I am running a logistic regression to examine the effect of year on the probability that a given cell contains off highway vehicle routes (binary response of Y or N). I am including two random effects cell ID (to take into account repeated sampling at a cell over time) and grid ID (to take into account differences in the quality of the imagery from which a given year’s cell value was estimated). I do not really care about my random effects effect, I only included them to account for known variance and repeated sampling. I have scaled the variable year prior to inclusion in the model, so year_sc represents the scaled values.

my model:

MOD_bin <- glmer(value_bin ~ year_sc + (1 | rstr_cl) + (1| grd_cll_yr), data = values_df_sub, family = binomial(link = "logit"),control = glmerControl(optimizer = "Nelder_Mead"))

I would like to interpret my results so that I can say “for each year that passed during the study period, the odds that a given cell contained OHV routes was predicted to be x times greater”.

To this end, I have two questions about the output of my model:

> summary(MOD_bin)$coefficients
            Estimate Std. Error z value
(Intercept)  -3.1362   0.005338 -587.55
year_sc       0.1042   0.004504   23.14

I know that because my variable of year is scaled, I must take this into account when back transforming the estimate value.

Question 1:
Is it appropriate to determine the OR (odds ratio) like this?

exp(0.1042*sd(values_df_sub$year))

This gives me a value of 5.796

By multiplying the effect by the sd of the variable year, am I accomplishing what I think I am — un-scaling my effect so that the output value represents the change in the odds with an increase in one year?

Question 2: How can I extract a confidence interval for the fixed effect only?

If I want to include some sort of confidence interval in my results interpretation, and I do not really care to say anything about the variance contributed by the random effects, can I simply find my 95% CI for the estiamte like so?

exp((0.1042+0.004504)*sd(values_df_sub$year)) #6.253 
exp((0.1042-0.004504)*sd(values_df_sub$year)) #5.372 

If this is not an appropriate way, what way would be better to determine the confidence interval for the fixed effect estimate ONLY?