topic Re: Randomized Complete Block Design (RCBD) at Multiple Sites in Statistical Procedures

Randomized Complete Block Design (RCBD) at Multiple Sites

tompatmck — Thu, 12 Jan 2023 19:24:22 GMT

Hello,

I'm analyzing data from a randomized complete block design replicated at multiple sites. There is only one treatment and the block effect at each site. I plan on using proc mixed with block as a random effect. I'm wondering if block should be nested within each site? And what else should go in the random effects?

proc mixed ;
class site block treatment ;
model biomass = site|treatment;
random block(site);
run;

Thanks.

Re: Randomized Complete Block Design (RCBD) at Multiple Sites

Ksharp — Fri, 13 Jan 2023 11:57:36 GMT

/*
Check the first example of PROC MIXED in its documentation.
Example 84.1: Split-Plot Design
*/


data sp;
input Block A B Y @@;
datalines;
1 1 1 56 1 1 2 41
1 2 1 50 1 2 2 36
1 3 1 39 1 3 2 35
2 1 1 30 2 1 2 25
2 2 1 36 2 2 2 28
2 3 1 33 2 3 2 30
3 1 1 32 3 1 2 24
3 2 1 31 3 2 2 27
3 3 1 15 3 3 2 19
4 1 1 30 4 1 2 25
4 2 1 35 4 2 2 30
4 3 1 17 4 3 2 18
;

proc mixed;
class A B Block;
model Y = A B A*B;
random Block A*Block;
run;


/* equivalent model */
proc mixed data=sp;
class A B Block;
model Y = A B A*B;
random intercept A / subject=Block;
run;

Re: Randomized Complete Block Design (RCBD) at Multiple Sites

tompatmck — Fri, 13 Jan 2023 19:25:04 GMT

Should all blocks be uniquely identifiable across sites in the data? For
example, there should not be a block 1 at Site X and a block 1 at Site Y?
Site X would have blocks 1 -4 and Site Y would have blocks 4-8, instead of
blocks 1-4 at both sites?

Thanks for the help.

Re: Randomized Complete Block Design (RCBD) at Multiple Sites

Ksharp — Sat, 14 Jan 2023 09:18:17 GMT

"Should all blocks be uniquely identifiable across sites in the data? "
Yes. It should be unique . You could take a BLOCK as a SUBJECT ID .
If it is not unique, you should nested it by siteid. Like:

random intercept siteid / subject=Block(siteid);

Re: Randomized Complete Block Design (RCBD) at Multiple Sites

StatsMan — Sun, 15 Jan 2023 14:04:14 GMT

That RANDOM statement is almost right. If you have block 1-4 in site A and block 1-4 in site B then you do need to nest block within site. Your RANDOM statement could be

random block(site);

random int / subject=block(site);

Re: Randomized Complete Block Design (RCBD) at Multiple Sites

tompatmck — Tue, 17 Jan 2023 16:04:54 GMT

Thanks for all the help.

Just to clarify:

If I have blocks identified as 1 through 4 at multiple sites, then block is nested within site and not listed on it's own in the random term. My random term would be as below:

proc mixed;

class site block treatment;

model response = site|treatment;

random block(site);

If all blocks have a unique identifier across sites, block would be included on it's own and the random term would be;

proc mixed;

class site block treatment;

model response = site|treatment;

random block block*site;