## A mixed split-plot analysis with repeated measures and nested factor??

Occasional Contributor
Posts: 19

# A mixed split-plot analysis with repeated measures and nested factor??

I have the following problem:

A study was conducted in 10 locations (random). In each location we have 5 blocks (random). Within each block we have 3 plots with treatment A (3 levels). Within each plot we have two factors B and C in every combination (full-factorial) which have two levels each - resulting in 4 subplots within each plot. Every subplot was measured 3 times over several weeks.

In my opinion:

-block should be nested within site

- the subplots within the plots result in a split-plot design

- the 3 measurements require a repeated-measures ANOVA

Right? Wrong? Does anybody has an idea how to write the model in SAS?

Thanks!!!

Occasional Contributor
Posts: 19

## Re: A mixed split-plot analysis with repeated measures and nested factor??

I now realize that this is not a repeated measures analysis since we did not measure the 4 subplots at 3 different sampling dates, but we had 12 subplots within the plots and we measured 4 of them at each of the 3 sampling dates. Thus, main plot factor is treatment A, subplot factors are treatment B and C and time (sampling date) has to be regarded as sub-sub-plot??

Posts: 2,655

## Re: A mixed split-plot analysis with repeated measures and nested factor??

I agree with the last statement.  This now looks like a split-split plot.  A good source for code would be SAS for Mixed Models, 2nd ed. by Littell et al.  If you don't have access to a copy, just think about writing the random statements so that the proper degrees of freedom/observational units are represented.

Steve Denham

Occasional Contributor
Posts: 19

## Re: A mixed split-plot analysis with repeated measures and nested factor??

Thanx Steve! We do not longer consider "location" as random since they are not chosen randomly but represent a certain gradient. Thus, the random statement includes block(site) and block(Site)*treatment A.

I have calculated the model in Proc Mixed but for the F-values of Location, Block(Site), Treatment A and the correspodning interactions i've got 0 (zero) error df and therefore no P-values! Why?

The syntax is as follows:

Proc Mixed;

class site block treatment_A treatment_B treatment_C sampling;

model trans =

site

block(site)

treatment

treatment*site

treatment_A*block(site)

treatment_C

treatment_C*site

treatment_B

treatment B*site

sampling

sampling*site

treatment C*treatment

treatment C*treatment*site

treatment B*treatment

treatment B*treatment*site

sampling*treatment

sampling*treatment*site

treatment C*treatment B

treatment C*treatment B*site

treatment C*sampling

treatment C*sampling*site

treatment B*sampling

treatment B*sampling*site

treatment C*treatment B*treatment

treatment C*treatment B*treatment*site

treatment C*treatment B*sampling

treatment C*treatment B*sampling*site

treatment C*treatment*sampling

treatment C*treatment*sampling*site

treatment B*treatment*sampling

treatment B*treatment*sampling*site

treatment C*treatment B*treatment*sampling

treatment C*treatment B*treatment*site;

random block(site) treatment*block(site);

run;

I've got F-avlues for all factors and interactions but 0 error df for site block(site) treatment A (and interactions)...help needed! Thanks!

Posts: 2,655

## Re: A mixed split-plot analysis with repeated measures and nested factor??

Try removing all of the block related terms from the model statement.  PROC MIXED differs from GLM in that only the fixed effect terms should appear in the model statement.  With the parameterization you present, I would suspect that there are insufficient observations to get valid tests.

Steve Denham

Occasional Contributor
Posts: 19