Generalized Linear Models (GLM)

GLM models for binary classification, count data, and other non-normal response distributions. All GLM models support optional Ridge regularization via the lambda_ parameter.

logistic

Logistic regression for binary classification.

ps.logistic(
    y: Union[pl.Expr, str],  # Binary (0/1)
    *x: Union[pl.Expr, str],
    lambda_: float = 0.0,        # L2 (Ridge) regularization strength
    with_intercept: bool = True,
) -> pl.Expr

Returns: See GLM Output

Example:

df.group_by("group").agg(ps.logistic("success", "x1", "x2").alias("model"))

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poisson

Poisson regression for count data.

ps.poisson(
    y: Union[pl.Expr, str],  # Non-negative counts
    *x: Union[pl.Expr, str],
    lambda_: float = 0.0,        # L2 (Ridge) regularization strength
    with_intercept: bool = True,
) -> pl.Expr

Returns: See GLM Output

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negative_binomial

Negative Binomial regression for overdispersed count data.

ps.negative_binomial(
    y: Union[pl.Expr, str],
    *x: Union[pl.Expr, str],
    theta: float | None = None,  # Dispersion; None = estimate
    lambda_: float = 0.0,        # L2 (Ridge) regularization strength
    with_intercept: bool = True,
) -> pl.Expr

Returns: See GLM Output

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tweedie

Tweedie GLM for flexible variance structures.

ps.tweedie(
    y: Union[pl.Expr, str],
    *x: Union[pl.Expr, str],
    var_power: float = 1.5,      # 0=Gaussian, 1=Poisson, 2=Gamma, 3=InvGaussian
    lambda_: float = 0.0,        # L2 (Ridge) regularization strength
    with_intercept: bool = True,
) -> pl.Expr

Returns: See GLM Output

Variance Power Interpretation: | var_power | Distribution | |-----------|--------------| | 0 | Gaussian (Normal) | | 1 | Poisson | | (1, 2) | Compound Poisson-Gamma | | 2 | Gamma | | 3 | Inverse Gaussian |

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probit

Probit regression for binary classification.

ps.probit(
    y: Union[pl.Expr, str],  # Binary (0/1)
    *x: Union[pl.Expr, str],
    lambda_: float = 0.0,        # L2 (Ridge) regularization strength
    with_intercept: bool = True,
) -> pl.Expr

Returns: See GLM Output

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cloglog

Complementary log-log regression for binary classification.

ps.cloglog(
    y: Union[pl.Expr, str],  # Binary (0/1)
    *x: Union[pl.Expr, str],
    lambda_: float = 0.0,        # L2 (Ridge) regularization strength
    with_intercept: bool = True,
) -> pl.Expr

Returns: See GLM Output

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Regularization

All GLM models support L2 (Ridge) regularization via the lambda_ parameter:

# Unregularized logistic regression
ps.logistic("y", "x1", "x2")

# Ridge-regularized logistic regression
ps.logistic("y", "x1", "x2", lambda_=1.0)

Regularization helps with: - Preventing overfitting - Stabilizing estimation when predictors are correlated - Handling quasi-separation in binary response models

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See Also

• Linear Models - Standard linear regression
• ALM - Augmented Linear Model with 24+ distributions
• Diagnostics - Quasi-separation detection