Bhupinder Singh
2009-05-28 00:13:53 UTC
Hi: =0A =0AI have ran the Split-Split-plot mixed model experiment and I am =
not sure if it is correct or not so need the help of experienced person who=
can just make a look and tell me if it is right or wrong. I am little conf=
used over the error terms generated by the model. =0A =0AOptionsps=3D50ls=
=3D74pageno=3D1;=0ADATAyield;=0AInfile"E:\Try-Yield\Sp_project.csv"delimite=
r=3D","firstobs=3D2;=0AInputYear location env Plot_no Block Tillplc$ Prate$=
Krate$ Yield;=0Acards;=0Arun;;=0Aprocmixeddata=3D yield method=3D Type3;=
=0Aclassenv Block Tillplc Prate Krate ;=0Amodelyield =3D Tillplc|Prate|Krat=
e/ddfm=3Dkr;=0Arandomenv block(env) =0Aenv*tillplc =0Atillplc*block(env)=0A=
env*Prate =0Aenv*tillplc*Prate =0Atillplc*Prate*block(env)=0Aenv*Krate =0Ae=
nv*tillplc*Krate =0Aenv*Prate*Krate =0Aenv*tillplc*Prate*Krate ;=0Alsmeanst=
illplc/adjust=3Dtukey;=0Alsmeansprate/adjust=3Dtukey;=0Alsmeanskrate/adjust=
=3Dtukey;=0Arun; =0Aquit;=0A =0AHelp required on repeated measures:-=0A=0AI=
have data on soil properties from four consective depths at two different =
times of the year. Do I need to check UN, CS, AR(1), AR(1)+RE, and TOEP str=
uctures and see which one give lower values of AIC, AICC and BIC. As this i=
s a complex experiment so I don't think it would be feasible to visualize p=
atterns of correlation between observations at different times.=0A =0ASimil=
arly, I have data of tissue analysis at various times of the year and I wan=
t to analyze it for repeated measures.=0A =0AI have never done the repeated=
measures but have studied in the course so little confused to put my knowl=
edge in to practical experience.=0A =0AThanks in advance=0ABhupinder=0A=0A_=
_______________________________=0A From: Susan Durham <***@BIOLOGY.USU.=
EDU>=0ATo: SAS-***@LISTSERV.UGA.EDU=0ASent: Wednesday, May 13, 2009 3:31:25 P=
M=0ASubject: Re: Split-Split-plot mixed model (problem to write random term=
s)=0A=0AOn Wed, 13 May 2009 11:47:00 -0500, Bhupinder Farmaha=0A<bhupi80sin=
***@YAHOO.CO.IN> wrote:=0A=0A>-----Original Message-----=0A>From: Susan Durh=
am [mailto:***@BIOLOGY.USU.EDU]=0A>Sent: Wednesday, May 13, 2009 11:08 =
AM=0A>To: SAS-***@LISTSERV.UGA.EDU; Bhupinder Farmaha=0A>Cc: Susan Durham=0A>=
Subject: Re: Split-Split-plot mixed model (problem to write random terms)=
=0A>=0A>On Mon, 11 May 2009 01:39:59 -0500, Bhupinder Farmaha=0A><bhupi80si=
***@YAHOO.CO.IN> wrote:=0A>=0A>>Hi Susan and SAS group=0A>>=0A>>I am hereby=
writing the full model I have written for my study. In this=0A>>model Y=3D=
yield E=3Denv, B=3Dblock, T=3Dtillage, P=3Dphosphorus, K=3Dpotassium, and=
=0A>>Err=3Derror term. Env and blocks are random terms while all other thre=
e=0A>>factors are fixed.=0A>>=0A>>Ylmijk =3D =C3=AF=C2=BF=C2=BD + El + B(l)=
m + Ti + ETli + Err1[BT(l)mi] +/ Pj + EPlj + TPij +=0A>>ETPlij + Err2[BP(l)=
mj + BTP(l)mij]=0A>>288 1 1 4 2 2 8 =
3=0A>>3 6 6 36=0A>>+/ Kk + EKlk + TKik + E=
TKljk + PKjk + EPKljk + TPKijk + ETPKlijk +=0A>>Err3[BK(l)mk + BTK(l)mik + =
BPK(l)mjk + BPTK(l)mijk=0A>> 3 3 6 6 9 =
9 18=0A>>18 144=0A>>=0A>>=0A>>I think this model sh=
ould use following terms to test the effects and their=0A>>interactions.=0A=
j , TPij & ETPlij will be tested by Err2=0A>>Kk , EKlk , TKik , ETKljk , PK=
jk , EPKljk , TPKijk & ETPKlijk will be tested=0A>>by Err3.=0A>>=0A>>=0A>>S=
AS coding for this is:-=0A>>=0A>>Options ps=3D50 ls=3D74 pageno=3D1;=0A>>DA=
TA Soybean_yield;=0A>>Infile "F:\Sp_project.csv" delimiter=3D"," firstobs=
