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I am reading through the book Practical Statistics for Data Scientists and I am on a section covering logistic regression. In this section the book covers how the coefficients to the logistic regression function are on the log-odds scale. As an example, there is some R output that specifies (among others) a coefficient called payment-to-income-ratio that is 0.07974.

The author gives an example regarding a change in X and what the means that I cannot follow. It says:
For example, the effect of increasing the payment-to-income ratio from, say, 5 to 6 increases the odds of the loan defaulting by factor of exp(0.08244) ~ 1.09

Where did .08244 come from? Why is it not exp(0.07974) since that is the coefficient value and the increase is by 1 unit? I am sure I am missing something very obvious. . .

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    $\begingroup$ Maybe it's a typo? The odds ratio should be exp(coefficient). $\endgroup$
    – gung - Reinstate Monica
    Commented Jan 7, 2022 at 20:18
  • $\begingroup$ I checked the errata but didn't see anything. So I just wanted to make sure I wasn't missing something $\endgroup$
    – mathfish
    Commented Jan 7, 2022 at 20:22

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I just looked at two editions of the book on line (Chapter 5, "Classification"; section "Logistic Regression," subsection "Logistic Regression and the GLM"). There is a discrepancy between the first and second editions that leads to questions about quality control in publication.

The logistic_model in question in the first edition apparently wasn't coded according to the claim (in both editions):

The response is outcome, which takes a 0 if the loan is paid off and 1 if the loan defaults,

as in the first edition things that clearly should have been associated with lower odds of default like borrower_score had positive coefficients, erroneously implying greater odds of default. In the first edition, even the direction stated in the explanatory text thus differed from that indicated by the model coefficient.

That pervasive problem was fixed in the second edition (evidently the version referenced by the OP), with all coefficients having signs reversed from the first-edition values. I suspect that the regression coefficient reported for payment_inc_ratio in the second edition, 0.07974, is correct and that the statement in the quote included in the OP is just another error from the first edition that wasn't caught in the second edition.

I suppose I could be missing something, but I don't see what. You might correspond with the authors.

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  • $\begingroup$ Thanks a bunch for looking into that. I have noticed a fair amount of oversights that are a bit irritating to head scratching. $\endgroup$
    – mathfish
    Commented Jan 8, 2022 at 19:28

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