GLM struggle - which distribution choose when no normality is found?

by Eva   Last Updated November 17, 2017 19:19 PM

I am trying to assess if one chemical and environmental conditions have an effect on my individuals.

In my dataset, I have one variable (continuous) and three factors (categorical and continuous) with several levels. My environmental factors have 2 levels, and my chemical factor has 3 levels.

I wish to look at the interactions between the three factors (if they impact my individuals). Unfortunately, my data do not follow a normal distribution despite the transformations I have tried, so I can't run an ANOVA. I am trying (quite miserably, so far) to perform a correct GLM.

Here are my questions:

1) Although I have no normality, should I do my formula such as: glm(variable~factor1*factor2*factor3, data=mydata, family=Gaussian) ?

It seems wrong to assume that I have a normal distribution, knowing that it is not the case. I would like to linearize my data, but I believe that adding a link(“log”) would be incorrect for a Gaussian distribution. However, when I do Gaussian distribution, I obtain p-values which seem rather OK considering my data. The binomial distribution does not work, and when I do poisson, I have no significant p-value, which is not consistant with my dataset.

2) How can I see if my model is “correct” or not, if it fits my values ? (Residual deviance?)

3) Finally, how can I see the interactions between my different factors? I have tried the glht function (multcomp package), but I struggle to find out how to see my three factors interacting together.

I know that these questions might seem stupid, but I have spent many hours on the internet, reading forums or packages, and I can’t find the proper answers to my questions. Especially, the dataset which are online are usually poisson or binomial, and I do not believe that it suits to my data.

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