Generalized Linear Models

Models for non-Gaussian response distributions: Poisson GLM and ALM (Augmented Linear Model).

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Poisson GLM

Generalized Linear Model for count data (event counts, defects, arrivals).

Parameters

Parameter	Type	Required	Default	Description
y	DOUBLE	Yes	-	Count target (non-negative integers)
x	LIST(DOUBLE)	Yes	-	Predictors
options	MAP	No	-	fit_intercept, max_iterations, tolerance

Example

SELECT
    production_line,
    (model).coefficients[2] as temperature_effect,
    exp((model).coefficients[2]) as rate_ratio,
    (model).p_values[2] as pvalue
FROM (
    SELECT
        production_line,
        anofox_stats_poisson_fit_agg(
            defect_count,
            [temperature, humidity, shift_hours]
        ) as model
    FROM quality_data
    GROUP BY production_line
);

Interpretation: Coefficients are on log scale. exp(coefficient) = rate ratio (multiplicative effect).

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ALM - Augmented Linear Model

Robust regression supporting 24 error distributions for non-normal data.

Parameters

Parameter	Type	Required	Default	Description
y	DOUBLE	Yes	-	Target values
x	LIST(DOUBLE)	Yes	-	Predictors
options	MAP	Yes	-	distribution, fit_intercept, max_iterations, tolerance

Supported Distributions

Distribution	Use Case
normal	Standard regression
student_t	Heavy tails, outliers
cauchy	Extreme outliers
laplace	LAD (median) regression
huber	Robust with breakdown
weibull	Survival, reliability
gamma	Positive, right-skewed
log_normal	Multiplicative errors

Example

SELECT anofox_stats_alm_fit_agg(
    revenue,
    [marketing_spend, competitor_activity],
    MAP {
        'distribution': 'student_t',
        'fit_intercept': 'true'
    }
) as model
FROM sales_with_outliers;

When to use ALM:

• Data has heavy tails or outliers
• Non-normal error distributions
• Robust estimation needed