TU-L0022 - Statistical Research Methods D, Lecture, 25.10.2022-29.3.2023

Mediation models are common in social science research because they allows us to study mechanisms through which one variable affects another one. Mediation model is typically presented with this kind of path diagram: So you have the X variable, the first cause, then you have the mediator variable through which the effect goes and then you have Y, the final dependent variable. For example we could study the effect of studying on your exam scores. So X is studying Y is the exam scores, and the more you study the better exam score you have. That effect is mediated by the amount of learning, so the more you study the more you learn, and the more you learn, the better your score.

The idea of a simple mediations model is that we have here two regression models. So we have model of M the mediator depends on X and then Y the final dependent variable depends on M and X. If this direct regression coefficient from X to Y is 0 then we say that it is a full mediation model. If this regression coefficient of Y on X is non zero, then we say its partial mediation. The idea of full mediation model is that any influence of X must go through M, and partial mediation means that there can be some other mechanisms as well.

Let's take an example, the studying and performing well in exam. If you study more but you don't really learn at all, then that studying hardly influences your exam scores. So that we could theorize that there is full mediation model. Studying only influences learning and learning influences exam scores. But if you don't learn when you study, then there is no positive effect. In fact we could argue that studying without learning has a negative effect, a small one, because if you study too much then you're tired when the exam starts and you're not gonna perform as well as if you had not studied at all and had slept well. If you study but don't learn then there is no effect. So that's the idea of mediation, we try to do these processes model how X influences Y.

The estimation of this kind of model requires that you estimate two regression models basically. So we have the first model Y is the function of X and M, and then you have M as a function of X. So how do we estimate these models. There are two main estimation strategies.

The first one is the so-called Baron & Kenny method, or causal steps method. The idea is that you run three regression analysis. The first regression analysis you regress Y on X. So you check whether there is an effect at all. If there is no effect of X on Y, then we conclude that there can't be mediation. So if X and Y are not correlated or there is no causal relationship, no regression relationship after the relevant controls, then we conclude there can't be mediation. Then we check if X is a potential cause of M, so we regress M on X and the controls, that are relevant. Then finally if there is a relationship then we can conclude that it's possible that there is mediation, because X influences M. Then we regress Y on X and M and that allows us to establish whether it's a full mediation or a partial mediation effect. So if  βy1 is non significant then we conclude that it's a full mediation, if  βy1 is significant and substantially large then we conclude that it is partial mediation. So there is a meaningful effect of X to Y even if we control for the effect through M. The mediation effect then is the product of these two paths so you have the path from X to M, and the path from M to Y, that's the mediation effect. So that's a simple strategy and that's the strategy that you should probably study first.

Then we have also another strategy which is simultaneous equations estimation. So we have this full model here, we have two dependent variables M and Y and we apply simultaneous equation techniques to estimated everything at once without having to estimate these separate regression analysis. This is slightly more appealing statistically and it's recommended in many books and articles now, but if you are just learning how to do mediation, then this Barron & Kenny matter, which is easier to apply, is probably good enough for you anyway.