I have a very small data set on solitary bee abundance that I am having trouble analysing. It’s count data, and almost all the counts are in one treatment with most of the zeroes in the other treatment. There are also a couple of very high values (one each at two of the six sites), so the distribution of the counts has an extremely long tail. I’m working in R. I have used two different packages: lme4 and glmmADMB.
Poisson mixed models didn’t fit: models were very overdispersed when random effects were not fitted (glm model), and underdispersed when random effects were fitted (glmer model). I don't understand why this is. The experimental design calls for nested random effects so I need to include them. A Poisson lognormal error distribution did not improve the fit. I tried negative binomial error distribution using glmer.nb and couldn’t get it to fit – iteration limit reached, even when changed the tolerance using glmerControl(tolPwrss=1e-3).
Because a lot of the zeroes will be due to the fact that I simply didn’t see the bees (they are often tiny black things), I next tried a zero-inflated model. The ZIP didn’t fit well. The ZINB was the best model fit so far, but I am still not too happy with the model fit. I am at a loss as to what to try next. I did try a hurdle model but couldn’t fit a truncated distribution to the non-zero outcomes– I think because so many of the zeroes are in the control treatment (the error message was “Error in model.frame.default(formula = s.bee ~ tmt + lu + : variable lengths differ (found for 'treatment')”).
In addition, I think that the interaction I have included is doing something strange to my data as the coefficients are unrealistically small – although the model containing the interaction was best when I compared models using AICctab in package bbmle.
I am including some R script that will pretty much reproduce my data set. Variables are as follows:
d=Julian date, df=Julian date (as factor) , d.sq=df squared (number of bees increases then falls throughout the summer), st=site, s.bee=count of bees, tmt=treatment, lu=type of land use, hab=percentage of semi natural habitat in surrounding landscape, ba=boundary area round fields.
Any suggestions as to how I can obtain a good model fit (alternative error distributions, different types of model etc) would be very gratefully received!
Thank you.
d <- c(80, 80, 121, 121, 180, 180, 86, 86, 116, 116, 144, 144, 74, 74, 143, 143, 163, 163, 71, 71,106, 106, 135, 135, 162, 162, 185, 185, 83, 83, 111, 111, 133, 133, 175, 175, 85, 85, 112, 112,137, 137, 168, 168, 186, 186, 64, 64, 95, 95, 127, 127, 156, 156, 175, 175, 91, 91, 119, 119,120, 120, 148, 148, 56, 56)
df <- as.factor(d)
d.sq <- d^2
st <- factor(rep(c("A", "B", "C", "D", "E", "F"), c(6,12,18,10,14,6)))
s.bee <- c(1,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,4,0,0,0,0,1,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,0,0,0,5,0,0,2,0,50,0,10,0,4,0,47,3)
tmt <- factor(c("AF","C","C","AF","AF","C","AF","C","AF","C","C","AF","AF","C","AF","C","AF","C","AF","C",
"C","AF","AF","C","AF","C","C","AF","AF","C","AF","C","AF","C","AF","C","AF","C","AF","C",
"C","AF","AF","C","AF","C","AF","C","AF","C","C","AF","C","AF","C","AF","AF","C","AF","C",
"AF","C","AF","C","AF","C"))
lu <- factor(rep(c("p","a","p","a","p"), c(6,12,28,14,6)))
hab <- rep(c(13,14,13,14,3,4,3,4,3,4,3,4,3,4,15,35,37,35,37,35,37,35,37,0,2,1,2,1,2,1),
c(1,2,2,1,1,1,1,2,2,1,1,1,1,1,18,1,1,1,2,2,1,1,1,14,1,1,1,1,1,1))
ba <- c(480,6520,6520,480,480,6520,855,1603,855,1603,1603,855,855,12526,855,5100,855,5100,2670,7679,7679,2670,
2670,7679,2670,7679,7679,2670,2670,7679,2670,7679,2670,7679,2670,7679,1595,3000,1595,3000,3000,1595,1595,3000,1595
,3000,4860,5460,4860,5460,5460,4860,5460,4860,5460,4860,4840,5460,4840,5460,3000,1410,3000,1410,3000,1410)
data <- data.frame(st,df,d.sq,tmt,lu,hab,ba,s.bee)
with(data, table(s.bee, tmt) )
# below is a much abbreviated summary of attempted models:
library(MASS)
library(lme4)
library(glmmADMB)
library(coefplot2)
###
### POISSON MIXED MODEL
m1 <- glmer(s.bee ~ tmt + lu + hab + (1|st/df), family=poisson)
summary(m1)
resdev<-sum(resid(m1)^2)
mdf<-length(fixef(m1))
rdf<-nrow(data)-mdf
resdev/rdf
# 0.2439303
# underdispersed. ???
###
### NEGATIVE BINOMIAL MIXED MODEL
m2 <- glmer.nb(s.bee ~ tmt + lu + hab + d.sq + (1|st/df))
# iteration limit reached. Can't make a model work.
###
### ZERO-INFLATED POISSON MIXED MODEL
fit_zipoiss <- glmmadmb(s.bee~tmt + lu + hab + ba + d.sq +
tmt:lu +
(1|st/df), data=data,
zeroInflation=TRUE,
family="poisson")
# has to have lots of variables to fit
# anyway Poisson is not a good fit
###
### ZERO-INFLATED NEGATIVE BINOMIAL MIXED MODELS
## BEST FITTING MODEL SO FAR:
fit_zinb <- glmmadmb(s.bee~tmt + lu + hab +
tmt:lu +
(1|st/df),data=data,
zeroInflation=TRUE,
family="nbinom")
summary(fit_zinb)
# coefficients are tiny, something odd going on with the interaction term
# but this was best model in AICctab comparison
# model check plots
qqnorm(resid(fit_zinb))
qqline(resid(fit_zinb))
coefplot2(fit_zinb)
resid_zinb <- resid(fit_zinb , type = "pearson")
hist(resid_zinb)
fitted_zinb <- fitted (fit_zinb)
plot(resid_zinb ~ fitted_zinb)
## MODEL WITHOUT INTERACTION TERM - the coefficients are more realistic:
fit_zinb2 <- glmmadmb(s.bee~tmt + lu + hab +
(1|st/df),data=data,
zeroInflation=TRUE,
family="nbinom")
# model check plots
qqnorm(resid(fit_zinb2))
qqline(resid(fit_zinb2))
coefplot2(fit_zinb2)
resid_zinb2 <- resid(fit_zinb2 , type = "pearson")
hist(resid_zinb2)
fitted_zinb2 <- fitted (fit_zinb2)
plot(resid_zinb2 ~ fitted_zinb2)
# ZINB models are best so far
# but I'm not happy with the model check plots
