1

This picture is from page 1290 in the Stata manual: Page 1290, Stata manual

The model can be made with the following code in Stata:

use https://www.stata-press.com/data/r16/auto

keep make mpg weight foreign


logit foreign weight mpg

As I understand the overall fit for the model is calculated with a chi2 test (Prob > chi2 = 0.0000), but how are the individual P-values (P>|z|) calculated?

Nick Cox
  • 56,404
  • 8
  • 127
  • 185
Sandahl
  • 13
  • Thank you for the answer.

    Can you elaborate a little bit? Could I write in my manuscript that the individual P-values are calculated with a z-test as I would write other P-values are calculated with a students t-test or a Pearson's chi2 test. Any references would be great.

     – Sandahl Aug 03 '21 at 09:04
  • The answer I was looking for was the one you can read below, but thank you for the comment! – Sandahl Aug 04 '21 at 06:42

1 Answers1

3

The tests shown by Stata for the individual coefficients are Wald tests whose test statistics have the form $$ W_j = \frac{\hat{\beta}_j}{\widehat{\operatorname{SE}}(\hat{\beta}_j)}\sim N(0,1) $$

Under the hypothesis than an individual coefficient is zero, these statistics will asymptotically follow the standard normal distribution. Hence, they are $z$-values. The corresponding $p$-values are calculated from the standard normal cdf $\Phi(x)$. Specifically, for two-sided $p$-values: $p=2\cdot\Phi(-|z|)$. For example in Stata for the coefficient for mpg:

di 2*normal(-abs(1.83))
.06724994

Reference

Hosmer DW, Lemeshow S, Sturdivant RX (2013): Applied Logistic Regression. 3rd ed. Wiley.

COOLSerdash
  • 30,198