[R-meta] SEM of correlational meta-analytic data?

Dear Gladys,

you write "most of the correlational studies I included in the 
meta-analysis (from which I extracted Pearson correlations) also 
performed a SEM showing that Human-nature connectedness mediates the 
effect."
Please correct me if I'm wrong but I'm getting the impression that 
you're assuming that building mediation models within the SEM framework 
automatically enables one making causal claims.
As Wolfgang has already said: causality is tricky.

In short, there are three main assumptions in social sciences:

1. Covariance. Checked - you mention that the relevant variables are 
correlated.

2. Excluding alternative explanations. Although it is possible to 
increase the plausibility that this assumption is met even when using 
correlational data (e.g., adjusting for confounding variables, 
propensity score matching) but it would require meta-analyzing 
regression weights, which is rather tricky in the meta-analytic context, 
considering that different researchers adjust for different variables. 
Thus, it is difficult to argue that this assumption is met when 
conducting MASEM using data from observational studies.

3. Time precedence: The Cause precedes the effect. In case of mediation 
models it usually requires using a longitudinal design with at least 
three time points and assessing each variable at each measurement 
occassion. However, there are some alternatives (e.g., half-longitudinal 
designs, using state variables rather than trait variables). 
Unfortunately, many (most?) mediation models violate this assumption.

This is well-documented See e.g.,
Fiedler , K., Harris, C., & Schott, M. (2018). Unwarranted inferences 
from statistical mediation tests. An analysis of articles published in 
2015. Journal of Experimental Social Psychology , 75 , 95 102. http:// 
doi.org/10.1016/j.jesp.2017.11.008
Lemmer , G., & Gollwitzer, M. (2017). The true ? indirect effect won?t 
(always) stand up : When and why reverse mediation testing fails . 
Journal of Experimental Social Psychology , 69 , 144 149. http:// 
doi.org/10.1016/j.jesp.2016.05.002
Pek , J., & Hoyle , R. H. (2016). On the ( validity of tests of simple 
mediation : Threats and solutions . Social and Personality Psychology 
Compass , 10 (3), 150 163. http://doi.org/10.1111/spc3.12237
Pirlott , A. G., & MacKinnon, D. P. (2016). Design approaches to 
experimental mediation . Journal of Experimental Social Psychology , 66 
, 29 38. http://doi.org/10.1016/j.jesp.2015.09.012

One could potentially use strict exclusion criteria in the meta-analysis 
to increase the plausibility of causality claims (e.g., only include 
longitudinal primary studies), but it is probably not feasible as there 
are probably not many studies that meet such strict criteria.

Summing up, due to the violation of assumptions #2 and #3 it is seldom 
possible to make causality claims when conducting a meta-analysis.

best wishes,
Lukasz