiased solution

2 2 2 2 2 2 2 2 2 2

.423 1.065 1.4097(1.065 .046 ) (.423 .751 ) (.046 .751 )a b

a bzb s a s

More accurate test of condition 4

Coefficient a= .423 with standard error .046

Coefficient b=1.065 with standard error .751

P-value =.1586

Partial Mediation

• X is the occurrence of an environmental stressor, such as a major flood, and which has a direct effect of increasing

• Y, the stress experienced by victims of the flood.

• M is coping behavior on part of the victim, which is initiated by X and which reduces Y.

Partial Mediation

• X may really have a direct effect upon Y in addition to its indirect effect on Y through M.

• X may have no direct effect on Y, but may have indirect effects on Y through M1 and M2. If, however, M2 is not included in the model, then the indirect effect of X on Y through M2 will be mistaken as being a direct effect of X on Y.

• There may be two subsets of subjects. In the one subset there may be only a direct effect of X on Y, and in the second subset there may be only an indirect effect of X on Y through M.

Partial Mediation

Causal Inferences from Mediation Analysis

• non-experimental data• Causal model fits well with the data, • But a everything is based on correlations….• There examples in which the data fits two

different mediation models

X Y

ZZ Y

X

More Advanced Solutions

• Mediation-Moderation• Moderation-Mediation• Direct Acyclic Graphs • Structural Equations Models

References• Quittner, AL. Re-examining research on stress and social support: the

importance of contextual factors. In: La Greca AM, Siegel LJ, Wallander JL, Walker CE, eds. Stress and Coping in Child Health.New York: Guilford Press; 1992:85– 115.

• Baron RM, Kenny DA. The moderator-mediator variable distinction in social psychological research: conceptual, strategic, and statistical considerations. J Pers Soc Psychol. 1986;51:1173– 1182.

• Sobel, M. E. (1982). Asymptotic confidence intervals for indirect effects in structural equation models. In S. Leinhardt (Ed.), Sociological Methodology 1982 (pp. 290-312). Washington DC: American Sociological Association.

• Dawn Iacobucci (2008), Mediation Analysis, Issue 156, Quantitative Applications in the Social Sciences