=3D2;=0A>>Input Year location env Plot_no Block Tillplc$ Prate$ Krate$ Yiel=
d;=0A>>cards;=0A>>=0A>>run;;=0A>>proc mixed data =3D soybean_yield method =
=3D Type3;=0A>>class env Block Tillplc Prate Krate ;=0A>>model yield =3D Ti=
llplc|Prate|Krate/ddfm=3Dkr;=0A>>random env block(env)=0A>>env*tillplc=0A>>=
tillplc*block(env)=0A>>env*Prate=0A>>env*tillplc*Prate=0A>>tillplc*Prate*bl=
ock(env)=0A>>env*Krate=0A>>env*tillplc*Krate=0A>>env*Prate*Krate=0A>>env*ti=
llplc*Prate*Krate ;=0A>>lsmeans tillplc/adjust =3Dtukey;=0A>>lsmeans prate/=
adjust =3Dtukey;=0A>>lsmeans krate/adjust =3Dtukey;=0A>>run;=0A>>quit;=0A>>=
=0A>>Could you guys please help me to find errors in this model and validat=
e=0A>>through SAS that correct errors terms are used to test the main effec=
ts and=0A>>their interactions.=0A>>=0A>>Thanks=0A>>Bhupinder=0A>>=0A>>-----=
Original Message-----=0A>>From: Susan Durham [mailto:***@BIOLOGY.USU.ED=
U]=0A>>Sent: Sunday, May 10, 2009 8:41 PM=0A>>To: SAS-***@LISTSERV.UGA.EDU; B=
hupinder Farmaha=0A>>Cc: Susan Durham=0A>>Subject: Re: Split-Split-plot mix=
ed model (problem to write random terms)=0A>>=0A>>On Fri, 8 May 2009 22:26:=
riables on soybean yield.=0A>>>=0A>>>I have RCBD with split-split-plot arra=
ngement. I have two different=0A>>>environments (random) and blocks (random=
) are nested within the=0A>>environment.=0A>>>Main plots are tillage (3 lev=
els), first split is Phosphorus (4 levels) and=0A>>>second split is Potassi=
um (4 levels). Tillage, Phosphorus and potassium are=0A>>>fixed effects.=0A=
=0A>>>=0A>>>=0A>>>Options ps=3D50 ls=3D74 pageno=3D1;=0A>>>DATA Soybean_yie=
ld;=0A>>>Infile "F:\Sp_project.csv" delimiter=3D"," firstobs=3D2;=0A>>>Inpu=
t Year location env Plot_no Block Tillplc$ Prate$ Krate$ Yield;=0A>>>cards;=
=0A>>>run;;=0A>>>=0A>>>proc mixed data =3D soybean_yield method =3D type3;=
=0A>>>class env Block env Tillplc Prate Krate Yield;=0A>>>model yield =3D T=
illplc|Prate|Krate/ddfm=3Dkr;=0A>>>=0A>>>random env block(env)=0A>>>env*til=
lplc tillplc*block(env) env*Prate env*tillplc*Prate=0A>>>tillplc*Prate*bloc=
k(env)=0A>>>env*Krate env*tillplc*Krate env*Prate*Krate env*tillplc*Prate*K=
rate ;=0A>>>run; quit;=0A>>>=0A>>>Any help will be much appreciated.=0A>>>=
=0A>>>Thanks=0A>>>=0A>>>Bhupinder=0A>>=0A>>Hi Bhupinder,=0A>>=0A>>The most =
obvious problem is that your response variable YIELD is listed in=0A>>the C=
LASS statement. The response variable cannot be a classification=0A>>facto=
r in the MIXED procedure.=0A>>=0A>>As a second issue, the choice of terms i=
n the RANDOM statement is puzzling.=0A>> If a study is a "true" split-plot =
where treatments are randomly assigned to=0A>>experimental units, random te=
rms within a hierarchical level (i.e., whole=0A>>plot, subplot, sub-subplot=
) of the design are often (but not always) pooled.=0A>> You have an odd com=
bination of terms; you include some that I might pool=0A>>into other terms =
and omit some that I probably would include.=0A>>=0A>>If you'd like feedbac=
k from the SAS-L group about the RANDOM statement,=0A>>you'll want to provi=
de more detailed information about your study, including=0A>>why you're spe=
cifying your RANDOM statement this way.=0A>>=0A>>Hope this helps,=0A>>Susan=
=0A>>=0A>>~~~=0A>>Susan Durham=0A>>Utah State University=0A>>Ecology Center=
=0A>=0A>Hi Bhupinder,=0A>=0A>In my experience, having both ENV and BLOCK(EN=
V) as random-effects factors=0A>in a study like yours generates statistical=
tests that can be, at first=0A>look, non-intuitive. Hopefully, we can res=
