Target Mean Analysis
 This analysis creates a plot featuring response curves.  Another, similar analysis is available BayesiaLab, which produces a tabular report with unit effects and related statistics. Please see Total Effects on Target.
Context
 This analysis visualizes the relationships of selected Driver Nodes in a network with the Target Node in the form of curves.
 Performing this analysis is often used as a reference point in a key driver analysis see Chapter 8.
Example
 The following example is taken from Chapter 8: Chapter 8: Probabilistic Structural Equation Models for Key Driver Analysis
 The network below features a the Target Node at the center of the network for which we want to analyze its response to changes of the Driver Nodes connected to it.
 The the node $Pleasure\_(4)$ is the Target Node.
 The nodes $Pleasure$, $Corresponds$, $Easy\, to\, wear$, and $Intensity$ are the Driver Nodes under investigation.
 In traditional statistics, the Target Node would be the dependent variable, and the Driver Nodes would be considered independent variables.
 While the term "driver" suggests a causal relationship between a Driver Node and the Target Node, we are only examining associations, which may or may not be causal.  So, the direction of the arcs in this network does not imply a causal direction.  For a formal treatment of causality, please see Chapter 10 — Causal Effect Estimation.
Usage
 Make sure you have defined a Target Node.
 In Validation Mode
F5
, select the of interest, i.e., the Driver Nodes, and go toMenu > Analysis > Visual > Target > Target's Posterior > Curves > Total Effects
.  If you have not selected any node, BayesiaLab will use all connected and observable nodes for the analysis.
 A window comes up, which allows you to set several options for the chart to be displayed.
 Given that our Driver Nodes were not all recorded on the same scale, and for the ease of interpretation, we check the
Delta Mean
boxes for bothVariables
andTarget
.  Clicking the
Show Sensitivity Chart
button brings up the plot.
 In this chart, we see two simulations:
 The xvalues of each Driver Node are simulated across their variation domain using Minimum CrossEntropy (see Chapter 7, Numerical Evidence — MinXEnt).
 These xvalues are used as inputs for inferring — with the network — the yvalues of the Target Node.
 The xy values pairs of Driver Nodes and Target Node produce a set of response curves, i.e., the Total Effects Curves.
 They are shown simultaneously and can be distinguished by their randomlyassigned colors.
Calculating Means
 In our example, all Driver Nodes are discrete with integer values. As a result, calculating the mean value of the Driver Nodes' states is straightforward.
 In alternative cases, BayesiaLab will compute mean values as follows:
 If a node is categorical, but has numerical values associated with its categorical states, the mean is computed from the associated values.
 If a node is continuous, its mean value is computed from the states' intervals.
 If none of the above applies, BayesiaLab uses a set of default values enumerating the states beginning with 0 for the first state.
Please note that the plotted response curves do not have any underlying equations. There are no functions and parameters that were estimated. The curves are purely the result of inference performed with the given the network.
Interpretation
 This visual analysis show how changes in the mean values of the selected Driver Nodes in a network are associated with changes of the mean value of the Target Node.
 To provide some intuition for the mean value simulations of the xvalues and the inferred yvalues, the following panels compare the marginal distributions of all nodes with their posterior distributions after simulating a oneunit increase (using MinXEnt) for $Corresponds$.
Marginal Distributions  Posterior Distributions 

$Corresponds=5.672$  $Corresponds=6.762\,(+1)$ 
$Pleasure\_(4)=5.872$  $Pleasure\_(4)=6.648$ 
 Compare the marginal distributions of the Target Node and the Driver Nodes (on the left) with the posterior distributions of the same nodes on the right
 Here, the +1 increase in $Corresponds$ is associated with a 0.78 increase in the mean value of the Target Node $Pleasure\_(4)$.
Workflow Illustration
Context
 This report calculates the Total Effect of each selected node (or all nodes) in the network on the Target Node.
 Generating this report is often used as a reference point in a key driver analysis see Chapter 8.
Total Effect Definition
 The Total Effect of a node on a Target Node is the derivative of the Total Effects Curve, computed at the a priori mean of that node, i.e., Delta Mean=0.
where $X$ is the node of interest and $Y$ is the Target Node.
 The Total Effect represents the impact of a small change of the "mean" of a node on the "mean" of a Target Node.
 The Total Effect is the ratio of these two values.
Total Effect Curve

The Total Effect Curve is plotted using BayesiaLab's Target Mean Value Analysis function.

For illustration purposes, we borrow a plot produced by another BayesiaLab function, the Target Mean Analysis.
 Delta Mean=0 is marked with a black dashed vertical line; the derivative of $Intensity$ is highlighted with a cyancolored dashed tangent.