How to Interpret Probit Results in Stata

Probit regression, a common tool in econometrics, is used to model binary outcome variables. Interpreting the results of a probit model can be challenging due to the non-linear nature of the model. This article provides a comprehensive guide on how to interpret probit results using Stata, breaking down each component of the output for clear understanding.

1. Understanding Probit Regression Output

The probit model estimates the probability that a binary outcome occurs based on one or more predictor variables. Here’s a step-by-step guide to interpreting the results from Stata:

1.1 Coefficient Estimates

• Coefficients: The output will show the coefficients for each predictor variable. Unlike linear regression coefficients, probit coefficients do not represent direct changes in the probability but rather the change in the z-score of the latent variable.
• Significance: Check the z-values and p-values to determine if the coefficients are statistically significant. A p-value below 0.05 typically indicates statistical significance.

1.2 Marginal Effects

• Marginal Effects at the Mean: The marginal effects show the change in the probability of the outcome occurring given a one-unit change in the predictor variable, holding other variables constant. Stata’s margins command is used to calculate these effects.
• Interpreting Marginal Effects: Marginal effects are easier to interpret as they provide a direct measure of the impact of each predictor on the probability of the outcome.

1.3 Predicted Probabilities

• Using predict Command: After fitting a probit model, use the predict command to obtain the predicted probabilities for each observation. This helps in understanding how the model performs and how each predictor influences the predicted outcome.
• Interpreting Predicted Probabilities: Analyze these probabilities to gauge how changes in predictors affect the likelihood of the binary outcome.

2. Model Fit and Diagnostics

2.1 Goodness of Fit

• Pseudo R-squared: This statistic, displayed in Stata, indicates the proportion of variance in the outcome explained by the model. While it is not directly comparable to R-squared in linear regression, it provides insight into model fit.
• Likelihood Ratio Test: This test compares the fitted model to a null model with no predictors, providing a measure of overall model significance.

2.2 Model Diagnostics

• Checking for Multicollinearity: Use variance inflation factors (VIFs) to ensure that predictor variables are not highly collinear, which can distort coefficient estimates.
• Outliers and Influence: Examine residuals and influence measures to identify any outliers that might affect model performance.

3. Practical Examples and Application

3.1 Example Dataset

• Dataset Description: Consider a dataset where the binary outcome is whether a person defaults on a loan (default), and predictor variables include income, loan amount, and credit score.
• Probit Model Estimation: Run a probit regression in Stata using the command probit default income loan_amount credit_score.
• Interpreting Results: Analyze the coefficients, marginal effects, and predicted probabilities to understand the impact of each predictor on the likelihood of default.

3.2 Application in Policy and Decision Making

• Policy Implications: Understanding how different predictors affect the probability of an outcome can inform policy decisions, such as adjusting lending criteria based on income and credit score.
• Decision Making: Use the model results to make informed decisions, such as assessing risk levels and potential interventions.

4. Common Pitfalls and Best Practices

4.1 Pitfalls

• Misinterpreting Coefficients: Avoid interpreting probit coefficients as direct changes in probability. Always use marginal effects for intuitive understanding.
• Ignoring Model Diagnostics: Ensure thorough model diagnostics to avoid issues with multicollinearity and outliers.

4.2 Best Practices

• Use Marginal Effects: Rely on marginal effects for a more practical interpretation of results.
• Verify Model Fit: Regularly check model fit and diagnostics to ensure the robustness of your results.

5. Conclusion

Interpreting probit results involves understanding coefficients, marginal effects, and predicted probabilities, while also ensuring good model fit and addressing potential pitfalls. By following these guidelines, you can effectively analyze and interpret your probit regression results in Stata, leading to more accurate and actionable insights.