I am performing mediation analysis using structural equation modelling (I'm using the lavaan package in 'R'). I am using the bootstrapping approach (rather than the causal steps approach) and just wanted to clarify two things;

1) My understanding is that using this approach, the the total effect and direct effect does not need to be significant in order for an indirect effect to be significant. So if the bootstrapped confidence intervals do not include zero, then you can state that a significant indirect effect has been found.

However, does the relationship between X->M (a) and M->Y (b) need to be significant?

2) Also, if the confidence intervals are negative (e.g. -.43, -.09), the direct effect is negative (and sig), the beta for (b) is negative (but non-sig) but the beta for (a) is positive (but non-sig), how do you interpret this? The positive relationship for (a) i.e. X->M is throwing me a bit when it comes to writing this up and trying to explain the relationships between the variables!

Thanks in advance!

Emma.