Question

ISYE 6414 For logistic regression, we reject the null hypothesis using a deviance test statistic with a t-distribution and n - 1 degrees of freedom. True or False?

Answer 1

The statement is false. For logistic regression, the deviance test statistic is typically compared against a chi-square distribution, not a t-distribution with n - 1 degrees of freedom.

Step-by-step explanation:

In logistic regression, we typically use the deviance, which is -2 times the log-likelihood ratio, to assess the fit of the model. However, the null hypothesis is not rejected using a t-distribution with n - 1 degrees of freedom. Instead, the deviance follows an approximate chi-square distribution under certain conditions. When comparing two nested models, the difference in deviance approximately follows a chi-square distribution with degrees of freedom equal to the difference in the number of parameters estimated.

For logistic regression, it's common to use the Wald test, likelihood ratio test, or score test for hypothesis testing, which can involve chi-square distributions, not t-distributions. Specifically:

• The Wald test uses the normal approximation to the distribution of estimates.
• The likelihood ratio test compares the deviance of two models.
• The score test assesses the derivative of the likelihood.

Therefore, the statement is False.