# 2D Extremity Temporal Decomposition

> **Part of the Overton Window Analysis.** See the [synthesis report](overton_window_synthesis.md) for the integrated narrative, or the [interactive article](overton_window.qmd) for the full story with charts.

**Goal:** Test whether the "flat single-dimension trend" masks diverging trajectories
when stylistic and material extremity scores are analyzed separately over time.

**Analysis period:** 2016-2026
**Data source (right-wing):** `extremity_scores_2d` (2,869 motions scored) joined with `right_wing_motions`
**Data source (all motions):** `extremity_scores_all` (29,570 motions scored) joined with `motions`
**Domains:** Migration = `asiel/vreemdelingen`; Non-migration = all other categories

> *Years with <50 scored motions are flagged for low confidence.

---

## 1. Key Findings

**Overall correlation r(stijl, materieel):** 0.472 (p=0.000000)
**Migration domain r(stijl, materieel):** N/A (p=N/A, n=0)
**Non-migration domain r(stijl, materieel):** 0.472 (p=0.000000, n=3030)

---

## 2. Pre/Post 2024 Comparison

| Dimension | Pre-2024 Mean | Post-2024 Mean | Δ |
|-----------|--------------|---------------|-----|
| Stylistic extremity | 1.725 | 1.797 | 0.072 |
| Material impact | 2.535 | 2.440 | -0.095 |
| Text score (original) | 2.063 | 2.190 | 0.127 |
| Gap (M-S) | 0.810 | 0.643 | -0.167 |

---

## 3. Yearly Data Table

| Year | N | Stylistic | Material | Text (orig) | Gap (M-S) | N Mig | Styl Mig | Mat Mig | N Non-Mig | Styl NM | Mat NM | r(stijl,mat) |
|------|---|-----------|----------|-------------|-----------|-------|----------|---------|-----------|----------|---------|---------------|
| 2016 * | 6 | 1.667 | 2.333 | 2.000 | 0.667 | 0 | N/A | N/A | 6 | 1.667 | 2.333 | N/A |
| 2017 * | 0 | N/A | N/A | N/A | N/A | 0 | N/A | N/A | 0 | N/A | N/A | N/A |
| 2018 * | 5 | 1.000 | 1.400 | 1.400 | 0.400 | 0 | N/A | N/A | 5 | 1.000 | 1.400 | N/A |
| 2019 | 195 | 2.046 | 2.913 | 2.138 | 0.867 | 0 | N/A | N/A | 195 | 2.046 | 2.913 | 0.491 |
| 2020 | 469 | 2.228 | 2.906 | 2.262 | 0.678 | 0 | N/A | N/A | 469 | 2.228 | 2.906 | 0.603 |
| 2021 | 425 | 1.755 | 2.976 | 2.240 | 1.221 | 0 | N/A | N/A | 425 | 1.755 | 2.976 | 0.503 |
| 2022 | 446 | 1.800 | 2.525 | 2.161 | 0.724 | 0 | N/A | N/A | 446 | 1.800 | 2.525 | 0.429 |
| 2023 | 365 | 1.575 | 2.690 | 2.238 | 1.115 | 0 | N/A | N/A | 365 | 1.575 | 2.690 | 0.346 |
| 2024 | 469 | 1.680 | 2.582 | 1.985 | 0.902 | 0 | N/A | N/A | 469 | 1.680 | 2.582 | 0.391 |
| 2025 | 455 | 1.695 | 2.332 | 2.253 | 0.637 | 0 | N/A | N/A | 455 | 1.695 | 2.332 | 0.592 |
| 2026 | 195 | 2.015 | 2.405 | 2.331 | 0.390 | 0 | N/A | N/A | 195 | 2.015 | 2.405 | 0.335 |

> * Years with <50 scored motions; confidence intervals are wider or N/A.

---

## 4. Divergence Test (Wilcoxon Signed-Rank)

**Test:** wilcoxon_signed_rank

**Statistic:** 0.0

**p-value:** 0.001953125

**N yearly pairs:** 10

**Conclusion:** Significant divergence: material and stylistic yearly means differ (W=0.0, p=0.0020)

The Wilcoxon signed-rank test compares yearly mean stylistic vs yearly mean material scores.
A significant result (p < 0.05) indicates the two dimensions systematically differ,
meaning the flat single-dimension trend masks a genuine divergence between stylistic
and material extremity.

