These three terms are often confusing, because they sound similar. Here are the fundamental differences:

• Moderator variables are those variables which act like a catalyst in a regression relationship. They interact with the independent variables either to shrink or enhance the relationship between the independent and dependent variables. In other words, the relationship between dependent and independent variables is a function of moderator variable (e.g., gender, age, income, education etc.).
• Mediators are more like translators which carry forward the influence of independent variable on the dependent variable. In simple words, mediator variables work like a “middleman” or “broker” between the independent and dependent variables. For example, the influence of “brand knowledge” on “brand loyalty” may be mediated by “attitude towards the brand.”
• Control variables are those independent variables which are not part of the research study, but their influence cannot be overlooked. For example, the “price of a product” impacts on “demand of that product”, but the influence of the “price of substitute products” cannot be ignored.

Hi Ramendra,

is this a question about AMOS or modeling itself?

Best, René

These three terms are often confusing, because they sound similar. Here are the fundamental differences:

• Moderator variables are those variables which act like a catalyst in a regression relationship. They interact with the independent variables either to shrink or enhance the relationship between the independent and dependent variables. In other words, the relationship between dependent and independent variables is a function of moderator variable (e.g., gender, age, income, education etc.).
• Mediators are more like translators which carry forward the influence of independent variable on the dependent variable. In simple words, mediator variables work like a “middleman” or “broker” between the independent and dependent variables. For example, the influence of “brand knowledge” on “brand loyalty” may be mediated by “attitude towards the brand.”
• Control variables are those independent variables which are not part of the research study, but their influence cannot be overlooked. For example, the “price of a product” impacts on “demand of that product”, but the influence of the “price of substitute products” cannot be ignored.

The best known article on mediator and moderator effects is by Baron & Kenny -- see attached.

Once you have read David Morgan's recommended classic, have a read of:

Preacher, K.J., Rucker, D.D., and A.F. Hayes (2007) Addressing Moderated Mediation Hypotheses: Theory, Methods, and Prescriptions MULTIVARIATE BEHAVIORAL RESEARCH, 42(1), 185–227 

Preacher et al (2007) started the discussion of Moderated Mediation which has now grown substantially.  I wish you all the best in your research journey.

Can't seem to get my attachment to work. The citation is to Baron & Kenny 1986, The Moderator-Mediator Variable Distinction in Social Psychological Research. Journal of Pe~nality and Social Psychology, 51, 1173-1182.

Dear Morgan et all, 

I will add this: 1) a moderator has no significant relationship with the "dependent variable Y"  but it has a signiificative relationship with X, and of course X affects Y; 2) a mediator is intented  to measure indirect effects of X in the dependent variable Y. The mediator receives an arrow (graphic) from X , and the mediator sends an arrow to Y. There is another arrow from X to Y (direct effect).

Have a nice time

Helena

Both Mediator and Moderator variables help to describe the relationships between Independent and Dependent variables.

Suppose the effects of an independent variable X and dependent variable Y is exist and significant.

Suppose we have a moderator variable namely Z to consider. If the effects of X on Y is only significant for certain level of Z only (say high level) and not significant for certain other level of Z (say low level), then we can say that Z is a moderator in the relationship between X and Y. The function of moderator variable is to moderate the relationship between the independent and dependent variables.

Now suppose we have a mediator namely M. If the direct effect of X on Y is  not significant, instead, the indirect effect of X on Y through M is significant, the we can say that M mediates the relationship between X and Y.  In this case, we believe that the variable X has a significant effect on M and that M has significant effect on Y. If the statement is true, then M is a mediator. The relationship between X and Y is mediated by M. The role of mediator is to mediate the relationship between Independent Variable and Dependent Variable.

There are two books which might help you for detail studies of moderation and mediation: 

1. Introduction to Mediation, Moderation, and Conditional Process Analysis (Andrew F. Hayes)

2. Statistical Mediation and Moderation (Paul-E-Jose)

One might look into this website (http://bookzz.org/) for free download.... Thanks in advance....

There is often confusion among control, moderator and mediator variables. As per my understanding of concepts, clarification is as like under: -

1. Control variables are those independent variables which are not part of the research study however their influence cannot be ignored. Therefore, we need to control them so that actual relations should be developed. In Hierarchical Regression analysis, it can be done very easily and effectively.

