When random effects exists, why are the results same from proc mixed and proc glm procedure

annaliseshen — Fri, 13 Jan 2017 21:04:49 GMT

When random effects exists, why are the results same from proc mixed and proc glm procedure ?

Say,This is a nonreplicated two-way cross-over study.

random effects is subject nested in sequence; fixed effects are treatment, sequence, period .

I mocked balanced data to try the proc mixed and proc glm , and find the same coefficient estimate there.

My main question is that as we know the

proc mixed treats random effect :subject within sequence as random effect

and

proc glm treats random effect as fixed effect.

Why for balanced data , they will produce the same result ?????

what is the rationale behind it. I have googled a lot of information, none of them provide me specific information.

So, if you know the answer, please help me! Thanks in advance .

The SAS DATASET, CODE AND RESULT are attached blow. (This is a mock).

DATA TRY;
INPUT SUBJECT$ TREATMENT$ PERIOD SEQUENCE CONC;

DATALINES;
001 A 1 1 2.90
002 A 1 1 3.14
003 A 1 1 3.49
004 A 1 1 5.28
005 B 1 2 2.39
006 B 1 2 3.7
007 A 1 1 3.68
008 B 1 2 1.8
009 B 1 2 2.28
010 B 1 2 2.44
001 B 2 1 2.65
002 B 2 1 1.96
003 B 2 1 3.18
004 B 2 1 3.66
005 A 2 2 3.83
006 A 2 2 4.62
007 B 2 1 2.22
008 A 2 2 3.5
009 A 2 2 1.76
010 A 2 2 4.88
;
RUN;

ods output lsmeans=result2;
ods output lsmeandiffcl=result1;
ods output overallanova=result3;
/*****/PROC GLM DATA=TRY;
CLASS TREATMENT PERIOD SEQUENCE SUBJECT;
MODEL CONC=TREATMENT PERIOD SEQUENCE SUBJECT(SEQUENCE)/SOLUTION;
RANDOM SUBJECT(SEQUENCE);
LSMEANS TREATMENT/STDERR PDIFF=control("A","B") CL ALPHA=0.1 ADJUST=T;
RUN;

/***/
ods output Estimates=result1;
ods output LSMeans=result2 ;
ods output Diffs=result3 ;
PROC MIXED DATA=TRY;
CLASS TREATMENT PERIOD SEQUENCE SUBJECT;
MODEL CONC=TREATMENT PERIOD SEQUENCE/SOLUTION;
RANDOM SUBJECT(SEQUENCE);
LSMEANS TREATMENT/PDIFF=control("A","B") CL ALPHA=0.1 ;
RUN;

The SAS System

The GLM Procedure

Class Level Information
Class	Levels	Values
TREATMENT	2	A B
PERIOD	2	1 2
SEQUENCE	2	1 2
SUBJECT	10	001 002 003 004 005 006 007 008 009 010

Number of Observations Read	20
Number of Observations Used	20

The SAS System

The GLM Procedure

Dependent Variable: CONC

Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	11	16.14470000	1.46770000	3.59	0.0402
Error	8	3.27122000	0.40890250
Corrected Total	19	19.41592000

R-Square	Coeff Var	Root MSE	CONC Mean
0.831519	20.18481	0.639455	3.168000

Source	DF	Type I SS	Mean Square	F Value	Pr > F
TREATMENT	1	5.83200000	5.83200000	14.26	0.0054
PERIOD	1	0.06728000	0.06728000	0.16	0.6956
SEQUENCE	1	0.04608000	0.04608000	0.11	0.7457
SUBJECT(SEQUENCE)	8	10.19934000	1.27491750	3.12	0.0641

Source	DF	Type III SS	Mean Square	F Value	Pr > F
TREATMENT	1	5.83200000	5.83200000	14.26	0.0054
PERIOD	1	0.06728000	0.06728000	0.16	0.6956
SEQUENCE	1	0.04608000	0.04608000	0.11	0.7457
SUBJECT(SEQUENCE)	8	10.19934000	1.27491750	3.12	0.0641

