# What to do with an outlier that once removed prevent model convergence?

So, I'm performing generalized linear mixed models with a poisson distribution and an offset. When looking at the Cook's distance, I found gigantic values (above 3000). When removing the concerned observation, the model fail to converge. Note that all independent variables have been scaled.

I would like to include my data for an example, but I don't know how to do that here. If someone can point me how-to, I will improve my question

1- Am I doing something wrong here? Like, using a function I'm not supposed to use.

2- What does it mean?

3- What should I do with this outlier?

The model, that converges:

mod1 <- glmer(C.cent ~ richness.s + Densit.s + richness.s:Densit.s + PIB.s + richness.s:PIB.s + offset(log(Dispo.cent)) + (1|Transect), family=poisson, data=data)

Calculating cook's distance:

imod1 <- influence(mod1, obs = TRUE) plot(cooks.distance.estex(imod1)) identify(cooks.distance.estex(imod1)) #Outlier : observation 85

Removing the outlier, the model doesn't converge:

temp <- data[c(1:84, 86:103),]

mod2 <- glmer(C.cent ~ richness.s + Densit.s + richness.s:Densit.s + PIB.s + richness.s:PIB.s + offset(log(Dispo.cent)) + (1|Transect), family=poisson, data=temp))