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Phase 7c — Bass Diffusion Fits
Separating broadcast-driven from peer-driven adoption across 60,470 names via Bass diffusion (p, q) parameter fits.
By Namesake ResearchApril 13, 2026
Phase 7c -- Bass Diffusion Fits
Research question. For each name's adoption curve, what are the Bass (p, q) parameters, and does the p vs q mix differ by cultural-event type?
Summary
- •**104,819** unique names in annual_panel
- •**60,470** names fitted successfully (57.7%)
- •**44,349** names skipped (no valid segment >= 5 years or fit diverged)
- •Minimum segment length: **5 years**
Parameter distributions
Innovation coefficient (p)
| Stat | Value |
|---|---|
| mean | 0.050979 |
| std | 0.094888 |
| min | 0.000001 |
| 25% | 0.006853 |
| 50% | 0.018949 |
| 75% | 0.047309 |
| max | 1.000000 |
Imitation coefficient (q)
| Stat | Value |
|---|---|
| mean | 0.118036 |
| std | 0.138361 |
| min | 0.000001 |
| 25% | 0.019606 |
| 50% | 0.088303 |
| 75% | 0.163316 |
| max | 2.690257 |
Fit quality (R-squared)
| Stat | Value |
|---|---|
| mean | 0.9666 |
| std | 0.0689 |
| min | 0.0154 |
| 25% | 0.9651 |
| 50% | 0.9916 |
| 75% | 0.9976 |
| max | 1.0000 |
Classification breakdown
| Classification | Count | Percentage |
|---|---|---|
| broadcast | 15,787 | 26.1% |
| peer | 25,818 | 42.7% |
| mixed | 16,222 | 26.8% |
| unfit | 2,643 | 4.4% |
Classification rules:
- •**broadcast**: p > 0.01 and p/(p+q) > 0.4 (innovation dominant)
- •**peer**: q > 0.1 and q/(p+q) > 0.7 (imitation dominant)
- •**mixed**: both p and q non-trivial
- •**unfit**: no suitable segment or fit diverged
Notable examples
Broadcast
- •Denzil (p=0.0188, q=0.0189, R2=1.000, segment 1914-1966)
- •Burrell (p=0.0228, q=0.0292, R2=1.000, segment 1912-1956)
- •Harmon (p=0.0236, q=0.0278, R2=1.000, segment 1912-1962)
- •Franklyn (p=0.0159, q=0.0231, R2=1.000, segment 1913-1974)
- •Suzana (p=0.0253, q=0.0059, R2=1.000, segment 1970-2020)
Peer
- •Barbara (p=0.0111, q=0.1045, R2=1.000, segment 1926-1967)
- •Glenda (p=0.0138, q=0.1261, R2=1.000, segment 1934-1970)
- •Jackson (p=0.0136, q=0.1318, R2=1.000, segment 1996-2024)
- •Angela (p=0.0132, q=0.1430, R2=1.000, segment 1957-1991)
- •Susan (p=0.0180, q=0.1413, R2=1.000, segment 1942-1972)
Mixed
- •Waymon (p=0.0085, q=0.0537, R2=1.000, segment 1911-1984)
- •Nelda (p=0.0075, q=0.0917, R2=1.000, segment 1914-1965)
- •Melinda (p=0.0116, q=0.0942, R2=1.000, segment 1949-1993)
- •Brian (p=0.0131, q=0.0891, R2=1.000, segment 1954-2004)
- •Ian (p=0.0074, q=0.0666, R2=1.000, segment 1974-2024)
Stratification by event type
| Event type | N | p (median) | q (median) | R2 (median) | Broadcast % | Peer % | Mixed % |
|---|---|---|---|---|---|---|---|
| book_character | 4 | 0.00917 | 0.03979 | 0.968 | 25.0% | 25.0% | 50.0% |
| celebrity_birth | 22 | 0.00426 | 0.09267 | 0.999 | 9.1% | 36.4% | 54.5% |
| celebrity_naming | 32 | 0.01690 | 0.03697 | 0.998 | 40.6% | 28.1% | 25.0% |
| film_character | 325 | 0.01221 | 0.06708 | 0.998 | 23.4% | 33.8% | 37.5% |
| music_chart | 93 | 0.01509 | 0.08862 | 0.998 | 17.2% | 34.4% | 48.4% |
| news_event | 168 | 0.01288 | 0.08375 | 0.998 | 13.7% | 35.7% | 45.2% |
| royal_event | 6 | 0.00316 | 0.03960 | 0.996 | 0.0% | 0.0% | 100.0% |
| sports_moment | 83 | 0.02776 | 0.11675 | 0.998 | 27.7% | 47.0% | 24.1% |
| tv_character | 322 | 0.01225 | 0.08797 | 0.998 | 11.8% | 37.6% | 43.5% |
| unknown | 6 | 0.02694 | 0.17613 | 0.995 | 0.0% | 33.3% | 66.7% |
| video_game | 8 | 0.00922 | 0.06322 | 0.994 | 0.0% | 25.0% | 75.0% |
Diagnostic expectation. Broadcast-dominant names should be disproportionately associated with film/TV events (innovation via media exposure). Peer-dominant names should appear more in categories where social transmission matters (celebrity_naming, celebrity_birth).
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Generated by `scripts/python/research/phase7_timeseries/bass_fit.py`