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I've got a completely randomized block design with 4 treatments and 3 replications (blocks). I figured that a mixed model with repeated measures as random terms should be appropriate to analyse this design. We have measured each plot (4 treatments x 3 replications = 12 plots), using means of 3 animals per plot, 4 times per year (Time, every 28 days). We are evaluating the average daily gain (ADG) of animals. Is my model correct?

fit1 <- lmer(ADG ~ Treatment + (1| BLOCO) + (1| Time), data = df)
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Your model assumes that the measurements taken at different times are uncorrelated, which will probably not be the case in a repeated measures design. One way to handle this with lmer is to fit random slopes for Time:

 lmer(ADG ~ Treatment + (Time| BLOCO), data = df)

Another approach, which I would favour, is to specify a correlation structure for the residual error (within persons). Often an AR(1) structure is appropriate. My approach to this would first be to try a completely unstructured covariance matrix, thus allowing the data to inform the structure. Sometimes such a model encounters trouble with convergence, since there are many more parameters to estimate. lme4::lmer does not support any other than the default covariance structure, so if you want to try others, you can use the mmrm or glmmTMBpackages - both use essentially the same syntax as lmer.

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