1
***********************************************;
2
*** Finish times in a 10 K race
***;
3
*** Data taken from various sites on the ***;
4
*** internet reporting race results
***;
5
***********************************************;
6
options ps=256 ls=80 nocenter nodate nonumber;
7
8
data one; length hometown $ 23 sex $ 3;
9
infile
9 !
"C:\Geaghan\EXST\EXST7015New\Spring2003\SAS\12q-MReg-Polynomial
9 ! Marathons.DAT" missover;
10
TITLE1 'EXST7015: Marathon Footrace Example';
11
input Marathon $ Age Sex $ TIME HomeTown $ 35-57;
12
if age eq 99 then age = .;
13
*(apparently 99 represents missing for 5 PA race participants);
14
*---+----1----+----2----+----3----+----4----+----5----+----6;
15
cards;
NOTE: The infile
"C:\Geaghan\EXST\EXST7015New\Spring2003\SAS\12q-MReg-Polynomial
Marathons.DAT" is:
File
Name=C:\Geaghan\EXST\EXST7015New\Spring2003\SAS\12q-MReg-Polynomial
Marathons.DAT,
RECFM=V,LRECL=256
NOTE: 6150 records were read from the infile
"C:\Geaghan\EXST\EXST7015New\Spring2003\SAS\12q-MReg-Polynomial
Marathons.DAT".
The
minimum record length was 29.
The
maximum record length was 57.
NOTE: The data set WORK.ONE has 6150 observations
and 5 variables.
NOTE: DATA statement used:
real
time 0.19
seconds
cpu
time
0.14 seconds
15
! run;
16
;
17
18
data two; set one; if marathon = 'VT052002';
NOTE: There were 6150 observations read from the
data set WORK.ONE.
NOTE: The data set WORK.TWO has 1490 observations
and 5 variables.
NOTE: DATA statement used:
real
time 0.05
seconds
cpu
time
0.05 seconds
19
proc sort data=two; by sex; RUN;
NOTE: There were 1490 observations read from the
data set WORK.TWO.
NOTE: The data set WORK.TWO has 1490 observations
and 5 variables.
NOTE: PROCEDURE SORT used:
real
time 0.07
seconds
cpu
time
0.07 seconds
20
21
proc mixed data=two method=type1; BY sex;
22
TITLE2 'Quartic model - separate by sex';
23
model time= age age*age age*age*age age*age*age*age
24
/ htype=1 3
DDFM=Satterthwaite
solution;
25
run;
NOTE: The PROCEDURE MIXED printed pages 1-2.
NOTE: PROCEDURE MIXED used:
real
time 0.13
seconds
cpu
time
0.12 seconds
EXST7015:
Marathon Footrace Example
Quartic model
- separate by sex
sex=F
The Mixed
Procedure
Model Information
Data
Set
WORK.TWO
Dependent
Variable
TIME
Covariance
Structure
Diagonal
Estimation
Method
Type
1
Residual
Variance Method
Factor
Fixed Effects
SE Method
Model-Based
Degrees of
Freedom Method
Residual
Dimensions
Covariance
Parameters
1
Columns in
X
5
Columns in
Z
0
Subjects
1
Max Obs Per
Subject
527
Observations
Used
527
Observations
Not
Used
0
Total
Observations
527
Type 1
Analysis of Variance
Sum
of
Error
Source
DF Squares
Mean Square Expected Mean
Square
Error Term
DF
F Value Pr > F
Age
1 4869.217307
4869.217307 Var(Residual)
+
MS(Residual)
522
8.34 0.0040
Q(Age,Age*Age,Age*Age* Age,Age*Age*Age*Age)
Age*Age
1 3535.615012
3535.615012 Var(Residual)
+
MS(Residual)
522
6.06 0.0142
Q(Age*Age,Age*Age*Age, Age*Age*Age*Age)
Age*Age*Age
1
262.700283 262.700283 Var(Residual)
+
MS(Residual)
522
0.45 0.5026
Q(Age*Age*Age,Age*Age*Age*Age)
Age*Age*Age*Age
1
1.495088 1.495088 Var(Residual) +
Q(Age*Age*Age*Age)
MS(Residual)
522
0.00 0.9597
Residual
522 304684
583.686674
Var(Residual)
.
. .
.
