Generalized Linear Models – Performing Post-Hoc Tests on GLMs with Gamma Distribution

gamma distributiongeneralized linear modelmultiple-comparisonspost-hocr

I am analyzing data that is gamma distributed. Hence, an ANVOA was a good choice but a GLM with gamma distribution worked well. To report the data I want to compare all groups to the control treatment and use the Holm method for adjusting the p-value. For this I used the glht function in r (multicomp package) and this also worked well.

My concern is the following:

Is it correct to use the glht or similar package (such as emmeans) if the data are not normally distributed or should I use a different way of performing the post-hoc tests?

Best Answer

There is no problem using those packages. They have methods that recognize the model was fitted with glm() instead of lm() and adjust appropriately.

Related Solutions

Solved – Post-hoc test after a GLM with binary data

The problem you haveg is that are abusing (misusing) the formula notation. You never use a formula like this:

Periosna$Periostitis ~ Periosna$Cemetery

because, as you've found out it, it totally breaks the logic that you want to then use for subsequent operations.

You asked mcp() to set up Tukey contrasts for the covariate Cemetery, yet you fitted a model with covariate name Periosna$Cemetery, hence it quite rightly told you that a variable of the stated name was not involved in the model fit.

Instead, the call should have been

glm(Periostitis ~ Cemetery, data = Periosna, family = binomial)

noting that we use the variable names directly, as they exist in Periosna, and we tell R where to locate the variables in the formula via the data argument.

Now when you call glht() it should be able to find the Cemetery variable.

Solved – Non normal residuals for Tweedie GLM

No, a Tweedie GLM assumes that the responses follow a Tweedie distribution so, obviously, neither the data nor the ordinary residuals are expected to follow a normal distribution.
No, a Shapiro test is not at all appropriate. The only practical way to examine residuals from a GLM such as this is to plot the quantile residuals. Unlike other types of residuals, the quantile residuals are normally distributed, even when y follows a mixed discrete-continuous distribution as in this case. For example, make a probability plot of the residuals:
```
res <- qresiduals(c1)
qnorm(res)
```
The plot of residuals vs the covariate would also useful:
```
plot(x, res)
```
Note that these plots are examining whether your fitted model is appropriate as much as they are examining the distribution of y. If the second plot shows a pattern, then that would suggest you might need more or different predictors on your model.
glht claims to work for any GLM, so presumably it will run on a Tweedie GLM. But there seems no reason why you need the glht function. It is easy to test the significance of your model using standard GLM functions in R:
```
summary(c1)
anova(c1, test="F")
```
Why make the analysis more complicated than necessary?
You code looks ok in principle, but obviously we can't vouch for whether your analysis is completely correct from the limited information you've given.
Yes, definitely. From the limited information you've given, this seems the sort of data that Tweedie GLMs are intended for. I might change my mind if you explained the physical meaning of your data, for example what your response variable actually is and what leads to exact zeros but, from what you've said so far, the Tweedie model seems appropriate.

By the way, I assume that you have set var.power=1.11 because that was the estimate from c0$p.max.

Best Answer

Related Solutions

Solved – Post-hoc test after a GLM with binary data

Solved – Non normal residuals for Tweedie GLM

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