In Logistic Regression, Wald Chi-Square is used to assess whether a variable is statistically significant or not. In other words, it assess the significance of individual coefficients (also known as parameters or predictors) in the model.
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| Logistic Regression : Wald Chi-Square |
To calculate the Wald chi-square for each coefficient in logistic regression, you need the following information:
- The coefficient estimate (β) for each predictor from the logistic regression model.
- The standard error (SE) of each coefficient estimate.
- The degrees of freedom (df) for each coefficient.
The formula to calculate the Wald chi-square for each coefficient is:
χ² = (β / SE)²
Wald Chi-Square = Square of (Coefficient Estimate / Standard Error)
Here are the steps to calculate the Wald chi-square for a coefficient in logistic regression:
- Obtain the coefficient estimate (β) and the standard error (SE) for the predictor of interest from the logistic regression output.
- Divide the coefficient estimate (β) by the standard error (SE) to get the z-score: Z = β / SE.
- Square the z-score to get the Wald chi-square: χ² = Z².
- Compare the calculated chi-square value with a critical chi-square value from the chi-square distribution table. The critical value depends on the desired significance level (e.g., 0.05 or 0.01) and the degrees of freedom.
- If the calculated chi-square value is greater than the critical value, the coefficient is considered statistically significant, indicating that the predictor has a significant impact on the outcome variable. Otherwise, the coefficient is not statistically significant.
Important Note:
- In SAS, PROC LOGISTIC returns Wald Chi-Square value by default.
- In R, glm package for logistic regression returns z-statistics. We need to take square of z-statistics to calculate wald chi-square.
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