Results Object Reference¶

This page provides complete documentation for the GLMResults and GLMModel objects.

GLMResults¶

Core results object returned when fitting a GLM. Contains all fitted model information.

Construction¶

result = rs.glm("y ~ x1 + x2", data, family="poisson").fit()

Coefficient Access¶

params¶

Fitted coefficients as NumPy array.

coefficients = result.params
print(coefficients)  # array([0.5, 0.3, -0.2])

coefficients¶

Alias for params (statsmodels compatibility).

Fitted Values¶

fittedvalues¶

Predicted means μ = g⁻¹(Xβ).

predicted = result.fittedvalues
print(f"Mean prediction: {predicted.mean():.4f}")

linear_predictor¶

Linear predictor η = Xβ + offset.

eta = result.linear_predictor

Model Information¶

deviance¶

Total model deviance.

print(f"Deviance: {result.deviance:.2f}")

iterations¶

Number of IRLS iterations until convergence.

print(f"Converged in {result.iterations} iterations")

converged¶

Whether the algorithm converged.

if not result.converged:
    print("Warning: Model did not converge!")

nobs¶

Number of observations.

n = result.nobs

df_resid¶

Residual degrees of freedom (n - p).

df = result.df_resid

df_model¶

Model degrees of freedom (p - 1, excluding intercept).

df = result.df_model

family¶

Family name as string.

print(result.family)  # "Poisson" or "NegativeBinomial(theta=2.34)"

Standard Errors and Inference¶

bse()¶

Standard errors of coefficients.

se = result.bse()

Formula: SE(β̂) = √(φ × diag((X'WX)⁻¹))

tvalues()¶

z-statistics (or t-statistics).

z = result.tvalues()

Formula: z = β̂ / SE(β̂)

pvalues()¶

Two-sided p-values from z-distribution.

p = result.pvalues()
for i, pval in enumerate(p):
    if pval < 0.05:
        print(f"Coefficient {i} is significant (p={pval:.4f})")

conf_int()¶

Confidence intervals for coefficients.

lower, upper = result.conf_int(alpha=0.05)  # 95% CI

Parameters: - alpha: Significance level (default 0.05)

significance_codes()¶

Get significance markers for each coefficient.

codes = result.significance_codes()
# ['***', '**', '*', ''] for p < 0.001, 0.01, 0.05, otherwise

Robust Standard Errors¶

Sandwich estimators that are robust to heteroscedasticity.

bse_robust()¶

Robust standard errors.

se_robust = result.bse_robust(hc_type="HC1")

HC Types: - "HC0": White's original estimator - "HC1": With (n/(n-p)) adjustment (default for most software) - "HC2": With leverage adjustment - "HC3": Jackknife-like (most conservative)

tvalues_robust()¶

z-statistics using robust SEs.

z_robust = result.tvalues_robust(hc_type="HC1")

pvalues_robust()¶

p-values using robust SEs.

p_robust = result.pvalues_robust(hc_type="HC1")

conf_int_robust()¶

Confidence intervals using robust SEs.

lower, upper = result.conf_int_robust(alpha=0.05, hc_type="HC1")

cov_robust()¶

Full robust covariance matrix.

cov = result.cov_robust(hc_type="HC1")

Covariance Matrices¶

cov_params_unscaled¶

Unscaled covariance matrix (X'WX)⁻¹.

cov_unscaled = result.cov_params_unscaled

cov_params()¶

Scaled covariance matrix φ(X'WX)⁻¹.

cov = result.cov_params()

Residuals¶

resid_response()¶

Response residuals: y - μ.

r = result.resid_response()

resid_pearson()¶

Pearson residuals: (y - μ) / √V(μ).

r = result.resid_pearson()
# Should be approximately N(0,1) if model is correct

resid_deviance()¶

Deviance residuals: sign(y - μ) × √d.

r = result.resid_deviance()
# Sum of squares equals deviance
print(f"Check: {(r**2).sum():.2f} ≈ {result.deviance:.2f}")

resid_working()¶

Working residuals: (y - μ) × g'(μ).

r = result.resid_working()

Fit Statistics¶

llf()¶

Log-likelihood of the fitted model.

ll = result.llf()

aic()¶

Akaike Information Criterion.

aic = result.aic()

Formula: AIC = -2 × loglik + 2p

bic()¶

Bayesian Information Criterion.

bic = result.bic()

Formula: BIC = -2 × loglik + p × log(n)

null_deviance()¶

Deviance of intercept-only model.

null_dev = result.null_deviance()
pseudo_r2 = 1 - result.deviance / null_dev

pearson_chi2()¶

Pearson chi-squared statistic.

chi2 = result.pearson_chi2()

Formula: Σ (y - μ)² / V(μ)

scale()¶

Dispersion parameter (deviance-based).

phi = result.scale()

For Poisson/Binomial: Always 1 For QuasiPoisson/QuasiBinomial: Estimated from Pearson residuals For Gaussian/Gamma: Deviance / df_resid

scale_pearson()¶

Dispersion parameter (Pearson-based).

phi = result.scale_pearson()

Formula: Pearson χ² / df_resid

Regularization Methods¶

n_nonzero()¶

Number of non-zero coefficients (for regularized models).

result = rs.glm("y ~ x1 + x2 + C(cat)", data).fit(alpha=0.1, l1_ratio=1.0)
print(f"Selected {result.n_nonzero()} of {len(result.params)} features")

selected_features()¶

Indices of non-zero coefficients.

indices = result.selected_features()
print(f"Selected features: {indices}")

Diagnostics Integration¶

diagnostics()¶

Compute comprehensive diagnostics.

diag = result.diagnostics(
    data=data,
    categorical_factors=["region"],
    continuous_factors=["age"],
)

diagnostics_json()¶

Get diagnostics as JSON string.

json_str = result.diagnostics_json(
    data=data,
    categorical_factors=["region"],
)

GLMModel¶

Extends GLMResults with formula-specific functionality.

feature_names¶

List of feature names.

names = result.feature_names
# ['Intercept', 'x1', 'C(region)_B', 'C(region)_C']

summary()¶

Print formatted summary table.

print(result.summary())

coef_table()¶

Coefficients as Polars DataFrame.

df = result.coef_table()

relativities()¶

Multiplicative effects (exp(coef)).

rel = result.relativities()

relativities_table()¶

Relativities as Polars DataFrame.

df = result.relativities_table()

predict()¶

Predict on new data.

predictions = result.predict(new_data)
predictions_link = result.predict(new_data, type="link")