Aldo Herman Yes, it is possible. Your model implies that the direct paths A --> D, A --> E, B --> D, and B --> E are zero in the population. The effects of A and B on D and E are fully mediated through C. This hypothesis can be tested through path analysis. The corresponding path model is overidentified (has > 0 degrees of freedom) because not all possible direct paths are estimated--some are constrained/fixed to zero. The model can therefore be tested against the observed data using statistical tests of model fit (e.g., a chi-square goodness of fit test) in programs for structural equation modeling such as Mplus, AMOS, or lavaan (in R).

If the path model with the above direct paths fixed to zero fits the data well, the hypothesis of full mediation does not have to be rejected. If one of the paths in question is different from zero in the population, the model with these paths constrained to zero may show misfit, leading to rejection of the full-mediation hypothesis (provided you have enough statistical power/a large enough sample to detect this effect).

If you type "full mediation" into Google Scholar, you should find plenty of references.

Hi Aldo Herman, I would want to add that whether you decide to estimate the direct paths or not, in structural equation modelling, all paths would be estimated automatically e.g., if you do the analysis in Mplus. So you do not need to worry. Once your model is identified just go ahead and conduct your analysis (you are on the right path). All the best with SEM.

Dear Herman,

You may refer to Hair's Book (A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM) Second Edition). Hair et.al (2017) identify three types of mediation, ONE OF THEM IS THE INDIRECT EFFECT APPROCACH

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