Probit Regression

What it does

Models a binary outcome through the standard normal distribution, with average marginal effects.

Use it as an alternative to logit, common in econometrics.

Data you need

• Binary dependent variable
• Independent variables

Supported data: Numeric, Binary. Level: Intermediate.

Formula and method

P(Y=1|X) = Φ(β₀ + β₁X₁ + … + βₖXₖ)

The likelihood uses the standard normal CDF as its link, and is maximised by Newton's method. Because the index has no direct probability scale, average marginal effects scale each coefficient by the normal density.

How to read the result

Read average marginal effects, because coefficients are on the index scale.

Worked example

Illustrative run on Simulated study data (teaching data). These figures are the actual output of this model on that example, and they say nothing about your own data.

• LR chi-square = 39.8135, p = <0.0001, McFadden R² = 0.1198, in-sample AUC = 0.7315.
• The joint contribution of the variables is statistically significant at the 5% level.

Limitations

• Coefficients are not directly comparable with logit

Numerical validation

Validated 16 of 16 automated checks passed, including numerical results, invalid input, missing values, small samples, constant variables, charts and the interpretation text.

Computed with python 3.13.2, numpy 2.2.5, scipy 1.14.1, pandas 2.3.3, statsmodels 0.14.4, scikit-learn 1.7.0, in your browser. A passing check confirms the listed comparison only. It does not make any result suitable for your data, and it is not a claim of equivalence with other statistical software.

Questions

Logit or probit?

They usually give similar predicted probabilities. Logit offers odds ratios; probit follows from a normal latent variable.