2. Moderator variables: A moderator variable changes the strength of a relationship between two variables. Moderators indicate when or under what conditions a particular effect can be expected. A moderator may increase or the strength of a relationship, or change the direction of a relationship. For example, the relationship between stress and depression may differ in strength at different levels of social support. It means that the stress may be more strongly associated with depression under conditions of low social support compared to conditions of high social support.

3. Mediators are like middlemen among two parties of interest. In other words, mediating relationships occur when a third variable plays an important role in governing the relationship between the other two variables.

Moderation answer the question WHY is A related to C. The answer is because A related to B and B related to C.

 Mediation answer the question WHEN is the relation of A to C exist. The answer is when B is high or B is low.  

 Control variable answer the question what are the variables that affect on the relation between A to C. 

One way to distinguish a mediator and moderator:

The association between X and Y can EXPLAINED by a mediator (usually a mediator is a continuous variable);

The association between X and Y differs by a moderator (usually a moderator is a categorical variable, e.g., gender).

Hope this helps,

--Jing

Thanks a lot to all.

Regards

Ramendra

Hi Ramendra,

Similar questions had been asked before, see the following RG link for the differences between mediator and moderator:

https://www.researchgate.net/post/What_is_the_different_between_mediating_and_moderating_constructs

See following for the differences between control variable & moderator:

https://www.researchgate.net/post/Is_there_any_different_between_control_variable_and_moderating_variable2

Wishing you all the best.

Regards,

Fung

I need to clarify the points above, which may be misleading: 

1) Mediators do not always need to be continuous variables. 

2) Moderators are not restricted to categorical variables. Moderation should be interpreted as: What is the relationship between A and B conditional upon different values of M? ie. age can be a moderator for the relationship between muscle mass and muscle strength. Older individuals have a weaker relationship between muscle mass and strength than younger individuals. 

You also need to PROBE the interaction in moderation analysis: 

1) Using the floodlight approach or Johnson-Neyman technique - examining all the values of the moderator at which the relationship between A and B hold true (or significant). 

2) Using pick a point approach - better for binary or categorical moderators - examining the relationship between A and B when M = 1; M= 2; M=3 etc. 

Baron & Kenny (1986) highlighted the importance of not using the terms moderator and mediator interchangeably.

Baron & Kenny (1986) wrote:

“The moderator function of third variables, which partitions a focal independent variable into subgroups that establish its domains of maximal effectiveness in regard to a given dependent variable. The mediator function of a third variable, which represents the generative mechanism through which the focal independent variable is able to influence the dependent variable of interest.”

Moderating Variable- moderator is a variable which will cancel the relationship with two variables. Moderator is a variable which will refuse the degree of relationship between two variables. Moderator can be totally canceled the relationship between two variables.

Moderating - changing

Eg: You feel sleep in the class after having a heavy lunch. So there is a relationship. But assume you don’t feel sleep in the class after having a huge lunch. The answer is the moderator, may be the interesting nature of the lecturer or exam fear.

Intervening variable alternatively called mediating variable

Intervening variable – Assume training and job performance, the relationship is positive. Greater the job training better the job performance. How does the training increase the job performance? If you have an answer, then the answer is the intervening variable. Learning is the acquisition of new knowledge and attitude. So training will result in learning which will result in job performance.

For more details please refer the articles given below.

References

Frazier, P.A., Tix, A.P. and Barron, K.E., 2004. Testing moderator and mediator effects in counseling psychology research. Journal of counseling psychology, 51(1), p.115.

Baron, R.M. and Kenny, D.A., 1986. The moderator–mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of personality and social psychology, 51(6), p.1173.

Moderator variables is a qualitative (e.g., sex, race, class) or quantitative (e.g., level of reward) variable that affects the direction and/or strength of the relation between an independent or predictor variable and a dependent or criterion variable. Specifically, within a cor-relational analysis framework, a moderator is a third variable that affects the zero-order correlation between two other variables.

Whereas, mediator variables in general, a given variable may be said to function as a mediator to the extent that it accounts for the relation between the predictor and the criterion.

Thanks every one