I'm currently working on an analysis where I standardized all data values by subtracting the mean and dividing by the standard deviation (Z-score). However, when I interpret the odds ratios then the scale is unit less (or lacks a tie to my original data values). Therefore, how would you calculate the odds ratios based on standardized coefficient estimates but on the raw variable scale? In other words, my raw variables are distance to features (e.g., 100-m to an agricultural field) but the z-scores are now unit less so I can't make statements currently like: for every 100-meter increase, turkeys are 1.38 times more likely to occur. I would greatly appreciate your assistance!
results<-glmer(ROA1~MP_Scaled_Z*Week1 + MPHW_Scaled_Z*Week1 + HW_Scaled_Z*Week1 + YP_Scaled_Z*Week1 + AG_Scaled_Z*Week1 + SB_Scaled_Z*Week1 + WET_Scaled_Z*Week1 + UB_Scaled_Z*Week1 + (1|Collar_ID),data=turkey.3rdorder,family=binomial)
summary(results)
Best Answer
To convert a standardized beta coefficient estimate to raw data scale in a logistic regression you need the standard deviation of the original raw variable. The the conversion is $OR_{raw} = exp( log(OR_{std})/SD_{raw})$, where $SD_{raw}$ is the standard deviation of the raw variable, $OR_{std}$ is the odds-ratio calculated from the standardized variable (i.e. z-score). You don't need to worry about the subtraction of the original variable's mean because it only affects the interpretation of the intercept.