Overview

Belief network analysis following Lydic, Torres-Grillo, Levine, Cosme et al. (2025). Pipeline: GLASSO partial correlation network → walktrap community detection → eigenvector centrality → combine with Hornik & Woolf PTG to identify priority targets.

Node selection note (2026-05-20): Subscale means are used only for batteries with internally consistent items (Cronbach α ≥ 0.65). Three batteries were revised: research_4 split into literacy/engagement (items 1–4, α = 0.750) and benefit beliefs (items 5, 7, 8, α = 0.677) — item 6 dropped (reverse-coded item that does not behave as expected empirically); govtfund_4 restricted to non-partisan stakeholder items (items 1–5, 11–13, α = 0.835) — partisan perception items (6–10) dropped; gotvfund_6 restricted to items 2–4, 7 (α = 0.694) — private-company comparison items and profit-motive item dropped. Node selection finalized at N = 300.

PTG note: Percentage-to-gain follows Hornik & Woolf (1999). For single Likert / binary items “strong” endorsement is the scale endpoint (“strongly (dis)agree”), matching the reference method. The four continuous composites have no natural endpoint, so for those (only) we substitute the top/bottom quartile. Thresholds based on full N = 300 sample. See Section 7.

Correspondence to the reference method (Lydic et al., 2025; OSF a6xf5):

Step Reference paper This script
Network model Gaussian Graphical Model, GLASSO-regularized (qgraph) qgraph::EBICglasso, γ = 0.5
Correlation input ordinal-appropriate (belief-network standard) qgraph::cor_auto (polychoric / polyserial / Pearson)
Community detection walktrap (igraph) cluster_walktrap on absolute weights
Centrality eigenvector; validated vs. belief–intention r (Fisher-z, abs) same
Promising beliefs Hornik & Woolf percentage-to-gain (scale endpoint) same (§7)

This revision (2026-07-15) fixed bugs in the prior version: (1) network estimated from ordinal-appropriate correlations (cor_auto) instead of Pearson; (2) all downstream objects keyed by node id, removing a fragile display-label round-trip that could mis-map communities/centrality; (3) percentage-to-gain now uses the H&W scale-endpoint rule for items (quartiles only for the four continuous composites) rather than a blanket 75th-percentile split; (4) added the Fisher-z transform to the centrality-validation step; (5) removed dead code and the stale “N = 10 pilot” note.

1. Data

1.1 Load and clean

## N = 299

1.2 Scale levels and numeric recoding

1.3 Intent outcomes

2. Node construction

Nodes are defined here.

Two types: - Subscale means — item batteries aggregated to a single score per construct (α ≥ 0.65) - Individual items — standalone items or small batteries where items are conceptually distinct

govtfund_5 is split into positive (items 1–5: benefits of govt funding) and negative (items 6–10: costs/risks of govt funding) subscales because they have opposite valences. research_4 is split into science literacy/engagement (items 1–4) and science benefit beliefs (items 5, 7, 8); item 6 (“Science makes our way of life change too fast”) is excluded because reversing it reduces rather than increases internal consistency, suggesting it measures a distinct construct. govtfund_4 uses items 1–5 and 11–13 (workers, students, scientists, general public, community members, health researchers, pharma, tech) — partisan/political perception items 6–10 are excluded (α = 0.209 for those items alone). gotvfund_6 uses items 2–4, 7 (oversight, everyday tools, daily benefits, objectivity of government-funded research); private-company comparison items and profit-motive item excluded.

## Total nodes: 58

2.1 Node registry

Human-readable labels and block membership for each node.

## Registry: 58 nodes

2.2 Node inclusion decisions

Documents all inclusion decisions relative to the full survey instrument. Cronbach’s α reported for subscale means; product composites do not have a traditional α.

Subscale means and composites

Individual items

All 54 individual items retained in the network:

Dropped batteries and items

3. Correlations: nodes × intent outcomes

Spearman r used throughout (ordinal data on different scales).

4. Belief network

4.1 Correlation matrix

The network is estimated from an association matrix among the nodes. Because most nodes are ordinal Likert items (and a few are binary), we do NOT use raw Pearson correlations — those assume continuous, normally distributed variables and distort associations among ordinal / binary items. Instead we use qgraph::cor_auto(), which automatically applies polychoric correlations to ordinal pairs, polyserial to ordinal–continuous pairs, and Pearson to continuous pairs (the product composites), and returns a positive-definite matrix suitable for GLASSO. This matches the belief-network standard (Turner-Zwinkels et al., 2022) that Lydic et al. (2025) follow.

4.2 Network estimator

EBIC-GLASSO Gaussian Graphical Model (partial-correlation network), following Lydic et al. (2025): graphical-LASSO regularization (Friedman et al., 2008) with EBIC model selection (qgraph::EBICglasso, tuning gamma = 0.5, the standard default). Regularization shrinks small partial correlations to exactly zero, yielding a sparse, interpretable network. GLASSO is stable at roughly N/p ≥ 5–10 observations per node. With 58 nodes and N = 299, N/p = 5.2 — at the lower end of the acceptable range, so edges should be read as exploratory (consistent with the “post-hoc” framing in the reference paper).

## GLASSO edges retained: 391 (of 1653 possible)

5. Community detection

Walktrap community detection on the absolute edge weights (Pons & Latapy, 2005), as in Lydic et al. (2025). Walktrap finds densely connected clusters via short random walks; absolute weights are used because community structure concerns connection strength, not sign.

## Communities detected: 10
## Modularity: 0.498

5.1 Community membership

5.2 Network plot with communities

6. Centrality

Eigenvector centrality: reflects both the number of connections and how influential those connections are. Predicts actual causal influence of nodes reasonably well (Dablander & Hinne, 2019).

6.1 Centrality plot

6.2 Centrality × correlation with composite

Replicates Figure 1C from Lydic et al. (2025): tests whether more central nodes are also more strongly correlated with the behavioral outcome.

## r(centrality, |Fisher z of Spearman r with composite|) = 0.22, p = 0.100

7. Percentage to gain (per node × per intent outcome)

Hornik & Woolf (1999) method, as used by Lydic et al. (2025). For each belief × intent item:

  • Outcome (“intender”) = top box of the 7-point intent scale (“Definitely will”).
  • “Strong” belief = the extreme scale point in the pro-intention direction. For each Likert / binary item we take the endpoint (the max value if the belief correlates positively with intent, the min value if it correlates negatively — this reproduces the H&W “strongly (dis)agree” reorientation). The four continuous composites have no natural scale endpoint, so for those (only) we substitute the top/bottom quartile. The rule actually used is reported per row in the rule column.
  • Percentage to gain = P(intender | strong belief) − P(intender overall), in points — exactly the Table 2 definition in the reference paper (a − b).

N = 299. A node × outcome cell returns NA when there is no “strong” group or no “other” group (no contrast can be formed).

8. Centrality × PTG: combined analysis

One plot per intent outcome. Upper-right quadrant = above-average on both centrality and PTG → highest-priority targets. Follows Figure 1C approach from Lydic et al. (2025).

8.1 Contact reps: oppose cuts

9 nodes above average on both metrics:

8.2 Talk to others about cuts

13 nodes above average on both metrics:

8.3 Share info online

7 nodes above average on both metrics:

8.4 Contact reps: support funding

8 nodes above average on both metrics:

9. Summary table

Full metrics for all nodes × all outcomes.

10. Export

## Saved: ~/Documents/GitHub/UniversityNews/Output/05_belief_network.csv
## Rows: 58 | Columns: 14