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



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


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