Cluster Interpretation: Dynamic Profile

Background & Context

• On this page, we present the Dynamic Profile for cluster interpretation as an alternative to Most Relevant Explanations for Cluster Interpretation.
• To provide further context for Most Relevant Explanations for Cluster Interpretation, we compare several other approaches that can help interpret individual Clusters:
  • Setting Evidence for Cluster Interpretation: Posterior Distributions, Relationship with Target Node, Mosaic Analysis, Posterior Mean Analysis, Segment Profile Analysis, Histograms, Tornado Diagrams
  • Optimization for Cluster Interpretation: Dynamic Profile, Target Optimization Tree
• More specifically, we compare all these approaches with regard to characterizing the state $\mathit{Cluster\ 3}$ of the Cluster Node $\mathit{Factor}_0$ in the reference network.
• All analyses and instructions on this page refer to this reference network, which you can download here:

Dynamic Profile for Cluster Interpretation

• We can use BayesiaLab’s optimization tools to work with more complex sets of evidence. One of these optimization tools is the Dynamic Profile.
• The Dynamic Profile uses a greedy search algorithm to simulate sets of evidence that maximize the probability of $\mathit{Cluster\ 3}$.
• It may seem counterintuitive to think of optimizing evidence to achieve membership in $\mathit{Cluster\ 3}$. After all, we cannot modify body measurements.
• However, we can think of those characteristics that assign a subject to $\mathit{Cluster\ 3}$ most quickly as prototypical traits of $\mathit{Cluster\ 3}$.
• To start Dynamic Profile, select Main Menu > Analysis > Target Optimization > Dynamic Profile.
• In the Dynamic Profile Settings, we need to specify that we want to maximize the probability of $\mathit{Cluster\ 3}$ by searching across Hard Evidence.

• Clicking OK starts the search and quickly produces a solutions table, which opens in a new window:

• The starting point is the row in the table marked A priori, which shows that $P(\mathit{Factor}_0=\mathit{C3})=12.955\%$, i.e., the marginal probability of $\mathit{C3}$.
• If we evaluate the hypothesis $3 - \mathit{Bicep\ Girth} \gt 36$, the posterior probability increases, i.e., $P(\mathit{Factor}_0=\mathit{C3} \mid 3 - \mathit{Bicep\ Girth} \gt 36)=41.096\%$.
• In this case, the Bayes Factor is 3.172, meaning that with this hypothesis, $\mathit{C3}$ membership is 3.172 times more probable than without it.
• Setting $7 - \mathit{Hip\ Girth} \le 101.8$, the probability of $\mathit{C3}$ membership increases further to 72.938%.
• With $4 - \mathit{Navel\ Girth} \le 85.2$ and $6 - \mathit{Forearm\ Girth} \gt 29.4$, we reach a $\mathit{C3}$ probability of 100%.
• As a result, we can interpret this set of evidence as a prototypical profile for a subject in $\mathit{C3}$:
  • $3 - \mathit{Bicep\ Girth} \gt 36$
  • $7 - \mathit{Hip\ Girth} \le 101.8$
  • $4 - \mathit{Navel\ Girth} \le 85.2$
  • $6 - \mathit{Forearm\ Girth} \gt 29.4$