olve any apparent confusion by=0A>thinking about the scope of inference for=
the study.=0A>=0A>I'm assuming that this is an agricultural field study, d=
one in two different=0A>locations (i.e., ENVs). Let me know if this is not=
the case. Regardless,=0A>the comments below are pertinent.=0A>=0A>If you =
were to analyze the data for each ENV level separately, BLOCK would=0A>serv=
e as the replicating factor, and error terms (and denominator degrees of=0A=
al=0A>treatments, you would add another BLOCK (i.e., you would add another=
=0A>replicate). In this scenario, BLOCKs are assumed to be a random sample=
, and=0A>as such, BLOCKs delineate the scope of inference--the statistical =
population=0A>to which inference is made--for the analysis. For your study=
, the scope of=0A>inference would be limited to the particular environment =
in which the blocks=0A>were located.=0A>=0A>Now say that you expand the sco=
pe of inference and that you consider the=0A>levels of ENV to be a random s=
ample from a larger statistical population.=0A>Notice that you have changed=
the scale and nature of your scope of=0A>inference. ENV is now the replic=
ating factor: if you wanted more=0A>independent information about this lar=
ger statistical population, you would=0A>add another ENV. You would not ge=
t more information by adding another=0A>BLOCK, because additional BLOCKs on=
ly give more information about the same=0A>ENV; in other words, BLOCKs are =
subsamples, not replicates. In this=0A>scenario, error terms (and denomina=
tor degrees of freedom) would be defined=0A>by interactions of the fixed-ef=
fects factors and ENV; with only two levels=0A>of ENV (i.e., two replicates=
), the denominator df for fixed-effects tests=0A>will be small.=0A>=0A>Your=
MIXED procedure code is pooling terms in accordance with your=0A>mathemati=
cal model. But I think you are finding that tests of fixed effects=0A>are =
not using the error terms that you had intended. Rather than reflecting=0A=
the=0A>METHOD=3DTYPE3 option that you've specified, if you haven't already.=
So your=0A>code is doing "a" right thing, but it might not be "the" right=
thing, and=0A>it's probably not what you had intended it to do.=0A>=0A>Wha=
t is "the" right thing? Without knowing more about the details of your=0A>=
study design (especially, what ENV represents, spatial layout, etc.), I=0A>=
can't offer a definite opinion. But here's a short list of possible=0Aappr=
oaches:=0A>1. Use ENV as a random-effects replicating factor, with BLOCK as=
a=0A>random-effects subsample factor. With only two levels of ENV, this a=
pproach=0A>could limited, both by the extent to which two environments repr=
esent the=0A>statistical population of environments and by the imprecision =
of variance=0A>estimates.=0A>2. Use ENV as a fixed-effects treatment factor=
, with BLOCK as a=0A>random-effects replicating factor. This approach rest=
ricts statistical=0A>inference to just the two environments used in the stu=
dy.=0A>3. Do separate analyses for each level of ENV with BLOCK as a random=
-effects=0A>replicating factor. This approach does not include statistical=
comparisons=0A>between ENVs.=0A>=0A>The following two references dive a bi=
t deeper into multi-location analysis:=0A>=0A>Littell, RC; Stroup, WW; and =
Freund, RJ. 2002. SAS for Linear Models, 4th=0A>ed. SAS Press. See Sect=
ion 11.8.=0A>Littell, RC; Milliken, GA; Stroup, WW; Wolfinger, RD; and Scha=
benberger, O.=0A> 2006. SAS for Mixed Models, 2nd ed. See p8 and Sections=
