When I teach multivariate correlational designs, students always end up asking, "What's the difference between multiple regression and mediation?"
Here's the better question. What they should be asking is, "What is the difference between using multiple regression analyses to rule out third variables, and using multiple regression analyses to test for mediation?" This LA times editorial provides an excellent example to illustrate the difference.
First things first: Lots of people believe that happy people live longer, and happiness researchers have previously found that happiness does predict longevity. However, a large-scale study published in the Lancet recently concluded that, in fact, happy people do not live longer. Their study was conducted on nearly a million women in the UK, so it's nicknamed "the million women study." The press covered the study by saying, "Good news for the grumpy." You can see one story about the big Lancet study here.
However, this LA Times editorial, written by three happiness psychologists, explained a problem with the Lancet study. The Lancet study used regression to look at the relationship between happiness at age 59 and their life span, while holding constant a variety of third variables, such as income, being in a romantic relationship, being religious, smoking, and exercising. From one perspective, this makes sense--they wanted to look for some relatively "pure" relationship between happiness and longevity controlling for these factors, and they did not find one. That is, happiness did not predict longevity when these variables were controlled for.
a) Students: can you sketch a regression table of the pattern described above? Label the criterion variable, the predictor variables, and think about what betas might have been associated with each predictor variable.
Now for the problem: The three happiness psychologists writing the editorial argued that by controlling for such variables as relationship status, smoking, and exercise, the Lancet study obscured the important features of the relationship--the mediators. Here's how they put it.
We ... have concerns with the authors' choice to statistically control so many other variables. In our work, we hypothesize that the key ways positive feelings influence health are through changes in behaviors. For example, research has shown that positive individuals sleep better, smoke less and exercise more, all of which are known to predict longevity. Thus, when the authors control for all these variables, they are taking away a major path through which happiness is likely to influence longevity. This is like trying to determine whether a hurricane causes damage after controlling for its wind speed. Again, the question is changed, from “Will happy people live longer” to “Will happy people live longer if we take away their healthier behavior?”
b) The authors are stating a mediator argument in the above paragraph. Draw the mediator pattern they are describing, using Figures 9.11 or 9.13 as models. (Hint: Draw only one proposed mediator at a time.)
When the authors of the editorial write, "we hypothesize that the key ways positive feelings influence health are through changes in behaviors" they are talking about a mediator. The "through" part is a way of stating the mediator.
The authors of the editorial, therefore, end up describing how multiple regression can be used for at least two purposes. Regression is simply a statistical tool, and it can be used for both ruling out third variable problems and for testing mediation. The Lancet article used regression to control for what it saw as "pesky" third variables such as smoking and relationship status to see if happiness, on its own, predicted longevity. In contrast, the three happiness researchers have used regression to see if mediators, such as smoking and relationship status, explain why happiness predicts longevity.
You might recall in Chapter 9's discussion of mediation, that mediation tests are conducted in several steps. Step 4, in fact, uses multiple regression (the text states, for example, "if physical activity is the mediator of the relationship [between recess and behavior problems,] then the relationship between recess and behavior problems should drop when physical activity is controlled for").
So there you go. A great example of how a single data set can be viewed in two very different, but ultimately two very legitimate ways, depending on one's research goals and hypotheses.
By the way, the three happiness psychologists also criticized the construct validity of the Lancet study's happiness measure, saying this:
the happiness measure used in the Lancet study is weak. In well-crafted research, social scientists think carefully about question and answer design, the ordering of items and how many questions are too many before the participant gives up and stops answering or stops answering honestly...The Million Women Study asked just one happiness question: How often do you feel happy (from “rarely/never” to “most of the time”). A better approach would have been to ask the question in more ways, with a broader range of positive emotions for participants to choose from.
