McFadden pseudo R²: what it means and how to read it

In the report: McFadden R Square — How much the model improves the log-likelihood over the model with the intercept only.

How to read it

Not a share of explained variance like R² of a linear regression, and it runs lower: McFadden himself called values of 0.2–0.4 an excellent fit.

In plain words

A teacher guessed who passes from study hours and wanted one number for how good the guesses are. She counted McFadden R Square and it came out 0.25: her guesses got a quarter of the way from a blind guess, the same chance for every student, to guesses that are always right. She worried it looked low, since a number with a similar name in other tables would mean a quarter of the differences. But this number is built another way and runs lower. McFadden called a fifth to two fifths of that way an excellent fit. Now she can say her guesses fit well, and she does not say that study hours account for a quarter of anything.

How it is computed

1 − LL / LL₀, LL₀ — the log-likelihood of the intercept-only model

Example

The cell with McFadden R Square 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).

Cox & Snell pseudo R² — A pseudo R² from the likelihood ratio; even a perfect model stays below 1.
Nagelkerke pseudo R² — Cox & Snell R² rescaled so that a perfect model reaches 1.
Classification accuracy — The share of rows classified correctly when a predicted probability of 0.5 or more is read as 1.
Odds ratio — The odds ratio: how many times the odds of Y = 1 multiply for one unit more of the predictor. In the Intercept column it is the odds of Y = 1 when every predictor is 0, not a ratio. Empty when lambda is above 0.
Multiple correlation R — The square root of R Square. For ordinary least squares it equals the correlation between the observed and the predicted Y; with lambda above 0 it does not.

Get it in your sheet

One formula in a cell gives the whole report, McFadden pseudo R² included. ALS Stats is a free add-on for Google Sheets™.

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