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If we wanted to add varying time-response slopes (by Employee), we should have used the following formulation, which indicates that we want both a random intercept and a time response by employee.  

What this would imply is that each employee's performance will change through time in a different way. Some employees will have an upward performance, some of them will have a flat one, and so on.

In either case, doing this in lme is rather easy: 

fit <- lme(Performance ~ Bonus + Sector + Time + Time:Bonus , random = list( ~1 + Time |Employee) , correlation = corAR1(form= ~Time|Employee), data = data_company) 

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