Is there method to deal with missing observation through adding weight in GLMM? - glm

Question

Is there method to deal with missing observation through adding weight in GLMM?
I wonder how to construct a GLMM model with count data where some observations lost. For me, I used yellow sticky board to trap ladybeetles, whose data type is count. And another variable is ratio of area of grass within 1km radius. IDs are ID of yellow sticky board. Each of cotton field put 3 pierce of boards. SITES are different cotton fields. Regions are that several sites belong to a certain region. I want to build GLMM model:
As you can see , I can create GLMM model as below:
library(lme4)
library(glmmTMB)
library(mgcv)
m1 = glmer(ladybeetles ~ Grass.perc + (1|Region\SITE) , data=df, family="poisson" ) #nbinomial tried
m2 = glmmTMB(ladybeetles ~ Grass.perc + (1|Region\SITE) , data=df, family="poisson" ) #nbinomial tried
But, I don't want to create it like that due to yellow stick boards trapping huge variance of count. I want to group factor variables and sum yellow boards' integer values. Therefore, I could do like this:
df =
df %>% group_by(Region,SITE) %>%
summarise(Ladybeetles = sum(Ladybeetles),
Grass.perc = mean(Grass.perc),
SampleNum = n()
) # sum ladybeetles of all yellow boards at each field
m1 = glmer(ladybeetles ~ Grass.perc + (1|Region) , data=df, family="poisson" ) #nbinomial tried
m2 = glmmTMB(ladybeetles ~ Grass.perc + (1|Region) , data=df, family="poisson" ) #nbinomial tried
However, you might see there're some problems in my data.
Most of boards are full in many fields. But site3,site4,site5 have problems: they lost a board due to windy or farmer's behavior(Mark red fill). Then I cannot sum ladybeetles like that. Someone could advice you can group and obtain mean value and construct GLMM models with family of gaussian or gamma error distribution. But from personal perspective, count number type linked poisson or negative binomial distribution supports an alternative for me because I have lots of other data like this which often violate assumptions.
I wonder if there's any model structure with weight to sample numbers to build GLMM model in lme4 or glmmTMB package so that it allows me still using poisson or negative binomial distribution function when special condition occurring like observations lost. So I add weight=SampleNum, but I have no idea whether the weightmethod is right. Hoping someone can help me.
glmer(ladybeetles ~ Grass.perc + (1|Region) ,
weight = SampleNum , # SampleNum is sample number I can group and create
data=df, family="poisson" )
glmmTMB(ladybeetles ~ Grass.perc + (1|Region) ,
weight = SampleNum, # SampleNum is sample number I can group and create
data=df, family="poisson" )
add weight = SampleNum
Here is my data.
df =
structure(list(Region = c("ITI", "ITI", "ITI", "ITI", "ITI",
"ITI", "ITI", "ITI", "ITI", "ITI", "ITI", "ITI", "ITI", "ITI",
"ITI", "KZ", "KZ", "KZ", "KZ", "KZ", "KZ", "KZ", "KZ", "KZ",
"KZ", "KZ", "KZ", "BST", "BST", "BST", "BST", "BST", "BST", "BST",
"BST", "BST", "BST", "BST", "BST"), SITE = c("site1", "site1",
"site1", "site2", "site2", "site2", "site3", "site3", "site4",
"site4", "site5", "site5", "site6", "site6", "site6", "site7",
"site7", "site7", "site8", "site8", "site8", "site9", "site9",
"site9", "site10", "site10", "site10", "site11", "site11", "site11",
"site12", "site12", "site12", "site13", "site13", "site13", "site14",
"site14", "site14"), ID = c("ID1", "ID2", "ID3", "ID1", "ID2",
"ID3", "ID1", "ID2", "ID1", "ID3", "ID2", "ID3", "ID1", "ID2",
"ID3", "ID1", "ID2", "ID3", "ID1", "ID2", "ID3", "ID1", "ID2",
"ID3", "ID1", "ID2", "ID3", "ID1", "ID2", "ID3", "ID1", "ID2",
"ID3", "ID1", "ID2", "ID3", "ID1", "ID2", "ID3"), Ladybeetles = c(0L,
1L, 7L, 7L, 2L, 8L, 4L, 0L, 3L, 3L, 9L, 10L, 22L, 10L, 15L, 0L,
7L, 1L, 6L, 0L, 0L, 5L, 2L, 2L, 12L, 5L, 5L, 7L, 9L, 6L, 4L,
5L, 4L, 11L, 13L, 27L, 8L, 1L, 7L), Grass.perc = c(5L, 5L, 5L,
13L, 13L, 13L, 4L, 4L, 21L, 21L, 13L, 13L, 5L, 5L, 5L, 2L, 2L,
2L, 1L, 1L, 1L, 3L, 3L, 3L, 3L, 3L, 3L, 10L, 10L, 10L, 11L, 11L,
11L, 15L, 15L, 15L, 19L, 19L, 19L)), class = "data.frame", row.names = c(NA,
-39L))

Answer 1

I think this is more of a CrossValidated question, but I'll give it a shot (it may be migrated).
tl;dr I don't think you should be trying to aggregate like this: this kind of unbalanced design is exactly where GLMMs are useful.
I think you should be using a negative binomial or other overdispersed model: the ratio of deviance()/df.residual() (a rough guide to overdispersion is greater than 2 (a Poisson model would be appropriate if the dispersion were close to 1).
The random effect of Region is estimated as zero — not surprising because your data set is fairly small, fairly noisy, and you have only 3 regions. You could simplify the model and replace (1|Region/SITE) with (1|SITE), if the differences among regions are not very interesting to you.
I fitted the model with (1|SITE) and family = "nbinom2", then I used the DHARMa package to explore residuals (plot(ss <- simulateResiduals(model)); plotResiduals(ss, df$Grass.perc)). I found there was some nonlinearity in the pattern. I also tried with nbinom1 rather than nbinom2 and found it improved the fit, so I ended up with:
glmmTMB(Ladybeetles ~ poly(Grass.perc,2) + (1|SITE) ,
data=df, family="nbinom1" )