Hi Bin,

the only two ways to adress is are first, using longitudinal data or second, identifying instrumental variable and empoying a tsls estimator or SEM.

Hard to come up with a solution post hoc. So if you cannot manage one of them, the only chance is to offer the reviewer to include a critical discussion in the limitation section.

Good luck

Holger

Holger Steinmetz How about using sensitivity analysis to demonstrate the robustness of a relationship? If the sensitivity analysis results support the robustness of the causal inference from X to M, can it to some extent exclude reverse causality?

There really is no conclusive statistical way to determine causal direction, unless you have a controlled experiment. Probably, your only option is to dig through literature and theories to affirm the direction by plausbility.

Consider a correlation between eating habits and intelligence. Can you find a plausible biological mechanism by which eating one carrot a day has such a dramatic influence on brain structure so that people get smarter? Or is it more plausible that smart people are eating more carrots, because they know it is better for their health? (Many studies have shown that smarter people tend to have a more healthy diet)

Martin Schmettow Thanks. It is not easy to consider the causal direction between eating habits and intelligence. However, intuitively, I believe more in what we eat that makes us smarter. For example, young mothers often rack their brains to design more nutritious recipes to make their babies smarter. On the contrary, smart individuals do not necessarily have healthy eating habits, such as Steve Jobs.

There simply is no easy way out! Giving cross-sectional data a plausible causal direction is only possible in so far as there is other evidence or a good theory. Not your intuition and certainly not anecdotes about young mothers qualify.

If you find a work that describes a process how, say, a deficiency in beta-carotine leads to damage of brain cells, that would be good. If you find a study that finds an association with social status, but not intelligence, that would be even better.

If there's pro and con, you're in for a full discussion, not just limitation section, if you want to write a really good paper. Just to make this clear again: There is no way to establish causal direction by statistical methods!

Martin Schmettow yes, statistical methods cannot establish causal direction. Thanks again.