−2 Log Likelihood (deviance): what it means and how to read it

In the report: -2 Log Likelihood — How far the predicted probabilities are from the observed 0s and 1s: −2 times the log-likelihood. Lower is better.

How to read it

On its own it says little. It compares models on the same rows: its drop from the intercept-only model is the chi-square of the omnibus test, and its drop from one step to the next shows what the added predictors bring.

In plain words

A doctor wanted to guess which patients would get better, giving each patient a chance somewhere between none and certain. She wanted to know how far her guesses were from what really happened. She counted the minus 2 log likelihood: with no information about the patients it came out 120, and after she added their age it dropped to 104. A lower number means the guesses sat closer to what really happened. On its own, 120 or 104 says little. But side by side, on the same patients, they show that the guesses with age were closer to reality.

How it is computed

−2LL = −2 Σ [yᵢ ln pᵢ + (1 − yᵢ) ln(1 − pᵢ)], pᵢ — the predicted probability of row i

Example

The cell with -2 Log Likelihood 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).

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.
Coefficient B — The coefficient of the predictor.

Get it in your sheet

One formula in a cell gives the whole report, −2 Log Likelihood (deviance) included. ALS Stats is a free add-on for Google Sheets™.

Install ALS Stats from Google Workspace Marketplace (opens in a new tab)