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Augmented Linear Model (ALM)

Flexible regression supporting 25 distributions with configurable link functions and loss criteria.

alm

ps.alm(
    y: Union[pl.Expr, str],
    *x: Union[pl.Expr, str],
    distribution: str = "normal",
    link: str | None = None,         # None = canonical link for the distribution
    loss: str = "likelihood",        # "likelihood" | "mse" | "mae" | "ham" | "role"
    role_trim: float | None = None,  # Trim fraction for the "role" loss
    extra_parameter: float | None = None,
    with_intercept: bool = True,
) -> pl.Expr

Returns: See ALM Output

Example: 

# Robust regression via Laplace likelihood
df.group_by("group").agg(
    ps.alm("y", "x1", "x2", distribution="laplace").alias("model")
)

# Gamma regression with log link
df.group_by("group").agg(
    ps.alm("y", "x1", distribution="gamma", link="log").alias("model")
)

Supported Distributions (25)

Category Distributions
Continuous normal, laplace, student_t, logistic, asymmetric_laplace, generalised_normal, s
Positive lognormal, loglaplace, logs, loggeneralisednormal, gamma, inverse_gaussian, exponential, folded_normal, rectified_normal
Bounded (0,1) beta, logit_normal
Count poisson, negative_binomial, binomial, geometric
Ordinal cumulative_logistic, cumulative_normal
Transformed boxcox_normal

When link=None ALM picks the canonical link for the distribution. Explicit options:

link Inverse Typical use
"identity" η Gaussian
"log" exp(η) Positive / count
"logit" 1 / (1 + exp(-η)) Binary, beta
"probit" Φ(η) Binary
"inverse" 1 / η Gamma
"sqrt" η² Poisson
"cloglog" 1 - exp(-exp(η)) Binary (asymmetric)

Loss Functions

loss Description
"likelihood" Maximum likelihood (default)
"mse" Mean squared error
"mae" Mean absolute error
"ham" Half-absolute-moment
"role" Robust loss with trimming via role_trim (default 0.05)

extra_parameter is required by distributions that take an auxiliary parameter (e.g. degrees of freedom for student_t, shape for generalised_normal).

Distribution Selection Guide

Use Case Recommended Distribution
Standard regression normal
Robust to outliers laplace, student_t
Heavy tails student_t
Positive continuous lognormal, gamma
Right-skewed positive gamma, inverse_gaussian
Proportions/rates beta, logit_normal
Count data poisson, negative_binomial
Overdispersed counts negative_binomial
Ordinal outcomes cumulative_logistic, cumulative_normal

See Also