# Path analysis and multiple mediators

I have a study with two potential mediators: M1 and M2. I obtain a main effect of my independent variable X on the dependent variable Y. Similarly, I obtain an effect of X on M1, but I do not have an effect of X on M2. Now, I have a mediation effect X - M1 - Y. However, I hypothesised that M1 could impact M2 and that this could, in turn, impact Y i.e. a model where X - M1 - M2 - Y. I did a SEM analysis where I compared the simple mediation model (X - M1 - Y), which was a good fit, with the more complicated model (X - M1 - M2 - Y), which was also a good fit. The models were not statistically different from each other and both were a good fit to the data. I am having trouble interpreting this. Can I conclude that the more complicated model is a good fit and a confirmation of my hypothesis even though a) both models are a good fit and b) I did not obtain an effect of X on M2? Any suggestions would be appreciated.

I have used the lavaan package in R for all the path analyses.

• I'm not sure X-->M1-->Y is a good comparison model for your sequential mediation model. But that matter aside, generally speaking, when comparing two models, you would retain the more parsimonious one if there is no difference in terms of fit between the two. Feb 8, 2016 at 22:52
• What do you mean by "were not statistically different"? How did you test this? It would be clearer if you could post code and output, so that we can understand exactly what you did. Feb 9, 2016 at 18:04
• Thanks for the response. What was meant was that there was no effect of independent variable on M2. My question, stated simply, would be: is it even possible to conclude that x -> M1 -> M2 -> Y is a good model if there was no effect of x on M2? Feb 10, 2016 at 14:51
• The logic of your approach for testing mediation seems to conform to the Baron & Kenny, or "causal steps" approach, which is undesirable for a few reasons (see my response here, for a more detailed explanation: stats.stackexchange.com/questions/185626/…). In a nutshell, requiring the a, b1, and b2 paths to all be significant is an underpowered approach to testing mediation; testing the a*b1*b2 coefficient itself (the estimated mediated effect) is a much more direct and efficient approach. Feb 11, 2016 at 17:45