Covariance
Parameter Estimates
Cov
Parm Estimate
Residual
583.69
Fit Statistics
-2 Res Log
Likelihood
4884.3
AIC (smaller
is better)
4886.3
AICC (smaller
is better)
4886.3
BIC (smaller
is better)
4890.5
Solution for
Fixed Effects
Standard
Effect
Estimate
Error DF
t Value Pr > |t|
Intercept
294.52 128.80
522
2.29 0.0226
Age
-3.6313 14.4413
522 -0.25
0.8016
Age*Age
0.07038 0.5872
522
0.12
0.9046
Age*Age*Age
-0.00010 0.01026
522 -0.01
0.9922
Age*Age*Age*Age
-3.3E-6 0.000065
522 -0.05
0.9597
Type 1 Tests
of Fixed Effects
Num Den
Effect
DF DF
F Value Pr > F
Age
1 522
8.34 0.0040
Age*Age
1 522
6.06 0.0142
Age*Age*Age
1 522
0.45 0.5026
Age*Age*Age*Age
1 522
0.00 0.9597
Type 3 Tests
of Fixed Effects
Num Den
Effect
DF DF
F Value Pr > F
Age
1 522
0.06 0.8016
Age*Age
1 522
0.01 0.9046
Age*Age*Age
1 522
0.00 0.9922
Age*Age*Age*Age
1 522
0.00 0.9597
EXST7015:
Marathon Footrace Example
Quartic model
- separate by sex
sex=M
The Mixed
Procedure
Model Information
Data
Set
WORK.TWO
Dependent
Variable
TIME
Covariance
Structure
Diagonal
Estimation
Method
Type
1
Residual
Variance Method
Factor
Fixed Effects
SE Method
Model-Based
Degrees of
Freedom Method
Residual
Dimensions
Covariance
Parameters
1
Columns in
X
5
Columns in
Z
0
Subjects
1
Max Obs Per
Subject
963
Observations
Used
963
Observations
Not
Used
0
Total
Observations
963
Type 1
Analysis of
Variance
Sum
of
Error
Source
DF Squares
Mean Square Expected Mean
Square
Error Term
DF
F Value Pr > F
Age
1
18395 18395
Var(Residual)
+
MS(Residual) 958
22.06
<.0001
Q(Age,Age*Age,Age*Age* Age,Age*Age*Age*Age)
Age*Age
1
13295 13295
Var(Residual)
+
MS(Residual) 958
15.95
<.0001
Q(Age*Age,Age*Age*Age,
Age*Age*Age*Age)
Age*Age*Age
1
170.139126 170.139126 Var(Residual)
+
MS(Residual)
958
0.20 0.6516
Q(Age*Age*Age,Age*Age*Age*Age)
Age*Age*Age*Age
1
381.349352 381.349352 Var(Residual) +
Q(Age*Age*Age*Age)
MS(Residual)
958
0.46 0.4990
Residual
958 798683
833.698204
Var(Residual)
.
.
. .
Covariance
Parameter Estimates
Cov
Parm Estimate
Residual
833.70
Fit Statistics
-2 Res Log
Likelihood
9244.6
AIC (smaller
is better)
9246.6
AICC (smaller
is better)
9246.6
BIC (smaller
is better) 9251.4
Solution for
Fixed Effects
Standard
Effect
Estimate
Error DF
t Value Pr > |t|
Intercept
163.89 130.38
958
1.26 0.2091
Age
8.0558 13.5596
958
0.59 0.5526
Age*Age
-0.3437 0.5108
958 -0.67
0.5012
Age*Age*Age
0.005870 0.008273
958
0.71 0.4782
Age*Age*Age*Age
-0.00003 0.000049
958 -0.68
0.4990
Type 1 Tests
of Fixed Effects
Num Den
Effect
DF DF
F Value Pr > F
Age
1 958
22.06 <.0001
Age*Age
1 958
15.95 <.0001
Age*Age*Age
1 958
0.20 0.6516
Age*Age*Age*Age
1 958
0.46 0.4990
Type 3 Tests
of Fixed Effects
Num Den
Effect
DF DF
F Value Pr > F
Age
1 958
0.35 0.5526
Age*Age
1
958 0.45 0.5012
Age*Age*Age
1 958
0.50 0.4782
Age*Age*Age*Age
1 958
0.46 0.4990
Modified: August 16, 2004
James P. Geaghan