Calculating CIs after mixed-effects poisson

[Wing Yuen]

Hi all, I'm trying to graph the results of a mixed-effects poisson model and have come across some issues calculating 95% confidence intervals.

This is the model and code I used to calculate CIs:

meqrpoisson count age c.age#c.age || _all: R.year || birthcohort:

// Store estimates, generate predicted values
estimates store m1
predict pred, mu

// Store fixed and random effects SEs
predict se_age, stdp
predict re_year re_cohort, reffects reses(se_year se_cohort)

 // Create predicted values to demonstrate effects
bysort cohort : egen RiskyBehaviours_cohort = mean(pred)
bysort age : egen RiskyBehaviours_age = mean(pred)
bysort year : egen RiskyBehaviours_year = mean(pred)

// Calculate 95% CIs
gen cohort_lower = RiskyBehaviours_cohort - (1.96*se_cohort)
gen cohort_upper = RiskyBehaviours_cohort + (1.96*se_cohort)

gen age_lower = RiskyBehaviours_age - (1.96*se_age)
gen age_upper = RiskyBehaviours_age + (1.96*se_age)

gen year_lower = RiskyBehaviours_year - (1.96*se_year)
gen year_upper = RiskyBehaviours_year + (1.96*se_year)

This results in the lower bound of some CIs being negative, which seems wrong for a poisson model. Is this method of calculating the CIs incorrect?

Thanks in advance for any advice.