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Output Structures

All return types from polars-statistics functions.

Linear Model Output

Returned by ols, ridge, elastic_net, wls, rls, bls, nnls.

Struct {
    intercept: Float64,
    coefficients: List[Float64],
    r_squared: Float64,
    adj_r_squared: Float64,
    mse: Float64,
    rmse: Float64,
    f_statistic: Float64,
    f_pvalue: Float64,
    aic: Float64,
    bic: Float64,
    n_observations: UInt32,
}

Quantile Regression Output

Returned by quantile.

Struct {
    intercept: Float64,
    coefficients: List[Float64],
    tau: Float64,
    pseudo_r_squared: Float64,
    check_loss: Float64,
    n_observations: UInt32,
}

Isotonic Regression Output

Returned by isotonic.

Struct {
    r_squared: Float64,
    increasing: Boolean,
    fitted_values: List[Float64],
    n_observations: UInt32,
}

Condition Number Output

Returned by condition_number.

Struct {
    condition_number: Float64,
    condition_number_xtx: Float64,
    singular_values: List[Float64],
    condition_indices: List[Float64],
    severity: String,           # "WellConditioned", "Moderate", "High", "Severe"
    warning: String,
}

Separation Check Output

Returned by check_binary_separation and check_count_sparsity.

Struct {
    has_separation: Boolean,
    separated_predictors: List[UInt32],
    separation_types: List[String],  # "Complete", "Quasi", "MonotonicResponse"
    warning: String,
}

VIF Output

Returned by vif.

Struct {
    terms: List[String],          # "x1", "x2", ...
    vif: List[Float64],
    n_observations: UInt32,
}

VIF Mask Output

Returned by high_vif_predictors.

Struct {
    is_high: List[Boolean],       # one per input feature column
    n_high: UInt32,
    n_features: UInt32,
}

GVIF Output

Returned by generalized_vif.

Struct {
    gvif: List[Float64],          # one value per group
    n_groups: UInt32,
}

Leverage Output

Returned by leverage.

Struct {
    leverage: List[Float64],      # one h_ii per input row
    n_observations: UInt32,
}

Cook's Distance Output

Returned by cooks_distance.

Struct {
    cooks_d: List[Float64],       # one D_i per input row
    n_observations: UInt32,
}

DFFITS Output

Returned by dffits.

Struct {
    dffits: List[Float64],        # one value per input row
    n_observations: UInt32,
}

Influence Mask Output

Returned by influential_cooks, influential_dffits, high_leverage_points.

Struct {
    is_influential: List[Boolean],
    n_influential: UInt32,
    n_observations: UInt32,
}

Residual Diagnostics Output

Returned by standardized_residuals, studentized_residuals, externally_studentized_residuals, and all GLM residual functions (logistic_*_residuals, poisson_*_residuals).

Struct {
    residuals: List[Float64],     # one residual per input row
    n_observations: UInt32,
}

Outlier Mask Output

Returned by residual_outliers.

Struct {
    is_outlier: List[Boolean],
    n_outliers: UInt32,
    n_observations: UInt32,
}

Chi-Squared Output

Returned by pearson_chi_squared_logistic and pearson_chi_squared_poisson.

Struct {
    chi_squared: Float64,
    df_resid: UInt32,
    n_observations: UInt32,
}

GLM Output

Returned by logistic, poisson, negative_binomial, tweedie, probit, cloglog.

Struct {
    intercept: Float64,
    coefficients: List[Float64],
    deviance: Float64,
    null_deviance: Float64,
    aic: Float64,
    bic: Float64,
    n_observations: UInt32,
}

ALM Output

Returned by alm.

Struct {
    intercept: Float64,
    coefficients: List[Float64],
    aic: Float64,
    bic: Float64,
    log_likelihood: Float64,
    n_observations: UInt32,
}

LmDynamic Output

Returned by lm_dynamic.

Struct {
    intercept: Float64,
    coefficients: List[Float64],
    r_squared: Float64,
    adj_r_squared: Float64,
    mse: Float64,
    rmse: Float64,
    n_observations: UInt32,
}

AID Output

Returned by aid.

Struct {
    demand_type: String,           # "regular" or "intermittent"
    is_intermittent: Boolean,
    is_fractional: Boolean,
    distribution: String,          # Best-fit distribution name
    mean: Float64,
    variance: Float64,
    zero_proportion: Float64,
    n_observations: UInt32,
    has_stockouts: Boolean,
    is_new_product: Boolean,
    is_obsolete_product: Boolean,
    stockout_count: UInt32,
    new_product_count: UInt32,
    obsolete_product_count: UInt32,
    high_outlier_count: UInt32,
    low_outlier_count: UInt32,
}

AID Anomalies Output

Returned by aid_anomalies. Per-row struct (use with .over() and .unnest()).

Struct {
    stockout: Boolean,
    new_product: Boolean,
    obsolete_product: Boolean,
    high_outlier: Boolean,
    low_outlier: Boolean,
}

Summary Output

Returned by *_summary functions.

List[Struct {
    term: String,
    estimate: Float64,
    std_error: Float64,
    statistic: Float64,
    p_value: Float64,
}]

Prediction Output

Returned by *_predict functions.

Struct {
    prediction: Float64,
    lower: Float64,
    upper: Float64,
}

Statistical Test Output

Returned by most statistical tests.

Struct {
    statistic: Float64,
    p_value: Float64,
}

Some tests include additional fields like df, n, estimate, ci_lower, ci_upper.

Correlation Output

Returned by pearson, spearman, kendall, distance_cor, partial_cor, semi_partial_cor, icc.

Struct {
    estimate: Float64,
    statistic: Float64,
    p_value: Float64,
    ci_lower: Float64,
    ci_upper: Float64,
    n: UInt32,
}

TOST Equivalence Output

Returned by all tost_* functions.

Struct {
    estimate: Float64,
    ci_lower: Float64,
    ci_upper: Float64,
    bound_lower: Float64,
    bound_upper: Float64,
    tost_p_value: Float64,
    equivalent: Boolean,
    alpha: Float64,
    n: UInt32,
}