Please experts here, help me interpret the following:
X-->Y ~ insignificant
X-->M ~ significant
M-->Y ~ significant
X-->Y (controlled for M) ~ impact of IV (X) on DV(Y) has decreased but is still insignificant, whereas M still predicts Y significantly, with the same values
Sobel's test ~ significant at 0.018
Can we claim mediation here?
Significance testing depends on the sample size. You would be better off to interpret results based on the standardized coefficients. It is very likely that you have a mediation here.
Also, instead of hierarchical regression, if you are using SPSS, perhaps using PROCESS MACRO plug-in written by Hayes and colleagues could be a good start.
https://www.processmacro.org/index.html
Metin Bulus
Thank you very much. Can you please recommend sources that will be helpful in understanding how can standardized coefficients help us conclude there's mediation in this case
What I mean is not to look at the significance level alone because it is sample size dependent. In your case, with or without mediator the direct path seems to remain statistically not significant. In this case one could argue in favor of a complete mediation (rather than partial mediation). But if the standardized coefficient is substantially large, but significance testing produced null results due to insufficient sample size, it could be misleading.
Regarding how to decide whether there is mediation, I would suggest reading pages from 113 to 121 in Hayes (2018).
Hayes, A. F. (2018). Introduction to mediation, moderation, and conditional process analysis: A regression-based approach. Guilford publications.
the trick with mixed (multi-level) models is getting the standard errors for each step right. using Stata or MPlus to run actual path models with random effects would be ideal. check out, e.g.,
https://www.statalist.org/forums/forum/general-stata-discussion/general/1396763-multilevel-mediation-2-2-1-with-observed-data
or
https://brightspotcdn.byu.edu/3c/7b/03b4b3f6428d8c4c4fde9d9a22d6/multilevel-mediation.pdf
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