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I'd like to ask for some help with a binary logistic regression. In SPSS I am building a binary logistic regression with 4 independent continuous variables (Sample size - 85).

However, with one of the variables (Bicaudatus_index) I get a huge odds ratio: enter image description here

Maybe the scale of this variable is very different than other variables: enter image description here

As this variable is a ratio of two measurements I try to multiply the variable 100 times and get a new variable. The odds ratio of the new variable in the same regression seems to be within normal range. However I don't know if it is appropriate to do that. If I multiply the variable not by 100, but e.g. 150 times, I get odds ratios that are different from the ones that I get with 100.

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  • $\begingroup$ What values for the coefficient do you get for the additional analyses which you mention? $\endgroup$
    – mdewey
    Oct 1, 2016 at 16:40

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Nothing seems to be awry here. Coefficients in logistic regression are indeed scale-dependent; predictors with smaller SDs will in general get larger coefficients. If you want the variables to be on comparable scales, you can standardize each continuous variable by subtracting its mean and dividing by twice its SD.

Gelman, A. (2008). Scaling regression inputs by dividing by two standard deviations. Statistics in Medicine, 27, 2865–2873. doi:10.1002/sim.3107

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  • $\begingroup$ What you say is undeniably true but an odds ratio in the billions when the ratio of the standard deviations is only about athousand does seem excessive. $\endgroup$
    – mdewey
    Oct 1, 2016 at 21:06
  • $\begingroup$ @mdewey That's probably because of the multiplicative scale of odds ratios. Looking at the log odds ratios, which are the model's raw coefficients, we see that the coefficient is only 28. $\endgroup$
    – Kodiologist
    Oct 1, 2016 at 22:08
  • $\begingroup$ Thank you for your answer. I've tried to standardize all the coefficients by subtracting its mean and dividing by its standard deviation and indeed it yielded valid results. But how does it change the way that I can interpret the results of the regression? I.e. before the standardization I could have said that the change of 1 in the DSST(a cognitive test value) result would decrease the odds of the second outcome by 0,942. How could I interpret the odds ratio after the standardization? $\endgroup$
    – NaRas
    Oct 2, 2016 at 8:43
  • $\begingroup$ @NaRas It's the same thing except now the coefficient corresponds to a 1-SD (or 1/2-SD) change in DSST instead of a 1-unit change. Gelman (2008) may be helpful. $\endgroup$
    – Kodiologist
    Oct 2, 2016 at 14:23

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