---

## 5. Per-Year Correlation Analysis

| Year | r(stijl,mat) | p | N | Domain |
|------|--------------|---|---|--------|
| 2016 | N/A | N/A | 6 | All |
| 2017 | N/A | N/A | 0 | All |
| 2018 | N/A | N/A | 5 | All |
| 2019 | 0.491 | 0.000000 | 195 | All |
| | 0.491 | 0.000000 | 195 | Non-migration |
| 2020 | 0.603 | 0.000000 | 469 | All |
| | 0.603 | 0.000000 | 469 | Non-migration |
| 2021 | 0.503 | 0.000000 | 425 | All |
| | 0.503 | 0.000000 | 425 | Non-migration |
| 2022 | 0.429 | 0.000000 | 446 | All |
| | 0.429 | 0.000000 | 446 | Non-migration |
| 2023 | 0.346 | 0.000000 | 365 | All |
| | 0.346 | 0.000000 | 365 | Non-migration |
| 2024 | 0.391 | 0.000000 | 469 | All |
| | 0.391 | 0.000000 | 469 | Non-migration |
| 2025 | 0.592 | 0.000000 | 455 | All |
| | 0.592 | 0.000000 | 455 | Non-migration |
| 2026 | 0.335 | 0.000002 | 195 | All |
| | 0.335 | 0.000002 | 195 | Non-migration |

---

## 6. Correlation Change Pre vs Post 2024

**Pre-2024 mean r(stijl,mat):** 0.475

**Post-2024 mean r(stijl,mat):** 0.439

**Change test (Mann-Whitney):** U=10.000, p=0.571

**Interpretation:** No significant change in stijl-material correlation (U=10.0, p=0.5714)

A significant change in the per-year stijl-material correlation would suggest
that the relationship between the two dimensions itself shifted across the break period —
e.g., if right-wing parties post-2024 began moderating style while maintaining material
impact, the correlation would decrease.

---

## 7. Gap Trajectory Interpretation

- **Pre-2024 mean gap:** 0.810
- **Post-2024 mean gap:** 0.643
- **Gap change:** -0.167

A widening gap (increasing material > stylistic) would indicate that right-wing motions
became less stylistically extreme but maintained or increased their material impact —
consistent with the 'strategic moderation of rhetoric' hypothesis.

A narrowing gap would suggest that stylistic and material dimensions are converging,
meaning the distinctions between the two become less meaningful over time.

A stable gap suggests the two dimensions move in parallel, and the flat single-dimension
trend is an accurate summary (no masked divergence).

---

## 8. Domain Stratification

| Domain | Pre Mean Stijl | Pre Mean Mat | Post Mean Stijl | Post Mean Mat | Pre Gap | Post Gap | Pre r | Post r |
|--------|---------------|-------------|----------------|---------------|---------|----------|-------|--------|
| Migration | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| Non-migration | 1.725 | 2.535 | 1.797 | 2.440 | 0.810 | 0.643 | 0.475 | 0.439 |

---

## 9. Gravity-Weighted Trends (Right-Wing)

Yearly means for right-wing motions filtered by material impact thresholds.
M≥3 = motions with substantive material impact (score ≥ 3).
M≥4 = motions with fundamental material impact (score ≥ 4).

| Year | N (all RW) | M≥3 N | M≥4 N | Stijl (all) | Stijl M≥3 | Stijl M≥4 | Mat (all) | Mat M≥3 | Mat M≥4 |
|------|-----------|-------|-------|-------------|-----------|-----------|-----------|---------|---------|
| 2016 | 6 | 2 | 1 | 1.667 | 3.000 | 3.000 | 2.333 | 3.500 | 4.000 |
| 2017 | 0 | 0 | 0 | N/A | N/A | N/A | N/A | N/A | N/A |
| 2018 | 5 | 0 | 0 | 1.000 | N/A | N/A | 1.400 | N/A | N/A |
| 2019 | 195 | 125 | 49 | 2.046 | 2.344 | 2.755 | 2.913 | 3.480 | 4.224 |
| 2020 | 469 | 307 | 109 | 2.228 | 2.603 | 3.119 | 2.906 | 3.450 | 4.266 |
| 2021 | 425 | 270 | 143 | 1.755 | 1.978 | 2.364 | 2.976 | 3.670 | 4.266 |
| 2022 | 446 | 216 | 60 | 1.800 | 2.065 | 2.467 | 2.525 | 3.324 | 4.167 |
| 2023 | 365 | 188 | 96 | 1.575 | 1.787 | 2.052 | 2.690 | 3.601 | 4.177 |
| 2024 | 469 | 259 | 75 | 1.680 | 1.965 | 2.067 | 2.582 | 3.320 | 4.107 |
| 2025 | 455 | 157 | 45 | 1.695 | 2.287 | 2.911 | 2.332 | 3.369 | 4.289 |
| 2026 | 195 | 76 | 15 | 2.015 | 2.263 | 3.000 | 2.405 | 3.211 | 4.067 |

| Bucket | Pre-2024 Mean Stijl | Pre-2024 Mean Mat | Post-2024 Mean Stijl | Post-2024 Mean Mat |
|--------|-------------------|-------------------|---------------------|-------------------|
| All RW | 1.725 | 2.535 | 1.797 | 2.440 |
| M≥3 | 2.296 | 3.504 | 2.172 | 3.300 |
| M≥4 | 2.626 | 4.183 | 2.659 | 4.154 |

