I decided to use a GLMM with a negative binomial distribution (glmer.nb function in R) to analyze my data due to the overdispersion in my dataset and the fact that I have a random factor. I am struggling with the post-hoc analysis, as the package "emmeans" is not entirely compatible with this model (it cannot identify the original dataset) and I cannot make the script work so that the comparisons are performed on the response scale and not on the log scale. Is there any other appropriate package that works with these type of models or should I switch to a model with a "quasipoisson" distribution instead?
Please always provide a working example to reproduce the error. If you use fake data, it should be resemble your real data close enough so that solutions that might be found for this data will also apply to your real data (otherwise we will go in circles).
Hi Jochen,
Thank you for the suggestion. My experiment consisted of dissecting female leafhoppers and counting how many eggs are present in their reproductive tract. These females came from parents who were either uninfected ("Un") or infected ("Inf") with a plant pathogen and were reared on different plant species from egg to adults (here, canola and barley). Moreover, for space purposes, I was not able to do all replicates at the same time, so these were split into two groups and done on two different dates ("A" and "B"). So far, this would be a two-factor experimental design, with "Time" as a random factor, and it could be modelled with a Poisson distribution, but there is overdispersion. For this reason, I switched to a model with a negative binomial distribution.
The data set would be the following:
canolaInf1
There is a work-around. Use a single, 4-level factor to specify the groups. This is equivalent to a 2x2 design including the interaction. You can then use glht() to test differences between any interesting contrast. Example:
#---------------------------------------------------------------------------------------------------------------------
> eggs$grp fit_grp contrasts H summary(H)
Simultaneous Tests for General Linear Hypotheses
Multiple Comparisons of Means: User-defined Contrasts
Fit: glmer(formula = Eggs ~ grp + (1 | Time), data = eggs, family = MASS::negative.binomial(theta = 2.34263377334411))
Linear Hypotheses:
Estimate Std. Error z value Pr(>|z|)
Barley.Inf - Barley.Un == 0 0.67449 0.07876 8.564
According to UCLA and Stata: https://stats.idre.ucla.edu/stata/output/negative-binomial-regression/
The regression coef tests are normai deviate tests so the usual tests like Bonferroni, Tukey, etc should apply. BTW see the attached. Since the bonferroni method (sort of conservative, but always applies) requires only the bonferronii inequality it applies everywhere. Best, D, Booth
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