6.6 and 6.7.=0A>=0A>Hope this helps!=0A>Susan=0A>=0A>Hello Susan=0A>=0A>Th=
anks for spending time and made through look at my experiment. Here, I am=
=0Aproviding more information that may help you to guide me better. This is=
an=0Aagricultural experiment and response and rate variables are same as I=
have=0Aspecified here in the heading. There are two adjacent fields in the=
study.=0AFirst year, experiment was conducted on field I and second year c=
onducted on=0Afield II. The reason being for different fields is that corn =
and soybean=0Awere rotated. This study is of soybean only. I am dong with t=
wo years of=0Aexperiment. In the third year, soybean will be planted back o=
n field I. The=0Atreatments will be applied in the same fashion as was desi=
gned originally no=0Amatter what is the crop and year. I have a made env as=
random variable and=0Ait is product of year*location. Blocks, year and env=
are all random=0Avariables. I understand that env * main effects will be m=
y error terms for=0Atesting. But looking at the results of this simulation,=
it made me feel that=0Athere might be something wrong that I am unable to =
catch. I was thinking=0Athat as we do pooling of error terms, the same way =
I might have to pool the=0Arandom terms. These are few confusions that are =
bothering me. I have already=0Ataken the help of both references you have m=
entioned but still I have the=0Aabove doubts in my mind.=0A>=0A>Thanks=0A>B=
hupinder=0A=0A=0AHi Bhupinder,=0A=0AWhat specifically do you see in the res=
ults that causes you to be concerned?=0A=0ACheers,=0ASusan=0A=0A=0A
not sure if it is correct or not so need the help of experienced person who=
can just make a look and tell me if it is right or wrong. I am little conf=
used over the error terms generated by the model. =0A =0AOptionsps=3D50ls=
=3D74pageno=3D1;=0ADATAyield;=0AInfile"E:\Try-Yield\Sp_project.csv"delimite=
r=3D","firstobs=3D2;=0AInputYear location env Plot_no Block Tillplc$ Prate$=
Krate$ Yield;=0Acards;=0Arun;;=0Aprocmixeddata=3D yield method=3D Type3;=
=0Aclassenv Block Tillplc Prate Krate ;=0Amodelyield =3D Tillplc|Prate|Krat=
e/ddfm=3Dkr;=0Arandomenv block(env) =0Aenv*tillplc =0Atillplc*block(env)=0A=
env*Prate =0Aenv*tillplc*Prate =0Atillplc*Prate*block(env)=0Aenv*Krate =0Ae=
nv*tillplc*Krate =0Aenv*Prate*Krate =0Aenv*tillplc*Prate*Krate ;=0Alsmeanst=
illplc/adjust=3Dtukey;=0Alsmeansprate/adjust=3Dtukey;=0Alsmeanskrate/adjust=
=3Dtukey;=0Arun; =0Aquit;=0A =0AHelp required on repeated measures:-=0A=0AI=
have data on soil properties from four consective depths at two different =
times of the year. Do I need to check UN, CS, AR(1), AR(1)+RE, and TOEP str=
uctures and see which one give lower values of AIC, AICC and BIC. As this i=
s a complex experiment so I don't think it would be feasible to visualize p=
atterns of correlation between observations at different times.=0A =0ASimil=
arly, I have data of tissue analysis at various times of the year and I wan=
t to analyze it for repeated measures.=0A =0AI have never done the repeated=
measures but have studied in the course so little confused to put my knowl=
edge in to practical experience.=0A =0AThanks in advance=0ABhupinder=0A=0A_=
_______________________________=0A From: Susan Durham <***@BIOLOGY.USU.=
EDU>=0ATo: SAS-***@LISTSERV.UGA.EDU=0ASent: Wednesday, May 13, 2009 3:31:25 P=
M=0ASubject: Re: Split-Split-plot mixed model (problem to write random term=
s)=0A=0AOn Wed, 13 May 2009 11:47:00 -0500, Bhupinder Farmaha=0A<bhupi80sin=