---

## 10. Figure

![2D Extremity Temporal Figure](extremity_2d_temporal_figure.png)

**Figure panels:**
- **Top panel:** Yearly mean stylistic (red) and material (blue) extremity scores with
  95% bootstrap confidence intervals. Grey dashed line = original single-dimension
  `text_score` for comparison. Gold/orange lines show material impact for M≥3 and M≥4 subsets.
- **Second panel:** Gap trajectory (material minus stylistic) for all domains, migration,
  and non-migration. Positive gap = material impact exceeds stylistic extremity.
  A widening gap indicates increasing divergence between dimensions.
- **Third panel:** Per-year Pearson correlation between stylistic and material scores.
  Declining correlation over time suggests the two dimensions are decoupling.
- **Fourth panel:** All-motion (dashed) vs right-wing (solid) comparison for both stylistic
  and material dimensions. Shows how right-wing trends compare to the full motion landscape.

---

## 11. Limitations

- **Yearly resolution:** Year-level aggregation necessarily smooths within-year trends.
  The quarterly framework from U1 provides finer resolution for other metrics.
- **Low-N years:** Some years (especially 2016-2018 and 2026) have fewer than 50 scored
  motions, reducing confidence in those yearly means.
- **2D scores are LLM-generated:** The `stijl_extremiteit` and `materiele_impact` scores
  come from LLM-based assessment and may contain systematic biases.
- **Correlation vs causation:** Per-year correlations describe association, not causation.
  A declining correlation could reflect scoring drift rather than genuine decoupling.
- **Domain imbalance:** Migration-domain motions are a minority of all right-wing motions,
  so domain-stratified analyses have lower statistical power.

---

## 12. All-Motion Comparison

Yearly means for ALL motions (from `extremity_scores_all`) compared to right-wing-only means.
This provides context for whether right-wing trends reflect party-specific dynamics or broader
parliamentary trends.

| Year | N (all) | All Stijl | All Mat | N (RW) | RW Stijl | RW Mat | Diff Stijl | Diff Mat |
|------|---------|-----------|---------|--------|----------|--------|------------|----------|
| 2016 | 162 | 1.037 | 1.796 | 6 | 1.667 | 2.333 | 0.630 | 0.537 |
| 2017 | 126 | 1.024 | 1.302 | 0 | N/A | N/A | N/A | N/A |
| 2018 | 124 | 1.000 | 1.540 | 5 | 1.000 | 1.400 | 0.000 | -0.140 |
| 2019 | 3374 | 1.276 | 2.055 | 195 | 2.046 | 2.913 | 0.770 | 0.858 |
| 2020 | 4223 | 1.370 | 2.146 | 469 | 2.228 | 2.906 | 0.858 | 0.760 |
| 2021 | 4283 | 1.378 | 2.144 | 425 | 1.755 | 2.976 | 0.378 | 0.832 |
| 2022 | 4115 | 1.379 | 2.154 | 446 | 1.800 | 2.525 | 0.422 | 0.371 |
| 2023 | 3272 | 1.356 | 2.250 | 365 | 1.575 | 2.690 | 0.219 | 0.441 |
| 2024 | 3965 | 1.371 | 2.203 | 469 | 1.680 | 2.582 | 0.309 | 0.380 |
| 2025 | 3712 | 1.420 | 2.174 | 455 | 1.695 | 2.332 | 0.274 | 0.158 |
| 2026 | 2214 | 1.383 | 1.747 | 195 | 2.015 | 2.405 | 0.633 | 0.658 |

| Period | All Stijl | All Mat | RW Stijl | RW Mat | Stijl Δ | Mat Δ |
|--------|-----------|---------|----------|--------|---------|-------|
| Pre-2024 | 1.227 | 1.923 | 1.725 | 2.535 | 0.497 | 0.612 |
| Post-2024 | 1.391 | 2.041 | 1.797 | 2.440 | 0.405 | 0.399 |

---

## 13. Conclusion

The overall stijl-materieel correlation is r=0.472 (p=0.000000),
consistent with the aggregate finding of r≈0.47.

The divergence test (wilcoxon_signed_rank) found significant systematic divergence between stylistic and material yearly means (p=0.002).

The pre/post correlation change analysis no significant change in stijl-material correlation (u=10.0, p=0.5714).

The gap (material minus stylistic) narrowed from 0.810 pre-2024 to 0.643 post-2024.