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I have been asked to fit the following models in R:

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The models are based on this data:

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I know the mediums are the blocks and the units of the active ingredient are the treatments. I understand how to fit the first model and what it means. My questions then are

  1. Can someone explain to me the meaning of the other models?
  2. How would I fit, for example, model 2 in R?
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1 Answer 1

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Your models are not fully specified. $M_i$, the block effect, should that be treated as a fixed or random effect? Apart from that, model (1) treats the treatment as categorical (unordered) which does not seem reasonable to me. Model (2) and (3), which are equivalent and will lead to the same conclusions, treats the treatment as categorical but ordered (this polynomial parameterization is the default for ordered factors in R.) Model (4) and (5) treats the treatment as numerical, with quadratic/linear effects. Model (6) a null model without treatment effects.

One way to estimate model (2) in R is

mod_2 <- lm(log(Kill) ~ as.factor(M) + poly(x, degree=3, simple=TRUE), 
             data=your_data_frame)
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