Skip to content

Summary and Prediction Functions

Functions for extracting coefficient statistics and making predictions with confidence intervals.

Summary Functions

Return coefficient statistics in tidy format (like R's broom::tidy).

Available Functions

ps.ols_summary(y, *x, with_intercept=True, alias_tolerance=1e-7) -> pl.Expr
ps.ridge_summary(y, *x, lambda_=1.0, with_intercept=True) -> pl.Expr
ps.elastic_net_summary(y, *x, lambda_=1.0, alpha=0.5, with_intercept=True) -> pl.Expr
ps.wls_summary(y, weights, *x, with_intercept=True, alias_tolerance=1e-7) -> pl.Expr
ps.rls_summary(y, *x, forgetting_factor=0.99, with_intercept=True, initial_p_diagonal=1e6) -> pl.Expr
ps.bls_summary(y, *x, lower_bound=None, upper_bound=None, with_intercept=True) -> pl.Expr
ps.logistic_summary(y, *x, with_intercept=True) -> pl.Expr
ps.poisson_summary(y, *x, with_intercept=True) -> pl.Expr
ps.negative_binomial_summary(y, *x, theta=None, with_intercept=True, estimate_dispersion=False) -> pl.Expr
ps.tweedie_summary(y, *x, var_power=1.5, with_intercept=True) -> pl.Expr
ps.probit_summary(y, *x, with_intercept=True) -> pl.Expr
ps.cloglog_summary(y, *x, with_intercept=True) -> pl.Expr
ps.alm_summary(y, *x, distribution="normal", with_intercept=True) -> pl.Expr
ps.quantile_summary(y, *x, tau=0.5, with_intercept=True) -> pl.Expr
ps.penalized_glm_summary(y, *x, family="poisson", vcov_type="laplace", conf_level=0.95, ...) -> pl.Expr
ps.aft_summary(time, event, *x, distribution="weibull", vcov_type="laplace", conf_level=0.95, ...) -> pl.Expr

Formula variants also available: ps.ols_formula_summary(formula, ...), etc.

penalized_glm_summary and aft_summary return a widened 7-field schema — the usual {term, estimate, std_error, statistic, p_value} plus trailing ci_lower/ci_upper (additive; the shared schema above and every other *_summary expression are unchanged). The intercept row is read directly from the upstream engine's own intercept inference, never recomputed locally. See Inference Summary Output, Penalized GLM, and Survival Regression (AFT).

Note on quantile_summary: Quantile regression has no analytic standard errors, so the std_error, statistic, and p_value columns are returned as NaN. The coefficient estimates themselves are still valid.

Note on ridge_summary (lambda_ > 0): std_error is the ridge sandwich standard error (sigma^2 * A @ X'X @ A', matching R), but statistic/p_value are NaN — a classical t-test on shrunken/biased coefficients is not statistically valid (anofox-regression 0.5.14 #37). lambda_ = 0 delegates fully to OLS inference (statistic/p_value populated). See Ridge for the class-level equivalent.

Note on negative_binomial_summary's estimate_dispersion: scales std_error by the Pearson chi2/df dispersion estimate (R summary.glm semantics); default False keeps dispersion fixed at 1.0. See NegativeBinomial.

Note on rls_summary's initial_p_diagonal: sets the initial covariance prior P0 = initial_p_diagonal * I; default 1e6 is identical to omitting it. See RLS.

alias_tolerance (0.8.0, ols_summary/wls_summary): R lm's configurable rank-deficiency tolerance, default 1e-7. A later column that is a linear combination of the intercept and earlier kept columns within this tolerance is aliased (NaN estimate/ std_error/statistic/p_value for that term). See Linear Models and Rank-deficient designs.

GLM intercept inference since 0.8.0 (anofox-regression 0.5.20 #66): every GLM *_summary (logistic_summary, poisson_summary, negative_binomial_summary, tweedie_summary, probit_summary, cloglog_summary) now reports the intercept row's std_error/statistic/p_value (previously NaN). tweedie_summary additionally reports t-based statistics/p-values (t on the residual df, as R's summary.glm) for every row, where they previously could be NaN. The Gamma PyModel's std_errors/p_values getters gained the same t-based values (no gamma_summary expression exists yet).

