Bayesian information criterion: what it means and how to read it

In the report: BIC — −2 Log Likelihood plus a penalty of ln(n) for every coefficient.

How to read it

Like AIC, but it punishes extra predictors harder as the sample grows, so it prefers simpler models. Lower is better; compare only converged models without lambda on the same rows.

In plain words

A school tested 300 students and had two ways to guess who passes: one used only study hours, the other study hours and shoe size. The head teacher wanted to know which way to keep. She counted BIC and got 410 for the first way and 418 for the second. Lower is better, so the simpler way wins. BIC is like AIC, but with many students it is stricter with every extra column, so it leans toward simple ways. Now she can say shoe size is not worth keeping. She only compares ways on the same students, and only when lambda is 0.

How it is computed

BIC = −2LL + k · ln(n)

Example

The cell with BIC 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).

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.
Standard error of B — How much B would vary from sample to sample.
Standard error of the estimate — The typical size of a residual: how far the observed Y is from the predicted one, in the units of Y.

Get it in your sheet

One formula in a cell gives the whole report, Bayesian information criterion included. ALS Stats is a free add-on for Google Sheets™.

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