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I have a dependent variable y (Concentration), an independent categorical variable (Strain), and a random variable (Date).

When I run a simple one-way ANOVA, my independent variable Strain is not significant (pval=0.3) and my AIC=158.

When I add Date as a random effect in the model (+(1|Date) in the lmer function in R), Strain appears to be significant (pval=0.013), the random effect Date is also significant (pval=0.008 using ranova in R), but the AIC is higher (160).

I have two questions :

  • Should I consider the pvalue from ranova (0.008) and keep the random effect in the model or remove it considering the AIC ?
  • My random effect is extremely unbalanced (see the plot below, the colors are the different strains and y is the concentration). For some dates I have only one strain, or only one value some strains. For most dates, I only have 3 out of the 5 strains. Is this a problem?

Boxplots

I couldn't find a clear answer on whether very unbalanced random variables are a problem.

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There is evidence of date*strain interactions in the boxplots, so I would not recommend either of the proposed models. Using random blocks can be useful to make the most of intra-block information from blocked data with incomplete blocks. That isn't necessarily a problem. However, it appears that there is something other than strain that is driving the differences in concentration which might be associated with different dates.

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