Parameter	Estimate		Standard Error	t Value	Pr > \|t\|
Intercept	3.178000000	B	0.49531959	6.42	0.0002
TREATMENT A	1.080000000	B	0.28597290	3.78	0.0054
TREATMENT B	0.000000000	B	.	.	.
PERIOD 1	-0.116000000	B	0.28597290	-0.41	0.6956
PERIOD 2	0.000000000	B	.	.	.
SEQUENCE 1	-0.710000000	B	0.63945485	-1.11	0.2991
SEQUENCE 2	0.000000000	B	.	.	.
SUBJECT(SEQUENCE) 001 1	-0.175000000	B	0.63945485	-0.27	0.7913
SUBJECT(SEQUENCE) 002 1	-0.400000000	B	0.63945485	-0.63	0.5490
SUBJECT(SEQUENCE) 003 1	0.385000000	B	0.63945485	0.60	0.5638
SUBJECT(SEQUENCE) 004 1	1.520000000	B	0.63945485	2.38	0.0448
SUBJECT(SEQUENCE) 007 1	0.000000000	B	.	.	.
SUBJECT(SEQUENCE) 005 2	-0.550000000	B	0.63945485	-0.86	0.4148
SUBJECT(SEQUENCE) 006 2	0.500000000	B	0.63945485	0.78	0.4568
SUBJECT(SEQUENCE) 008 2	-1.010000000	B	0.63945485	-1.58	0.1529
SUBJECT(SEQUENCE) 009 2	-1.640000000	B	0.63945485	-2.56	0.0334
SUBJECT(SEQUENCE) 010 2	0.000000000	B	.	.	.

Note:

The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by the letter 'B' are not uniquely estimable.

The SAS System

The GLM Procedure

Source	Type III Expected Mean Square
TREATMENT	Var(Error) + Q(TREATMENT)
PERIOD	Var(Error) + Q(PERIOD)
SEQUENCE	Var(Error) + 2 Var(SUBJECT(SEQUENCE)) + Q(SEQUENCE)
SUBJECT(SEQUENCE)	Var(Error) + 2 Var(SUBJECT(SEQUENCE))

The SAS System

The GLM Procedure

Least Squares Means

TREATMENT	CONC LSMEAN	Standard Error	H0:LSMEAN=0	H0:LSMean1=LSMean2
Pr > \|t\|	Pr > \|t\|
A	3.70800000	0.20221338	<.0001	0.0054
B	2.62800000	0.20221338	<.0001

TREATMENT	CONC LSMEAN	90% Confidence Limits
A	3.708000	3.331975	4.084025
B	2.628000	2.251975	3.004025

Least Squares Means for Effect TREATMENT
i	j	Difference Between Means	90% Confidence Limits for LSMean(i)-LSMean(j)
2	1	-1.080000	-1.611780	-0.548220

Proc mixed

The SAS System

The Mixed Procedure

Model Information
Data Set	WORK.TRY
Dependent Variable	CONC
Covariance Structure	Variance Components
Estimation Method	REML
Residual Variance Method	Profile
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Containment

Class Level Information
Class	Levels	Values
TREATMENT	2	A B
PERIOD	2	1 2
SEQUENCE	2	1 2
SUBJECT	10	001 002 003 004 005 006 007 008 009 010

Dimensions
Covariance Parameters	2
Columns in X	7
Columns in Z	10
Subjects	1
Max Obs Per Subject	20

Number of Observations
Number of Observations Read	20
Number of Observations Used	20
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	50.47676453
1	1	48.01890254	0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm	Estimate
SUBJECT(SEQUENCE)	0.4330
Residual	0.4089

Fit Statistics
-2 Res Log Likelihood	48.0
AIC (smaller is better)	52.0
AICC (smaller is better)	52.9
BIC (smaller is better)	52.6

Solution for Fixed Effects
Effect	TREATMENT	PERIOD	SEQUENCE	Estimate	Standard Error	DF	t Value	Pr > \|t\|
Intercept				2.6380	0.4103	8	6.43	0.0002
TREATMENT	A			1.0800	0.2860	8	3.78	0.0054
TREATMENT	B			0	.	.	.	.
PERIOD		1		-0.1160	0.2860	8	-0.41	0.6956
PERIOD		2		0	.	.	.	.
SEQUENCE			1	0.09600	0.5050	8	0.19	0.8540
SEQUENCE			2	0	.	.	.	.

Type 3 Tests of Fixed Effects
Effect	Num DF	Den DF	F Value	Pr > F
TREATMENT	1	8	14.26	0.0054
PERIOD	1	8	0.16	0.6956
SEQUENCE	1	8	0.04	0.8540

Least Squares Means
Effect	TREATMENT	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
TREATMENT	A	3.7080	0.2902	8	12.78	<.0001	0.1	3.1684	4.2476
TREATMENT	B	2.6280	0.2902	8	9.06	<.0001	0.1	2.0884	3.1676

Differences of Least Squares Means
Effect	TREATMENT	_TREATMENT	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
TREATMENT	B	A	-1.0800	0.2860	8	-3.78	0.0054	0.1	-1.6118	-0.5482

topic Re: When random effects exists, why are the results same from proc mixed and proc glm procedure in Statistical Procedures

When random effects exists, why are the results same from proc mixed and proc glm procedure

Re: When random effects exists, why are the results same from proc mixed and proc glm procedure

Re: When random effects exists, why are the results same from proc mixed and proc glm procedure

Re: When random effects exists, why are the results same from proc mixed and proc glm procedure