Returns: See Summary Output

Example

# Get coefficient table per group
df.group_by("group").agg(
    ps.ols_summary("y", "x1", "x2").alias("coef")
).explode("coef").unnest("coef")

Output: | group | term | estimate | std_error | statistic | p_value | |-------|------|----------|-----------|-----------|---------| | A | intercept | 1.234 | 0.123 | 10.03 | 0.000 | | A | x1 | 0.567 | 0.045 | 12.60 | 0.000 | | A | x2 | -0.234 | 0.067 | -3.49 | 0.001 |

Prediction Functions

Return per-row predictions with optional confidence/prediction intervals.

Signature

ps.ols_predict(
    y: Union[pl.Expr, str],
    *x: Union[pl.Expr, str],
    add_intercept: bool = True,
    interval: str | None = None,  # None, "confidence", "prediction"
    level: float = 0.95,
    null_policy: str = "drop",    # "drop", "drop_y_zero_x"
    alias_tolerance: float = 1e-7,
) -> pl.Expr

ols_predict/wls_predict also accept alias_tolerance (default 1e-7) — same rank-deficiency tolerance as ols/wls (see the note above); a column aliased at fit time contributes NaN to the prediction wherever that column is involved.

Available Functions

All models have prediction functions: - ols_predict, ridge_predict, elastic_net_predict - wls_predict, rls_predict, bls_predict, nnls_predict - logistic_predict, poisson_predict, negative_binomial_predict - tweedie_predict, probit_predict, cloglog_predict - alm_predict - quantile_predict, isotonic_predict, lm_dynamic_predict - penalized_glm_predict (predict_type="response" or "link") - aft_predict_quantile, aft_predict_median, aft_predict_survival, aft_predict_cdf

Formula variants also available: ps.ols_formula_predict(formula, ...), etc.

penalized_glm_predict/aft_predict_* have no analytic intervals — lower/upper are always NaN; neither FittedPenalizedGlm nor FittedAft has an interval-prediction method upstream. See Penalized GLM and Survival Regression (AFT) for the full parameter lists (predict_type/null_policy for the former; p/t/null_policy for the latter's four variants).

Models without analytic intervals. The following predictors return lower / upper as NaN — point predictions only:

Function Why no intervals
quantile_predict Quantile regression intervals require bootstrap (not yet wired through).
isotonic_predict Step-function fit with no parametric uncertainty estimate.
lm_dynamic_predict Predictions use time-averaged coefficients from the dynamic model.
penalized_glm_predict FittedPenalizedGlm has no interval-prediction method upstream.
aft_predict_quantile/_median/_survival/_cdf FittedAft has no interval-prediction method upstream.

ridge_predict's intervals use the sandwich variance factor (anofox-regression 0.5.14 #37): interval="confidence"/"prediction" widths are computed from the ridge sandwich covariance (A @ X'X @ A'), which is narrower than the pre-0.8.0 interval width for lambda_ > 0.

negative_binomial_predict/negative_binomial_summary accept estimate_dispersion (default False) — see the Summary Functions note above. Note: negative_binomial_predict itself has no theta kwarg (theta is always estimated for prediction).

rls_predict/rls_summary accept initial_p_diagonal (default 1e6) — see the Summary Functions note above.

# Quantile regression predictions
df.with_columns(
    ps.quantile_predict("y", "x1", "x2", tau=0.5).over("group").alias("p")
).unnest("p")

# Isotonic step-function predictions (single feature)
df.with_columns(
    ps.isotonic_predict("y", "x").alias("p")
).unnest("p")

# Dynamic linear model predictions
df.with_columns(
    ps.lm_dynamic_predict("y", "x1", "x2").over("group").alias("p")
).unnest("p")

Returns: See Prediction Output

Parameters

Parameter Description
interval None (point only), "confidence" (mean interval), "prediction" (individual interval)
level Confidence level (default 0.95 for 95% intervals)
null_policy How to handle missing values: "drop" or "drop_y_zero_x"

Example

# Per-group predictions with 95% prediction intervals
df.with_columns(
    ps.ols_predict("y", "x1", "x2", interval="prediction", level=0.95)
        .over("group").alias("pred")
).unnest("pred")

Output: | group | y | x1 | x2 | prediction | lower | upper | |-------|---|----|----|------------|-------|-------| | A | 5.2 | 1.0 | 2.0 | 5.15 | 3.21 | 7.09 | | A | 3.8 | 0.5 | 1.5 | 3.92 | 1.98 | 5.86 |

Interval Types

Type Description Use Case
None Point prediction only Fast prediction
"confidence" Interval for mean response Uncertainty about regression line
"prediction" Interval for individual observation Forecasting new observations

Note: Prediction intervals are always wider than confidence intervals because they account for both uncertainty in the regression line and individual observation variance.

See Also