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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