***@YAHOO.CO.IN> wrote:=0A=0A>-----Original Message-----=0A>From: Susan Durh=
am [mailto:***@BIOLOGY.USU.EDU]=0A>Sent: Wednesday, May 13, 2009 11:08 =
AM=0A>To: SAS-***@LISTSERV.UGA.EDU; Bhupinder Farmaha=0A>Cc: Susan Durham=0A>=
Subject: Re: Split-Split-plot mixed model (problem to write random terms)=
=0A>=0A>On Mon, 11 May 2009 01:39:59 -0500, Bhupinder Farmaha=0A><bhupi80si=
***@YAHOO.CO.IN> wrote:=0A>=0A>>Hi Susan and SAS group=0A>>=0A>>I am hereby=
writing the full model I have written for my study. In this=0A>>model Y=3D=
yield E=3Denv, B=3Dblock, T=3Dtillage, P=3Dphosphorus, K=3Dpotassium, and=
=0A>>Err=3Derror term. Env and blocks are random terms while all other thre=
e=0A>>factors are fixed.=0A>>=0A>>Ylmijk =3D =C3=AF=C2=BF=C2=BD + El + B(l)=
m + Ti + ETli + Err1[BT(l)mi] +/ Pj + EPlj + TPij +=0A>>ETPlij + Err2[BP(l)=
mj + BTP(l)mij]=0A>>288 1 1 4 2 2 8 =
3=0A>>3 6 6 36=0A>>+/ Kk + EKlk + TKik + E=
TKljk + PKjk + EPKljk + TPKijk + ETPKlijk +=0A>>Err3[BK(l)mk + BTK(l)mik + =
BPK(l)mjk + BPTK(l)mijk=0A>> 3 3 6 6 9 =
9 18=0A>>18 144=0A>>=0A>>=0A>>I think this model sh=
ould use following terms to test the effects and their=0A>>interactions.=0A=
=0A>>El, Ti & ETli =C3=AF=C2=BF=C2=BD will be tested by Err1=0A>>Pj , EPl=
jk , EPKljk , TPKijk & ETPKlijk will be tested=0A>>by Err3.=0A>>=0A>>=0A>>S=
AS coding for this is:-=0A>>=0A>>Options ps=3D50 ls=3D74 pageno=3D1;=0A>>DA=
TA Soybean_yield;=0A>>Infile "F:\Sp_project.csv" delimiter=3D"," firstobs=
=3D2;=0A>>Input Year location env Plot_no Block Tillplc$ Prate$ Krate$ Yiel=
d;=0A>>cards;=0A>>=0A>>run;;=0A>>proc mixed data =3D soybean_yield method =
=3D Type3;=0A>>class env Block Tillplc Prate Krate ;=0A>>model yield =3D Ti=
llplc|Prate|Krate/ddfm=3Dkr;=0A>>random env block(env)=0A>>env*tillplc=0A>>=
tillplc*block(env)=0A>>env*Prate=0A>>env*tillplc*Prate=0A>>tillplc*Prate*bl=
ock(env)=0A>>env*Krate=0A>>env*tillplc*Krate=0A>>env*Prate*Krate=0A>>env*ti=
llplc*Prate*Krate ;=0A>>lsmeans tillplc/adjust =3Dtukey;=0A>>lsmeans prate/=
adjust =3Dtukey;=0A>>lsmeans krate/adjust =3Dtukey;=0A>>run;=0A>>quit;=0A>>=
=0A>>Could you guys please help me to find errors in this model and validat=
e=0A>>through SAS that correct errors terms are used to test the main effec=
ts and=0A>>their interactions.=0A>>=0A>>Thanks=0A>>Bhupinder=0A>>=0A>>-----=
Original Message-----=0A>>From: Susan Durham [mailto:***@BIOLOGY.USU.ED=
U]=0A>>Sent: Sunday, May 10, 2009 8:41 PM=0A>>To: SAS-***@LISTSERV.UGA.EDU; B=
hupinder Farmaha=0A>>Cc: Susan Durham=0A>>Subject: Re: Split-Split-plot mix=
ed model (problem to write random terms)=0A>>=0A>>On Fri, 8 May 2009 22:26:=
Hello friends=0A>>>=0A>>>I am having hard time to find error in my SAS mix=
ed model. Here is my=0A>>>problem. I am=0A>>>looking the effect of three va=riables on soybean yield.=0A>>>=0A>>>I have RCBD with split-split-plot arra=
ngement. I have two different=0A>>>environments (random) and blocks (random=
) are nested within the=0A>>environment.=0A>>>Main plots are tillage (3 lev=
els), first split is Phosphorus (4 levels) and=0A>>>second split is Potassi=
um (4 levels). Tillage, Phosphorus and potassium are=0A>>>fixed effects.=0A=
=0A>>>I have written the following model but unable to find the error.=
ld;=0A>>>Infile "F:\Sp_project.csv" delimiter=3D"," firstobs=3D2;=0A>>>Inpu=
t Year location env Plot_no Block Tillplc$ Prate$ Krate$ Yield;=0A>>>cards;=
=0A>>>run;;=0A>>>=0A>>>proc mixed data =3D soybean_yield method =3D type3;=
=0A>>>class env Block env Tillplc Prate Krate Yield;=0A>>>model yield =3D T=
