# Binomial GLMM for proportion (glmmTMB/lme4)

Hopefully this will be a straightforward question for anyone experienced with GLMMs.

I'm trying to model aggregation of parasites on different locations on their host. I'd like to approach this by using the proportion of parasites found on a particular site on the host (e.g. count.on.neck/total.intensity) as the response variable, and different host characters (like "size" and "color"), total number of parasites found on each host, and the presence of other parasitic species ("coinfection") as fixed effects. The date of collection ("group") will be a random effect. I'd like to fit a model for each site, then do a correction.

My data looks something like this, with n = 100:

      Site.A Site.B   Size   Color Coinfected Total.Parasites Group
[1,]  0.800  0.200 58.259 139.274          0              30     1
[2,]  0.600  0.400 52.591  97.640          1              35     1
[3,]  0.607  0.393 58.523 103.129          0              28     1
[4,]  0.758  0.242 52.515 131.666          1              33     1
[5,]  0.615  0.385 52.095 142.782          1              26     2
[6,]  0.560  0.440 65.298 132.273          0              25     2
[7,]  0.700  0.300 62.211 179.932          1              30     2
[8,]  0.750  0.250 61.942 108.947          1              24     3
[9,]  0.840  0.160 52.978 126.832          0              25     3
[10,]  0.727  0.273 62.676 146.999          0              33     3


I've fit a binomial GLMM with the glmmTMB package:

A <- glmmTMB(Site.A ~ Size + Color + Coinfected + Total.Parasites + (1|Group),
data = attachment.example, family = "binomial",
weights = Total.Parasites)


My understanding of what this does is that it treats the attachment of each parasite on each host's "site A" as a success/failure. I'm concerned because a) I have no real training with generalized linear models and b) I get low p-values compared to a lmm with an arcsine-root transformation of the proportion at each site, though the overall interpretation is similar. At least for the first site the residuals for both models look fine.

Choice of fixed effects aside, is this a valid approach? Is it improper to use total parasite intensity as both a fixed effect and as the weight? If the approach is invalid, what would good alternatives look like? Is it impossible to answer this question because the best approach depends on my real data?

• You should not use Total.Parasites as a fixed effect; you have correctly specified it as "weight". Why do you put it in as a fixed effect too? – amoeba Apr 27 '18 at 7:50
• I included it as a fixed effect because some of the sites on the hosts body have less area for attachment, and these sites seem to be more preferable from the parasites' perspective. So at low intensities, I expect a higher proportion of parasites at the more preferable sites, and the proportion at other sites should rise as crowding kicks in. But maybe this is already captured by including size? – Dylan Apr 27 '18 at 8:19
• I did not fully understand your motivation but I assure you that Total count should NOT be included as fixed effect. – amoeba Apr 27 '18 at 8:37
• I don't think the Total.Parasites a problem, but why do you have Site.A as response? I thought Coinfected would be the response. What is Site.A? – Florian Hartig Apr 27 '18 at 10:30
• More specifically, in the first line, Total.Parasites = 34, and Site.A = 0.96. If multiply 0.96*34, I'm not getting 32.64, not an integer number, but I suppose that in this case 33 of the 34 were on Site.A, or where is this value coming from? – Florian Hartig Apr 27 '18 at 10:40