I'm trying to formulate, for a report for non-scientists, the ouptut of a binomial model. However, I have some troubles with the log odds ratios, probabilities and stuff. I read some related topic but did not find help for multiple regressions.
I'm trying to predict for example the sex (Female/Male) based on two numeric personality variables: Antagonism and Negative Affect.
Here's a reproducible example:
library(neuropsychology) fit <- glm(Sex~Antagonism*Negative_Affect, data=neuropsychology::personality, family=binomial(link = "logit"))
Here's the output of the summary:
glm(formula = Sex ~ Antagonism * Negative_Affect, family = binomial(link = "logit"), data = df) Deviance Residuals: Min 1Q Median 3Q Max -1.9404 -0.6662 -0.5104 -0.3404 2.6423 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) -1.66100 0.33549 -4.951 7.38e-07 *** Antagonism 0.96291 0.16068 5.993 2.06e-09 *** Negative_Affect -0.31413 0.10650 -2.950 0.00318 ** Antagonism:Negative_Affect -0.09675 0.04401 -2.198 0.02794 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: 1351.6 on 1326 degrees of freedom Residual deviance: 1194.7 on 1323 degrees of freedom AIC: 1202.7 Number of Fisher Scoring iterations: 5
What interest me are the coefficients obtained by running
(Intercept) Antagonism Negative_Affect Antagonism:Negative_Affect -1.6609981 0.9629119 -0.3141261 -0.0967504
I understood that these coefficients are expressed in terms of log odd ratios.
So, when my two variables are 0, the odds for being a Male are
exp(-1.66)=0.18. If I transform that to probabilities, it returns
neuropsychology::odds_to_probs(0.18, log=F)=0.15, so 15%. However, the other coefficients are somehow hard to interpret. Indeed, An increase of 1 on the antagonism scale should increase the log odds of being a Male of 0.96. But does that mean that it increases the probability of
neuropsychology::odds_to_probs(0.96, log=T)=0.72, 72% ? Or that the log odds change from -1.66 to -1.66 + 0.96 = -0.7, which corresponds to 33% ? (a change of 33 - 15 = 18%)?
And what about the interaction effect?
Is there a way to explain it to people with no scientific background, in terms of probability change? Thanks!