# glm output interpretation help

I am using the residuals from a linear mixed effect model from the below formula ( having family structure as a random effect as the individuals are related.

 mod<- lmer(Genes ~ Age + Gender + Medication + (1|Familystructure)

summary(mod)\$res


I am then using these residuals in a glm to determine the association between the genes and the odds of disease

res<-glm(Disease ~ residuals, family=binomial)


If I am understanding this correctly- As an example, for gene 1, the odds ratio is 0.58, which shows that per unit increase in gene 1 there is a 58 % reduced odds of developing the disease.

 Logit odds = -0.49775
Exp(logit odds) = 0.60
Lower 95% CI= 0.3984
Upper 95% CI= 0.927928


I know when running an lmer to look at how these genes change as a response to disease that this gene 1 significantly reduces in disease vs control, which is in accordance with the fact that an increase results in less of a likelihood of disease.

Could anybody advise please as to whether I can only infer that a unit decrease of this gene would result in an increased odds of disease? I was unsure whether exp(0.49775) ( changing the sign of the logit odds), yielding an odds of 1.645, corresponds to this?

• Could you add a reference describing this approach? Commented Jun 26, 2020 at 20:15
• @MichaelM Please could you clarify what for ( the use of the residuals from lmer as a predictor in the glm?). If there may be any problems using this approach, please also comment if possible. Commented Jun 26, 2020 at 22:36