I am using Process Macro model and the indirect effect (path a*b) is significant. However, the relationship between the predictor (X) and mediator (M) variables is non-significant. How would that be interpreted? Could it still be claimed that M is mediating the relationship between X and Y when there is no relationship between X and M?
Tests of statistical significance have the obvious issues (e.g., lack of power due to a small sample), and the test(s) for ab are different from the test for the simple a coefficient (the product ab is often not normally distributed and therefore typically tested using asymmetric bootstrap confidence intervals, whereas the a path is usually tested with a regular t test). Therefore, the tests can lead to different results/conclusions in practice. In particular, if the b path is strong, this may lead to a "significant" ab product even when the a path alone is not statistically significant.
I personally would be cautious when the a path is of questionable (small) magnitude. To me it does not make sense to say there is mediation when X does not influence M.