Dynamic Linear Model (LmDynamic)

Time-varying coefficient regression using information criterion-weighted model averaging with optional LOWESS smoothing.

lm_dynamic

ps.lm_dynamic(
    y: Union[pl.Expr, str],
    *x: Union[pl.Expr, str],
    ic: str = "aicc",              # "aic", "aicc", "bic"
    distribution: str = "normal",  # "normal", "laplace", "student_t", etc.
    lowess_span: float = 0.3,      # LOWESS smoothing span (0.05-1.0)
    max_models: int = 64,          # Max candidate models
    with_intercept: bool = True,
) -> pl.Expr

Returns: See LmDynamic Output

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Parameters

Parameter	Description
ic	Information criterion for model weighting: "aic", "aicc" (default), or "bic"
distribution	Error distribution for ALM fitting
lowess_span	LOWESS smoothing bandwidth (0.05-1.0). Lower = more local, Higher = smoother
max_models	Maximum number of candidate models to consider

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How It Works

1. Model Generation: Creates candidate models with different predictor subsets
2. Per-Observation IC: Computes information criterion values at each observation
3. Model Weighting: Weights models based on IC values (Akaike weights)
4. Coefficient Averaging: Combines coefficients using weights at each time point
5. LOWESS Smoothing: Optionally smooths the time-varying weights

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Example

# Fit dynamic model per group
result = df.group_by("group").agg(
    ps.lm_dynamic("y", "x1", "x2", lowess_span=0.3).alias("model")
).unnest("model")

# Access time-varying coefficients (via model class)
from polars_statistics import LmDynamic
model = LmDynamic(lowess_span=0.3)
model.fit(X, y)
print(model.dynamic_coefficients)  # (n_obs x n_coef) array

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See Also

• ALM - Augmented Linear Model distributions
• Linear Models - Standard regression