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Regression Diagnostics

Tools for detecting multicollinearity, quasi-separation, and other model issues.

condition_number

Compute condition number diagnostics to detect multicollinearity in design matrices.

ps.condition_number(
    *x: Union[pl.Expr, str],
    with_intercept: bool = True,
) -> pl.Expr

Returns: See Condition Number Output

Example: 

df.select(ps.condition_number("x1", "x2", "x3").alias("diagnostics"))

Interpretation:

Condition Number Severity Recommendation
< 30 Well-conditioned Numerically stable
30 - 100 Moderate Monitor for instability
100 - 1000 High Consider regularization or removing predictors
> 1000 Severe Strong multicollinearity present

check_binary_separation

Detect quasi-separation in binary response data (logistic/probit regression).

ps.check_binary_separation(
    y: Union[pl.Expr, str],      # Binary (0/1)
    *x: Union[pl.Expr, str],
) -> pl.Expr

Returns: See Separation Check Output

Example: 

df.select(ps.check_binary_separation("success", "predictor1", "predictor2"))

Separation Types: - Complete: Predictor perfectly divides the classes (MLE does not exist) - Quasi: Nearly perfect separation with 1-2 observations crossing - MonotonicResponse: Each predictor level has all observations in same class

When Separation is Detected: - Consider using penalized regression (lambda_ > 0) - Remove or combine problematic predictors - Use Firth's bias-reduced logistic regression (if available)

check_count_sparsity

Detect sparsity-induced separation in count data (Poisson/NegBin regression).

ps.check_count_sparsity(
    y: Union[pl.Expr, str],      # Non-negative counts
    *x: Union[pl.Expr, str],
) -> pl.Expr

Returns: See Separation Check Output

Example: 

df.select(ps.check_count_sparsity("count", "x1", "x2"))

When Sparsity is Detected: - Use regularization (lambda_ > 0) - Consider zero-inflated models - Check for sparse predictor-response combinations

Diagnostic Workflow

import polars as pl
import polars_statistics as ps

# 1. Check multicollinearity before fitting
cond = df.select(ps.condition_number("x1", "x2", "x3"))
print(cond)

# 2. For binary outcomes, check separation
sep = df.select(ps.check_binary_separation("y", "x1", "x2"))
if sep["has_separation"][0]:
    print("Warning: separation detected")
    # Use regularization
    model = df.select(ps.logistic("y", "x1", "x2", lambda_=1.0))
else:
    model = df.select(ps.logistic("y", "x1", "x2"))

# 3. For count data, check sparsity
sparse = df.select(ps.check_count_sparsity("count", "x1", "x2"))

See Also