*Bounty: 50*

*Bounty: 50*

I have a dataset as follows:

```
library(nlme)
library(ggplot2)
library(multcomp)
treatment = c(rep("AB",14), rep("aB",15), rep("Ab",15), rep("ab",15))
experiment = sample(c(29,30), length(treatment), replace = TRUE)
rate = c(runif(29, min=0, max=0.2), runif(30, min=0, max=1))
d = data.frame(treatment = treatment, experiment = experiment, rate = rate)
```

There are basically four treatment groups (one has 14 samples, the others have 15 samples). Each sample was collected on one of two experiment dates (29 or 30). Each sample also recorded a “rate” (response variable of interest) between the values of 0 and 1.

I am interested to see which pairs of treatment groups show significant differences. After plotting the data, I could see that there was pretty large unequal variances. In the MWE data, this looks as follows:

```
ggplot(d, aes(x=treatment, y=rate)) + geom_boxplot(fill="palegreen2")
```

For now, I ran a linear mixed model and Tukey post-hoc comparison the data, as follows:

```
mortcomp2 = lme(rate ~ treatment, data=d, random = ~1|experiment)
summary(glht(mortcomp2, linfct=mcp(treatment="Tukey")))
```

I wanted to inquire for opinions on whether there are other models to apply for this situation? Particularly, are there alternative models that would better take into account the unequal variance in my data?

Any ideas greatly welcomed!