I know that this is a moderation analysis, but what statistical test should be used to test the moderation effect of one variable on the correlation (not causal relationship) between two other variable.
It is the partial correlation of Y and Z given X that should be calculated and tested for significance. This can be done using the t or z test.
partial correlation is used to measure correlation between Y and Z with removing the effect of X, which is not what i want.
The effect of X upon the correlation is rYZ-rYZ.X (where the former is the simple and the latter the partial correlation controlling for X).
In a way, you are both right. If you know the partial correlation and the correlation, you know the effect of X on the correlation!
I think Copula theory is a suitable tool to check the relationship.
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