illplc|Prate|Krate/ddfm=3Dkr;=0A>>>=0A>>>random env block(env)=0A>>>env*til=
lplc tillplc*block(env) env*Prate env*tillplc*Prate=0A>>>tillplc*Prate*bloc=
k(env)=0A>>>env*Krate env*tillplc*Krate env*Prate*Krate env*tillplc*Prate*K=
rate ;=0A>>>run; quit;=0A>>>=0A>>>Any help will be much appreciated.=0A>>>=
=0A>>>Thanks=0A>>>=0A>>>Bhupinder=0A>>=0A>>Hi Bhupinder,=0A>>=0A>>The most =
obvious problem is that your response variable YIELD is listed in=0A>>the C=
LASS statement. The response variable cannot be a classification=0A>>facto=
r in the MIXED procedure.=0A>>=0A>>As a second issue, the choice of terms i=
n the RANDOM statement is puzzling.=0A>> If a study is a "true" split-plot =
where treatments are randomly assigned to=0A>>experimental units, random te=
rms within a hierarchical level (i.e., whole=0A>>plot, subplot, sub-subplot=
) of the design are often (but not always) pooled.=0A>> You have an odd com=
bination of terms; you include some that I might pool=0A>>into other terms =
and omit some that I probably would include.=0A>>=0A>>If you'd like feedbac=
k from the SAS-L group about the RANDOM statement,=0A>>you'll want to provi=
de more detailed information about your study, including=0A>>why you're spe=
cifying your RANDOM statement this way.=0A>>=0A>>Hope this helps,=0A>>Susan=
=0A>>=0A>>~~~=0A>>Susan Durham=0A>>Utah State University=0A>>Ecology Center=
=0A>=0A>Hi Bhupinder,=0A>=0A>In my experience, having both ENV and BLOCK(EN=
V) as random-effects factors=0A>in a study like yours generates statistical=
tests that can be, at first=0A>look, non-intuitive. Hopefully, we can res=
olve any apparent confusion by=0A>thinking about the scope of inference for=
the study.=0A>=0A>I'm assuming that this is an agricultural field study, d=
one in two different=0A>locations (i.e., ENVs). Let me know if this is not=
the case. Regardless,=0A>the comments below are pertinent.=0A>=0A>If you =
were to analyze the data for each ENV level separately, BLOCK would=0A>serv=
e as the replicating factor, and error terms (and denominator degrees of=0A=
freedom) would be defined by interactions of the fixed-effects factors and=
=0A>BLOCK. If you wanted more independent information about the experiment=al=0A>treatments, you would add another BLOCK (i.e., you would add another=
=0A>replicate). In this scenario, BLOCKs are assumed to be a random sample=
, and=0A>as such, BLOCKs delineate the scope of inference--the statistical =
population=0A>to which inference is made--for the analysis. For your study=
, the scope of=0A>inference would be limited to the particular environment =
in which the blocks=0A>were located.=0A>=0A>Now say that you expand the sco=
pe of inference and that you consider the=0A>levels of ENV to be a random s=
ample from a larger statistical population.=0A>Notice that you have changed=
the scale and nature of your scope of=0A>inference. ENV is now the replic=
ating factor: if you wanted more=0A>independent information about this lar=
ger statistical population, you would=0A>add another ENV. You would not ge=
t more information by adding another=0A>BLOCK, because additional BLOCKs on=
ly give more information about the same=0A>ENV; in other words, BLOCKs are =
subsamples, not replicates. In this=0A>scenario, error terms (and denomina=
tor degrees of freedom) would be defined=0A>by interactions of the fixed-ef=
fects factors and ENV; with only two levels=0A>of ENV (i.e., two replicates=
), the denominator df for fixed-effects tests=0A>will be small.=0A>=0A>Your=
