I'm using generalized linear mixed models (GLMMs) with the package nlme (Pinheiro et al., 2018), employing a Gaussian distribution. My study only has 6 samples with 72 replicas (Petri dishes). After some considerations, we have a fix factor with 2 levels and two random factors with 2 and 6 levels. The subjects are soil fungi that were given different edaphic parameters. My question are: Is it proper to add other parameters as random factor considering our reduced number of samples?
Sorry, my questions are: Is it proper to add other parameters as random factor considering our reduced number of samples? Are correct the employment of 2 levels? According to the literature, is correct at least 5 or 6
In principle, you can add as much random factors as you like. The benefit would be, that with each random effects factor you can detect underlying systematic variation within your samples. If you think it is reasonable to assume that each factor adds to explaining this variance than you can go ahead including more random factors. However, with each random factor you risk overfitting your data and that your model can not be computetd.
You might thus consider identifying relevant factors beforehand (e.g., by correlation matrix) in order to find the factors that are most likely to explain the most variance. You can also compare models on the basis of information criteria (AIc, BIC, ...) which also penalizes random factors that do not add explanatory power to the model.
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