[R-sig-ME] Need advice on model specification for repeated measures on split-plot design

[Taylor, Jason]

Hello,
I sent this earlier this week but realized my data table had been unfolded in the email.  Here is my post again with the data table formatted correctly.

Thanks,
Jason

I am new to the mixed-model world.  I posted a couple of weeks ago but received no feedback so I have plowed on ahead and tried to figure things out on my own.   Any feedback on my current perspective would be very useful.

I essentially have a split plot design with repeated measurements.

I have 12 experimental sampling units.

Each sampling unit is assigned to one of 3 nutrient treatments (4 replicates per treatment).

Within each sampling unit I have a grazed and ungrazed treatment.

Each sampling unit was sampled repeatedly on day 0 (before nutrients and grazer manipulations began), day 14 and day 28.

I am interested in the fixed effects of nutrient, grazing, time and their interactions but also want to account for potential random differences in sampling units.

First few lines of data are listed below for reference.

obs      Sample unit     Date     Nut     Graz     Response
1         S1                  DAY0    Low     G         2.014

2         S5                  DAY0    Low     G         2.487

3         S8                  DAY0    Low     G         2.144

4         S11                DAY0    Low     G         1.946

5         S1                  DAY0    Low     UG       2.199

6         S5                  DAY0    Low     UG       1.666

7         S8                  DAY0    Low     UG       1.642

8        S11                 DAY0    Low      UG      2.288

9        S3                   DAY0    Med      G       2.786

10      S6                   DAY0    Med      G       1.766

11      S7                   DAY0    Med      G       1.756

12      S12                 DAY0    Med      G       0.943

13      S3                   DAY0    Med      UG     2.124

14      S6                   DAY0    Med      UG     1.33

15      S7                   DAY0    Med      UG     1.847

16      S12                 DAY0    Med      UG     1.424

17      S2                   DAY0    High      G      1.775

18      S4                   DAY0    High      G      1.838

19      S9                   DAY0    High      G      2.971

20     S10                  DAY0    High      G      2.14



21     S1                   DAY14    Low     G         2.014

22    .......


I believe the correct code for a starting model in lme4 that accounts for the fixed effects and their interactions + the random effect of sample unit would be:

model.1<-lmer(response~Nut*Graz*Date+(1|Sample unit))

I realize now that if I wanted to do any nested random effects my data is currently coded poorly (implicit nesting of the variables).  However, if I understand correctly,  I don't need to incorporate (1|Stream:Graz) or (1|Stream:Date) as nested random effects because:


1)      autocorrelation between Graz or Date treatments within a sample unit will be accounted for by treating the sample unit as a random effect,

2)      they are not pseudo-replicates but actual fixed factors that I am interested in, and

3)      Graz only has 2 groups and I may only use day 14 and 28 for date (also resulting in 2 groups) since Day 0 was not influenced by any of the treatment effects.  Estimating variance from only 2 groups would be pointless.


Thanks in advance for any comments,

Cheers,
Jason