Probit and Logit with Average Marginal Effects
Estimate probit and logit models for a yes/no outcome and report average marginal effects, the change in probability for a one-unit change in each regressor, with delta-method standard errors.
Updated · By Bibin XavierData 500 × 11
| IDnumeric | Log_Wagenumeric | Educationnumeric | Experiencenumeric | Femalenumeric · coded | Unionnumeric · coded | Distance_Collegenumeric | Father_Educnumeric | Employednumeric · coded | Doctor_Visitsnumeric | Agenumeric |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2.47 | 12 | 0 | 0 | 0 | 5.7 | 9 | 0 | 1 | 18 |
| 2 | 1.83 | 14 | 21 | 0 | 1 | 0 | 9 | 1 | 0 | 41 |
| 3 | 2.56 | 11 | 12 | 0 | 0 | 0 | 12 | 0 | 0 | 29 |
| 4 | 2.02 | 10 | 14 | 0 | 0 | 27.2 | 13 | 0 | 0 | 30 |
| 5 | 1.75 | 12 | 21 | 1 | 1 | 21.6 | 9 | 1 | 1 | 39 |
| 6 | 2.73 | 10 | 10 | 0 | 0 | 0 | 9 | 1 | 0 | 26 |
| 7 | 1.54 | 11 | 14 | 1 | 0 | 13.8 | 10 | 0 | 0 | 31 |
| 8 | 1.46 | 11 | 9 | 1 | 1 | 7.2 | 8 | 1 | 2 | 26 |
Variables and options
Results
500 rows · example dataAverage marginal effects (change in probability)
| Variable | Probit AME | SE | p | Logit AME | SE | p |
|---|---|---|---|---|---|---|
| Education | 0.0773 | 0.0099 | < .001 | 0.0769 | 0.0099 | < .001 |
| Experience | 0.0080 | 0.0028 | .004 | 0.0079 | 0.0028 | .005 |
| Female | -0.1270 | 0.0408 | .002 | -0.1266 | 0.0407 | .002 |
Note. Average of the individual marginal effects ∂P(y=1)/∂x over the sample; delta-method standard errors. For a 0/1 variable this approximates the difference in probability.
Probit coefficients
| Variable | Coefficient | SE | z | p | 95% CI |
|---|---|---|---|---|---|
| Constant | -2.6622 | 0.4059 | -6.558 | < .001 | [-3.458, -1.867] |
| Education | 0.2159 | 0.0322 | 6.711 | < .001 | [0.153, 0.279] |
| Experience | 0.0224 | 0.0080 | 2.800 | .005 | [0.007, 0.038] |
| Female | -0.3545 | 0.1171 | -3.028 | .002 | [-0.584, -0.125] |
Note. Log-likelihood = -313.85; LR χ²(3) = 64.64, p < .001; McFadden R² = .093; AIC = 635.7; correctly classified 64.2%.
Logit coefficients
| Variable | Coefficient | SE | z | p | 95% CI | Odds ratio |
|---|---|---|---|---|---|---|
| Constant | -4.3192 | 0.6790 | -6.361 | < .001 | [-5.650, -2.988] | 0.013 |
| Education | 0.3510 | 0.0540 | 6.494 | < .001 | [0.245, 0.457] | 1.421 |
| Experience | 0.0361 | 0.0131 | 2.750 | .006 | [0.010, 0.062] | 1.037 |
| Female | -0.5779 | 0.1920 | -3.009 | .003 | [-0.954, -0.202] | 0.561 |
Note. Log-likelihood = -313.98; LR χ²(3) = 64.40, p < .001; McFadden R² = .093; AIC = 636.0; correctly classified 63.8%.
Interpretation
A one-unit increase in Education changes the probability of Employed = 1 by 7.7 percentage points; A one-unit increase in Experience changes the probability of Employed = 1 by 0.8 percentage points; A one-unit increase in Female changes the probability of Employed = 1 by -12.7 percentage points.
How to cite this tool
Using these results in a thesis, journal article, report or class assignment? Please cite this free tool so others can find it. It keeps the site free.
APA 7
Xavier, B. (2026). Probit and Logit with Average Marginal Effects [Web application]. FreeStatisticalTools.com. https://freestatisticaltools.com/probit-logit-marginal-effects/
BibTeX
@software{xavier_probitlogitmarginaleffects_2026,
author = {Xavier, Bibin},
title = {Probit and Logit with Average Marginal Effects},
publisher = {FreeStatisticalTools.com},
year = {2026},
url = {https://freestatisticaltools.com/probit-logit-marginal-effects/},
note = {Web application}
}Suggested sentence for your methods section: “The analysis was carried out with the free Probit and Logit with Average Marginal Effects tool on FreeStatisticalTools.com (Xavier, 2026).”
What is probit and logit with marginal effects?
Probit and logit models are the standard tools for binary outcomes in econometrics. Because their coefficients are on a latent scale, results are reported as average marginal effects: the average change in the probability of the outcome for a one-unit change in each regressor.
When to use probit and logit with marginal effects
Use probit or logit for binary outcomes. Report average marginal effects, because raw coefficients have no direct probability interpretation.
How to use this tool
- Enter your data. Paste columns from Excel, Google Sheets or SPSS with variable names in the first row, or upload a CSV or Excel file. The example data shows the expected layout.
- Choose the variables. Select the binary outcome, event (coded 1) and regressors.
- Set the options. Fill in model.
- Read the results. Results update automatically. Read the plain-English interpretation, then use Copy table to paste APA-style tables into Word and Copy for the results sentence.
How to report probit and logit with marginal effects in APA style
Report AMEs with standard errors, plus the log-likelihood, LR test and pseudo R².
Frequently asked questions
Probit or logit?
They usually give almost identical marginal effects. Logit coefficients convert to odds ratios; probit is common in economics.
What is an average marginal effect?
The derivative of the predicted probability with respect to a regressor, averaged over all observations in the sample.
Why not interpret the coefficients directly?
Coefficients give the direction of an effect but not its size in probability terms, which depends on the values of all regressors.
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