MIXED procedure code is pooling terms in accordance with your=0A>mathemati=
cal model. But I think you are finding that tests of fixed effects=0A>are =
not using the error terms that you had intended. Rather than reflecting=0A=
BLOCKs as replicates, the error terms are using ENVs as replicates. You=
=0A>could verify this by looking at the Expected Mean Squares generated by =the=0A>METHOD=3DTYPE3 option that you've specified, if you haven't already.=
So your=0A>code is doing "a" right thing, but it might not be "the" right=
thing, and=0A>it's probably not what you had intended it to do.=0A>=0A>Wha=
t is "the" right thing? Without knowing more about the details of your=0A>=
study design (especially, what ENV represents, spatial layout, etc.), I=0A>=
can't offer a definite opinion. But here's a short list of possible=0Aappr=
oaches:=0A>1. Use ENV as a random-effects replicating factor, with BLOCK as=
a=0A>random-effects subsample factor. With only two levels of ENV, this a=
pproach=0A>could limited, both by the extent to which two environments repr=
esent the=0A>statistical population of environments and by the imprecision =
of variance=0A>estimates.=0A>2. Use ENV as a fixed-effects treatment factor=
, with BLOCK as a=0A>random-effects replicating factor. This approach rest=
ricts statistical=0A>inference to just the two environments used in the stu=
dy.=0A>3. Do separate analyses for each level of ENV with BLOCK as a random=
-effects=0A>replicating factor. This approach does not include statistical=
comparisons=0A>between ENVs.=0A>=0A>The following two references dive a bi=
t deeper into multi-location analysis:=0A>=0A>Littell, RC; Stroup, WW; and =
Freund, RJ. 2002. SAS for Linear Models, 4th=0A>ed. SAS Press. See Sect=
ion 11.8.=0A>Littell, RC; Milliken, GA; Stroup, WW; Wolfinger, RD; and Scha=
benberger, O.=0A> 2006. SAS for Mixed Models, 2nd ed. See p8 and Sections=
6.6 and 6.7.=0A>=0A>Hope this helps!=0A>Susan=0A>=0A>Hello Susan=0A>=0A>Th=
anks for spending time and made through look at my experiment. Here, I am=
=0Aproviding more information that may help you to guide me better. This is=
an=0Aagricultural experiment and response and rate variables are same as I=
have=0Aspecified here in the heading. There are two adjacent fields in the=
study.=0AFirst year, experiment was conducted on field I and second year c=
onducted on=0Afield II. The reason being for different fields is that corn =
and soybean=0Awere rotated. This study is of soybean only. I am dong with t=
wo years of=0Aexperiment. In the third year, soybean will be planted back o=
n field I. The=0Atreatments will be applied in the same fashion as was desi=
gned originally no=0Amatter what is the crop and year. I have a made env as=
random variable and=0Ait is product of year*location. Blocks, year and env=
are all random=0Avariables. I understand that env * main effects will be m=
y error terms for=0Atesting. But looking at the results of this simulation,=
it made me feel that=0Athere might be something wrong that I am unable to =
catch. I was thinking=0Athat as we do pooling of error terms, the same way =
I might have to pool the=0Arandom terms. These are few confusions that are =
bothering me. I have already=0Ataken the help of both references you have m=
entioned but still I have the=0Aabove doubts in my mind.=0A>=0A>Thanks=0A>B=
hupinder=0A=0A=0AHi Bhupinder,=0A=0AWhat specifically do you see in the res=
ults that causes you to be concerned?=0A=0ACheers,=0ASusan=0A=0A=0A