Report and Interpret Odds Ratios

Question

I need to interpret odds ratios from a multiple logistic regression predicting self esteem ("SelfEsteemHigh")from 2 predictor variables (agreeableness & conscientiousness).

> exp(coef(mlog2))
(Intercept)               agreeableness 
        0.1999042         1.0607966 
conscientiousness 
        1.2209377

    > exp(confint(mlog2))
                               2.5 %       97.5 %
(Intercept)              0.007521561        4.390917
agreeableness            0.787426218        1.440916
conscientiousness       0.875694846        1.735260

These are the outcomes for odds ratios & 95% CI, the example for interpretation that was given to us was "A logistic regression predicting high stress from selfesteem (high / low) showed that students who had low selfesteem were expected to have 1.27 odds of being high stress, [95% CI 0.58 - 2.87]. Being in the high vs low self esteem group was associated with 0.08 times the odds of being high stress, [95% CI 0.02 - 0.30], p < .001. A graph of these results follows"

The issue is that my two predictor variables are continuous (not low/high) So I am unsure how to adapt my results to fit this interpretation example. please help!

Answer 1

Your coefficients (or more specifically, the exponentiation of your coefficients) are the ratios of the odds at X and X+1, or the ratio of odds per unit change of the predictor variable. Mathematically,

$\frac{Odds(Y=1|X=x+1)} {Odds(Y=1|X=x )}=e^{\beta_i}$