Repeated randomized complete block design at multiple sites

[tompatmck]

Hello, 

I'm analyzing data from a randomized complete block design at multiple sites across multiple years.  There are 4 blocks (1-4) at each site, so block is nested within each site (block(site)).  I am trying to run this as a simple mixed model and also as a repeated measures.  I would just like to know if my coding is correct for both.  Any insight would be appreciated.  Thanks.

A single year analysis to start :

proc mixed ;
class Site Block Treatment;
model biomass = Site|Treatment;
random Block(Site);
 run;

Multiple years without repeated statement.

Random terms:  block nested within site and then block*site*treatment to account for multiple observations across years.

proc mixed ;
class Year Site Block Treatment;
model biomass = Year|Site|Treatment;
random Block(Site)  Block*Site*Treatment;
 run;

Multiple years with repeated measures, but I'm unsure how to show that block is nested within each site (maybe the interaction accounts for this).

proc mixed ;
class Year Site Block Treatment;
model biomass = Year|Site|Treatment/ddfm=kr;
repeated Year / SUB= Site*Block*Treatment type=un ;
run;

[SteveDenham · Accepted solution]

these look good to me. My only suggestion would be on the multiple years without a repeated statement. Consider rewriting the RANDOM statement with block(site) as a subject. You would then have a random intercept and random slope model:

proc mixed ;
class Year Site Block Treatment;
model biomass = Year|Site|Treatment;
random intercept Treatment/subject=Block(Site) type=un;
 run;

I added type=un to handle any potential correlation between the intercept and Treatment.  This one does bother me a bit. I don't have an issue with a fixed effect being modeled as an R-side effect (repeated measures approach), but I think you will run into convergence and/or G matrix issues with Treatment as both random and fixed.

SteveDenham