# Leverage

Compute the hat-matrix diagonal decomposed into fixed-effect and random-effect
components, following Demidenko & Stukel (2005) and Nobre & Singer (2007).

```{eval-rst}
.. autofunction:: interlace.leverage
```

## Returned columns

| Column | Description |
|---|---|
| `overall` | H1 + H2 (total leverage) |
| `fixef` | H1 — fixed-effect leverage |
| `ranef` | H2 — random-effect leverage (Demidenko & Stukel) |
| `ranef.uc` | Unconfounded H2 (Nobre & Singer) |

## Example

```python
import interlace

result = interlace.fit("rt ~ condition", data=df, groups=["subject", "item"])
lev = interlace.leverage(result)

# Flag high-leverage observations (rule of thumb: overall > 2p/n)
p = len(result.fe_params)
n = result.nobs
lev_high = lev[lev["overall"] > 2 * p / n]
print(f"{len(lev_high)} high-leverage observations")
```

## Structure helpers

These functions extract the model structures needed to dispatch leverage
computation to the correct code path. They are part of the stable public API
and are used by downstream consumers (e.g. `gpgap`) to inspect model layout.

```{eval-rst}
.. autofunction:: interlace.crossed_structures

.. autofunction:: interlace.statsmodels_structures
```

## See also

- {doc}`influence` — Cook's distance and MDFFITS (impact on estimates, not just fit)
- {doc}`augment` — append leverage + influence metrics to the original DataFrame
- {doc}`residuals` — residual diagnostics