When using Target Analysis which approach should be used for what purpose? Total Effects on Target vs. Correlation with Target Node: The former computes standardized Total Effects, the latter yields the relative significance, right?
The Standard Target Mean Analysis (STMA: Analysis | Visual | Target Mean Analysis | Standard) returns the Total Effect function. The STMA uses the mean value evidence (based on the MinXEnt) to go through the variation domain of the variable X and for measuring the impact of X on the target’s mean.
Total Effect (TE) is the derivative of this Total Effect function (TEf), taken at the a-priori mean value of X. For a linear TEf, TE reflects the overall strength of the relation with the target node. If TEf is nonlinear, TE is just a local measure of the strength of the relation at the mean value of X.
The Direct Effect Target Mean Analysis (DETMA: Analysis | Visual | Target Mean Analysis | Direct Effect) returns the Direct Effect function. The DETMA uses the mean value evidence to go through the variation domain of X and for measuring its impact on the target’s mean while holding fixed the probability distributions of all the other variables, except:
- The Not-Observable variables belonging to the Class “Factor”
- The variables belonging to the Class “Non_Confounder” .
Similarly to TE, Direct Effect (DE) is the derivative of the Direct Effect function (DEf), taken at the a-priori mean values of the variables. The nonlinearity of the DEf has then the same consequences on the scope of the measure.
The Correlation with Target Node (Analysis menu – Report – Target Analysis) is based on Mutual Information. Mutual Information (MI) is defined as the difference between the Marginal Entropy H(T) of the target variable and its Conditional Entropy H(T|X). The form of the dependency between and X and T does not have any impact on MI, which is then always global.