Use cultural dimension labels
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@@ -33,7 +33,7 @@ The V4 Stan model (`stan_model_2dim_v4.stan`) uses these mappings to produce **i
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3. **Expert data constrains individuals directly.** A CHES rating of CDU in 2019 maps to `theta[dim, rr_CDU_2019]` with no averaging. This is what identifies the *difference* between constituents.
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4. **Identification depends on data availability:**
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- **Periods with individual expert data** (e.g., CHES 1999-2024): Constituent estimates separate meaningfully. CSU appears more conservative on galtan than CDU, matching known ground truth.
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- **Periods with individual expert data** (e.g., CHES 1999-2024): Constituent estimates separate meaningfully. CSU appears more traditionalist on the cultural dimension than CDU, matching known ground truth.
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- **Periods without individual expert data** (e.g., 1950s-1990s): Only the shared manifesto constrains the mean. The random walk prior pulls constituents toward similar values, so CDU ≈ CSU with wide credible intervals on the gap. The estimates gradually differentiate as expert data appears.
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5. **Backwards compatible.** With an empty `union_mapping.csv`, all observations have `n_const=1` and V4 reduces exactly to V3.
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