Direct Effects

Direct Effects analysis measures the effect of a node on the Target node while all other nodes are held fixed. This contrasts with the Total Effect, in which the posterior probability distributions of the other associated nodes are allowed to change in response to the input. As a result, the direct effect of a node can be very different from its total effect.

Report

This analysis extends the Total Effects analysis with the Direct Effects analysis by automatically fixing the probability distributions of the nodes, except the Not-Observable nodes belonging to the class “Factor” and the nodes belonging to the class “Non Confounder”.

The report provides the following measures.

Direct Effect:

De_x = \frac{\delta_y}{\delta_x}

Standardized Direct Effect:

SDe_x = \frac{\delta_y}{\delta_x} \times \frac{\sigma_x}{\sigma_y}

Contribution:

C_x = \frac{\lvert SDe_x \rvert}{\sum_{x_i \in x_a} \lvert SDe_{x_i} \rvert}

Elasticity:

E_x = \frac{\delta_y/(max_y - min_y)}{\delta_x/(max_x-min_x)}

The contribution $C$ is computed only for the nodes specifically selected for this analysis.

Quadrants

Target Direct Effect Analysis

The contribution values can be shown directly as labels on the corresponding arcs. As above, the contribution is computed for the selected nodes only; selecting a single node would yield a contribution value of 100%.

Target Mean Analysis

The Target Mean Analysis is also extended with the Direct Effects, allowing the Direct Effect Function to be graphed. The Direct Effect is the derivative of the Direct Effect Function computed at the a priori mean value (delta = 0).