# 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))

## 2 Answers

After consulting a professionnal statistician, it seems that although I had verified dispersion, the poisson distribution wasn't right. By changing the distribution to negative binomial, the problem is fixed.

It may be useful to examine your models again using the RLM function in R, which is in the MASS package. In doing so, you won't necessarily need to remove the outliers.

• Can you expand a bit your answer? – Joe_74 Mar 2 '17 at 16:28
• The RLM command in R attenuates the influence of outliers in regression models. Therefore, outliers (aka influence cases indicated by high leverage statistics), are weighted downward. The result is that regression coefficients are more accurate than if outlier cases were not adjusted with a weight. – Ben Mar 2 '17 at 16:40