Ridge penalty: what it means and how to read it
In the report: lambda — The ridge penalty: 0 — ordinary logistic regression; above 0 the slopes are shrunk toward 0.
How to read it
Leave it at 0 unless the predictors are strongly related to each other or the estimation does not converge.
With lambda above 0 the report gives no standard errors, Wald, Sig. or odds-ratio intervals: a penalized model has no ordinary tests.
In plain words
A teacher guessed who passes from study hours and sleep hours, and these two columns went together a lot. With lambda at 0, the number for study hours came out 12 on one list of students and minus 8 on a nearly identical list, so it jumped around. With lambda at 0.5, it came out 3 on both lists, calm and steady: lambda pulls such numbers in toward zero. With two columns this alike, the steady answer is the fair one. But with lambda above zero the report leaves out the usual checks of whether a number could be luck. So she keeps lambda at zero unless the columns go together a lot or the add-on cannot finish its counting.
How it is computed
The model maximizes log-likelihood − (λ/2) · Σ B², the intercept not penalized. Empty in the formula — the value from Settings (0 by default).Example
The cell with lambda is selected in each report; point at a label to see its note.
- — the sample data (50 rows) the examples use
- — two steps; pass is coded 0 and 1
=STATS_LOGISTIC(Data!A1:T51, "pass", "x1,x2|x", 0, 50, 1e-8)
Where you see it
STATS_LOGISTIC— Binary logistic regression with optional ridge regularization (lambda >= 0).
Related values
- −2 Log Likelihood (deviance) — How far the predicted probabilities are from the observed 0s and 1s: −2 times the log-likelihood. Lower is better.
- Akaike information criterion — −2 Log Likelihood plus a penalty of 2 for every coefficient.
- Bayesian information criterion — −2 Log Likelihood plus a penalty of ln(n) for every coefficient.
- Omnibus test of the model — Whether the model as a whole predicts better than the intercept alone — the likelihood-ratio test. It is the Model row of the SPSS table of the same name: at a later step it tests the whole model, not only the predictors that step adds (SPSS's Step and Block rows are not reported).
- Intercept — The constant of the model: the prediction when every predictor is 0.
Get it in your sheet
One formula in a cell gives the whole report, Ridge penalty included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)