It is possible that treatment could have an effect on variances in addition to its effect on the mean. Investigate this possibility by replacing the identity matrix with two diagonal matrices \(D_{0}\) and \(D_{1}\) such that \(D_{0}+D_{1}=I_{n}\), and using some version of the code

Report the two estimated variances. Use the log likelihood ratio statistic in support of your conclusion.

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reg_fit lme fit regress (log (y)-site+treat, ~rat) 1mer (log (y) ~site+treat+ (1|rat)).