Check that the \(F\)-ratio for brand differences is in approximate agreement with the Welham-Thompson REML statistic computed in Exercise 2.4. Explain why you need \(m=6-1\) rather than \(m=36-9\) in this comparison.

Data From Exercise 2.4

Use the method described by Welham and Thompson (1997) to compute the REML likelihood-ratio statistic for comparing the two linear models
\[
\mathcal{X}_{0}=\text { species }+ \text { bark }+ \text { team }, \quad \mathcal{X}_{1}=\text { species }+ \text { bark }+ \text { team }+ \text { brand }
\]
in the setting where saw.id occurs as a variance component. You may use R code as follows:

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fit0