# Scaled Odds Ratio and Interpretation

I'm trying to calculate a scaled odds ratio for an analysis that I'm working on. I have two types of independent variables in the model: 1) percentage data (0-100%) and 2) Euclidean distance to nearest roads. The distance to road data was collected in 1-meter increments; therefore, the odds ratio below for roads_eucl would read for every 1 unit change in distance to nearest road, I would expect a 0.3% decline in use. This doesn't seem very informative given the scale of 1-meter. How would you scale the distance to represent every 10-meters or every 100-meters? In addition, how would you interpret the odds ratio for the percentage data? For example, would you state: for every 1-unit increase in MPHW_Perc, I would expect a 0.8% increase in use? This seems low; therefore, would you scale the percentage somehow? Thanks for the help!

                  OR     2.5 %    97.5 %

(Intercept) 0.7143840 0.6550213 0.7789487
MPHW_Perc   1.0089051 1.0077426 1.0100719
HW_Perc     1.0016561 0.9998965 1.0034183
AG_Perc     1.0084294 1.0071395 1.0097238
Shrub_Perc  1.0129566 1.0095038 1.0164309
MP_Perc     1.0050919 1.0039986 1.0061888


If you want to look at the decline in odds for a 100 meter change instead of 1 meter change in distance you just raise the odds ratio to the power 100, so 100 meter increase in distance to a road decreases the odds by 21%. If you want to look at a 10 percentage point increase instead of a 1 percentage point increase in MPHW (whatever that may be) you raise that odds ratio to the power 10. So 10 percentage point increase in MPHW results in 9% increase in the odds of whatever you are studying.

Alternatively, you can just create new variables that are roads_eucl / 100 and MPHW_Perc / 10 and add those new variables instead of the old variables.This is my prefered solution, as it is generally a good idea to make sure your variables have the scale you want. It makes it easier to quickly spot errors while doing your analysis and to re-read your log-files when you have received your Revice and Resubmit after 6 months.

• ...is there a way to calculate scaled odds ratios in R rather than by hand? I would like to also include a confidence interval for the scaled odds ratio. Thanks again for the help! Current R code: #odds ratios and 95% CI exp(cbind(OR = coef(glm.catfinal), confint(glm.catfinal))) – Buck2079 Feb 10 '15 at 15:47
• I updated the answer to answer that question too. – Maarten Buis Feb 11 '15 at 8:31
• I assume you meant roads_eucl / 100 and not roads_eucl / 1000? Would this affect the model fit at all if a number of your road_eucl distances range from 0-200-meters? Thanks! – Buck2079 Feb 11 '15 at 16:09
• thanks, I corrected the answer. It won't affect the model fit at all. The two models are mathematically equivalent, as it just involves a linear transformation of variables. – Maarten Buis Feb 12 '15 at 8:27
• Great! Thank you for your input! Due to model convergence issues on another modelling procedure, I need to re-scale my variables (or standardize by subtracting the mean and dividing by the standard deviation. How would you interpret the odds ratios on scaled data like this? – Buck2079 Feb 12 '15 at 11:06