ols¶

Ordinary least squares fitting with formulaic design matrices and HC3 robust standard errors. Statsmodels-free drop-in replacement for statsmodels.OLS. Accepts any narwhals-compatible DataFrame (pandas, polars, …).

ols(formula, data)[source]¶

Fit an OLS model using a formulaic formula string.

Parameters:

formula – Formula string, e.g. "y ~ x1 + x2".
data – DataFrame containing all variables. Any narwhals-compatible frame (pandas, polars, …) is accepted.

Return type:

OLSResult

Returns:

OLSResult – Drop-in replacement for statsmodels OLS results.

Parameters:

formula (str)
data (Any)

Examples

>>> import interlace
>>> result = interlace.ols("y ~ x1 + x2", df)
>>> result.params

OLSResult attributes¶

Attribute	Type	Description
`params`	`pd.Series`	Named coefficient estimates; supports `.get(name)` and `.values`
`resid`	`np.ndarray` (n,)	Residuals `y − X β̂`
`fittedvalues`	`np.ndarray` (n,)	Fitted values `X β̂`
`normalized_cov_params`	`np.ndarray` (p, p)	`(XᵀX)⁻¹` — unscaled covariance matrix
`model.exog`	`np.ndarray` (n, p)	Design matrix
`model.endog`	`np.ndarray` (n,)	Response vector
`model.exog_names`	`list[str]`	Column names from the formula
`model.formula`	`str`	Original formula string
`model.data.frame`	native frame	Original data as passed by the caller
`df_resid`	`float`	Residual degrees of freedom: `n − p`, matching statsmodels
`mse_resid`	`float`	Mean squared error of residuals: `RSS / df_resid`, matching statsmodels

OLSResult methods¶

`hc3_bse()`¶

HC3 heteroskedasticity-consistent standard errors, matching statsmodels to 6 significant figures.

h_ii    = diag(X (XᵀX)⁻¹ Xᵀ)
d_i     = eᵢ² / (1 − hᵢᵢ)²
cov_HC3 = (XᵀX)⁻¹ (Xᵀ diag(d) X) (XᵀX)⁻¹
se_HC3  = sqrt(diag(cov_HC3))

Returns np.ndarray of shape (p,).

`predict(data)`¶

Re-evaluates the RHS formula on new data via the stored formulaic ModelSpec. Accepts any narwhals-compatible frame. Returns np.ndarray of shape (n_new,).

Examples¶

Basic fit¶

import interlace

result = interlace.ols("score ~ age + education", data=df)

print(result.params)
# Intercept    50.0
# age            1.5
# education      3.2
# dtype: float64

HC3 robust standard errors¶

se = result.hc3_bse()
import pandas as pd
print(pd.Series(se, index=result.params.index))

Prediction on new data¶

import pandas as pd

new_df = pd.DataFrame({"age": [30, 40], "education": [16, 18]})
preds = result.predict(new_df)

Polars input¶

import polars as pl

df_pl = pl.from_pandas(df)
result = interlace.ols("score ~ age + education", data=df_pl)