Direct comparison
Ridge vs Lasso Regression: Shrink or Select
Ridge shrinks every coefficient toward zero; LASSO can zero them out entirely. A worked example shows when that difference changes your final model.
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How do Ridge regression, LASSO regression compare side by side?
The table below compares Ridge regression, LASSO regression across 10 procurement-relevant dimensions, from penalty type through combines both behaviors.
Side-by-side comparison
| Dimension | Ridge regression | LASSO regression |
|---|---|---|
| Penalty type | L2 — sum of squared coefficients | L1 — sum of absolute coefficients |
| Effect on coefficients | Shrinks every coefficient toward zero, proportionally | Can shrink a coefficient exactly to zero |
| Performs variable selection? | No — every predictor stays in the model | Yes — zeroed predictors are effectively dropped |
| Behavior on correlated predictors | Shrinks the correlated group together ("grouping effect") | Tends to pick one predictor from the group somewhat arbitrarily and zero the rest |
| Resulting model shape | Dense — all predictors present, all shrunk | Sparse — some predictors present, others absent |
| Well-posed when predictors > observations? | Yes | Yes, but selects at most n non-zero coefficients |
| Best default when… | You want to keep every predictor and just control overfitting | You want a smaller, more interpretable final model |
| Tuning parameter | λ (lambda), selected by cross-validation | λ (lambda), selected by cross-validation |
| Origin | Hoerl and Kennard, 1970 | Tibshirani, 1996 |
| Combines both behaviors | See elastic net (α = 0 recovers ridge) | See elastic net (α = 1 recovers lasso) |
Common questions
Common questions about Ridge regression vs LASSO regression
Does LASSO always give a simpler, better model than ridge?
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Not automatically. LASSO gives a sparser model, but sparsity isn't the same as accuracy — when predictors are correlated, LASSO's variable selection can be unstable (which predictor it keeps can change with small changes in the sample), and a properly cross-validated ridge model can predict just as well or better while keeping every predictor. Which one wins on prediction accuracy is an empirical question for the specific dataset, not a rule.
What does it mean if LASSO zeroes out a coefficient I expected to matter?
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It usually means that predictor's information is redundant with another predictor still in the model, not that it has no real relationship with the outcome. This is especially likely if the zeroed predictor is correlated with one that survived — LASSO is picking one representative from a correlated group, not concluding the dropped variable is irrelevant.
Can I use ridge and LASSO together instead of choosing?
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Yes — that combination is elastic net regression, which blends the L1 and L2 penalties with a mixing parameter and is specifically designed to keep LASSO's sparsity while fixing its instability on correlated predictors.
Do ridge and LASSO need the same data preparation?
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Yes. Both penalties are scale-dependent, so predictors should be standardized (mean zero, unit variance) before fitting either model — otherwise a predictor measured in larger units gets penalized more heavily purely because of its scale.
Going deeper
