# why are confidence intervals so wide with nested random effects design for factorial linear model?

I am analyzing historical data conducted from a factorial experimental field study with nested random effects. The investigator counted indicated breeding pairs of ducks per hectare (ip.ha) in experimental plots that were mowed or tilled (basin treatment) to either 30:70, 50:50, or 70:30 vegetation-to-water interspersion (veg.water).

The investigator repeatedly surveyed ducks in the morning, afternoon, and evening of weeks 1-6 in 1977, and weeks 1-5 in 1978. Therefore, I believe a nested random effects model structure is appropriate to control for the nested experimental design.

For each species I established the model structure as follows:

species1 <- lmer(sqrt(ip.ha)) ~ veg.water * treatment + (1|year/week/period), data = species1.dat

anova(sp1)

emmeans(sp1, pairwise~veg.water, type = "response")


I have a few concerns with the output. Namely, the confidence intervals for the estimated marginal means are extremely wide (with lower CL = 0) for all/most species models and treatment effects (example picture below), yet the anova III tables indicate strong significance.

However, I analyzed within-year variation of indicated breeding pairs with the same model structure and the output seems reasonable (code for 1 species and picture of all species below)

species1.1977 <- lmer(sqrt(ip.ha)) ~ veg.water * treatment + (1|week/period), data = species1.dat
anova(sp1.1977)
emmeans(sp1.1977, pairwise~veg.water, type = "response")

species1.1978 <- lmer(sqrt(ip.ha)) ~ veg.water * treatment + (1|week/period), data = species1.dat
anova(sp1.1978)
emmeans(sp1.1978, pairwise~veg.water, type = "response")


So my specific questions are 1) did I specify the overall model correctly where I nested period within week within year and 2) why do models with random intercept of year produce extremely variable estimated marginal means/is it appropriate to calculate CIs with the emmeans package for this type of linear mixed model?

Any thoughts or suggestions are appreciated.