Understanding Wald Chi-Square in Plain English

Deepanshu Bhalla 1 Comment ,

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.

The Ultimate Guide to Understanding and Calculating Wald Chi-Square
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:

  1. Obtain the coefficient estimate (β) and the standard error (SE) for the predictor of interest from the logistic regression output.
  2. Divide the coefficient estimate (β) by the standard error (SE) to get the z-score: Z = β / SE.
  3. Square the z-score to get the Wald chi-square: χ² = Z².
  4. 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.
  5. 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:

  1. In SAS, PROC LOGISTIC returns Wald Chi-Square value by default.
  2. 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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About Author:
Deepanshu Bhalla

Deepanshu founded ListenData with a simple objective - Make analytics easy to understand and follow. He has over 10 years of experience in data science. During his tenure, he worked with global clients in various domains like Banking, Insurance, Private Equity, Telecom and HR.

Post Comment 1 Response to "Understanding Wald Chi-Square in Plain English"
  1. I got answer from here easily
    Putting output product of SPSS may improve many question arouse of students

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