Table 5.1 on page 78, Table 5.2 on page 79 using data file gpa.
proc glm data = gpa; class sex; model gpa1-gpa6 = sex highgpa /nouni ; repeated gpa 6 polynomial / summary; run; quit;
Repeated Measures Analysis of Variance
Manova Test Criteria and Exact F Statistics for the Hypothesis of no gpa Effect
H = Type III SSCP Matrix for gpa
E = Error SSCP Matrix
S=1 M=1.5 N=95.5
Statistic Value F Value Num DF Den DF Pr > F
Wilks' Lambda 0.89503663 4.53 5 193 0.0006
Pillai's Trace 0.10496337 4.53 5 193 0.0006
Hotelling-Lawley Trace 0.11727271 4.53 5 193 0.0006
Roy's Greatest Root 0.11727271 4.53 5 193 0.0006
Manova Test Criteria and Exact F Statistics for the Hypothesis of no gpa*SEX Effect
H = Type III SSCP Matrix for gpa*SEX
E = Error SSCP Matrix
S=1 M=1.5 N=95.5
Statistic Value F Value Num DF Den DF Pr > F
Wilks' Lambda 0.96457680 1.42 5 193 0.2196
Pillai's Trace 0.03542320 1.42 5 193 0.2196
Hotelling-Lawley Trace 0.03672408 1.42 5 193 0.2196
Roy's Greatest Root 0.03672408 1.42 5 193 0.2196
Manova Test Criteria and Exact F Statistics for the Hypothesis of no gpa*HIGHGPA Effect
H = Type III SSCP Matrix for gpa*HIGHGPA
E = Error SSCP Matrix
S=1 M=1.5 N=95.5
Statistic Value F Value Num DF Den DF Pr > F
Wilks' Lambda 0.97806928 0.87 5 193 0.5053
Pillai's Trace 0.02193072 0.87 5 193 0.5053
Hotelling-Lawley Trace 0.02242246 0.87 5 193 0.5053
Roy's Greatest Root 0.02242246 0.87 5 193 0.5053
Tests of Hypotheses for Between Subjects Effects
Source DF Type III SS Mean Square F Value Pr > F
SEX 1 7.22715867 7.22715867 18.37 <.0001
HIGHGPA 1 3.60320801 3.60320801 9.16 0.0028
Error 197 77.49355890 0.39336832
proc means data = gpa mean std N; class sex; var gpa1 - gpa6; run;
The MEANS Procedure
N
SEX Obs Variable Mean Std Dev N
--------------------------------------------------------------------------------------------------------
1 95 GPA1 2.5547368 0.3137855 95
GPA2 2.6663158 0.3177750 95
GPA3 2.7421053 0.3630776 95
GPA4 2.8178947 0.3509801 95
GPA5 2.9147368 0.3587711 95
GPA6 3.0284211 0.3752058 95
2 105 GPA1 2.6285714 0.3071940 105
GPA2 2.7600000 0.3476846 105
GPA3 2.8714286 0.3350414 105
GPA4 3.0085714 0.3354430 105
GPA5 3.1133333 0.3319716 105
GPA6 3.2295238 0.3538045 105
--------------------------------------------------------------------------------------------------------
Figure 5.3 on page 80 using data file gpachp5.
proc univariate data = gpachp5 noprint;
histogram gpa /normal vscale=count
nohlabel cfill = grey midpoints=(1.75 to 4 by .25);
inset mean std n;
run;
Table 5.3 on page 81 using data file gpa4chp5. Notice that the results for Part 3 and Part 4 are a little different from the book.
Part 1: Null model.
proc mixed data = gpachp5 covtest method = ml; model gpa = /solution; random intercept /subject = student; run;
The Mixed Procedure
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
Intercept STUDENT 0.05677 0.007339 7.73 <.0001
Residual 0.09759 0.004364 22.36 <.0001
Fit Statistics
-2 Log Likelihood 913.5
AIC (smaller is better) 919.5
AICC (smaller is better) 919.5
BIC (smaller is better) 929.4
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 2.8650 0.01911 199 149.93 <.0001
Part 2: With additional variable time which is created as follow.
proc mixed data = gpachp5 covtest method = ml; model gpa = time /solution; random intercept /subject = student; run;
The Mixed Procedure
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
Intercept STUDENT 0.06336 0.007316 8.66 <.0001
Residual 0.05803 0.002595 22.36 <.0001
Fit Statistics
-2 Log Likelihood 393.6
AIC (smaller is better) 401.6
AICC (smaller is better) 401.7
BIC (smaller is better) 414.8
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 2.5992 0.02165 199 120.05 <.0001
TIME 0.1063 0.004072 999 26.11 <.0001
Part 3: The variable job is added.
proc mixed data = gpachp5 covtest method = ml; model gpa = time job /solution; random intercept /subject = student type = un; run;
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) STUDENT 0.05336 0.006371 8.38 <.0001
Residual 0.05561 0.002494 22.30 <.0001
Fit Statistics
-2 Log Likelihood 320.3
AIC (smaller is better) 330.3
AICC (smaller is better) 330.3
BIC (smaller is better) 346.8
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 2.9458 0.04446 199 66.26 <.0001
TIME 0.1032 0.004002 998 25.78 <.0001
JOB -0.1609 0.01836 998 -8.76 <.0001
Part 4: The variable highgpa and sex are added to the model and sex should be treated as categorical variable.
proc mixed data = gpachp5 covtest method = ml; class sex; model gpa = time job highgpa sex /solution; random intercept /subject = student type=un; run;
Covariance Parameter Estimates
Standard Z Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) STUDENT 0.04576 0.005606 8.16 <.0001 Residual 0.05562 0.002495 22.29 <.0001
Fit Statistics
-2 Log Likelihood 294.5 AIC (smaller is better) 308.5 AICC (smaller is better) 308.6 BIC (smaller is better) 331.6
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
1 333.27 <.0001
Solution for Fixed Effects
student Standard Effect gender Estimate Error DF t Value Pr > |t|
Intercept 2.7618 0.09548 197 28.93 <.0001 TIME 0.1031 0.004002 998 25.77 <.0001 JOB -0.1618 0.01830 998 -8.84 <.0001 HIGHGPA 0.08584 0.02798 998 3.07 0.0022 SEX 1 -0.1484 0.03331 998 -4.45 <.0001 SEX 2 0 . . . .
Table 5.4 on page 83.
Part 1: The variable time is included as a random effect.
proc mixed data = gpachp5 covtest method = ml; class sex; model gpa = time job highgpa sex /solution; random intercept time/subject = student type=un; run;
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) STUDENT 0.03897 0.006221 6.26 <.0001
UN(2,1) STUDENT -0.00256 0.001558 -1.65 0.0999
UN(2,2) STUDENT 0.003912 0.000646 6.06 <.0001
Residual 0.04176 0.002099 19.89 <.0001
Fit Statistics
-2 Log Likelihood 180.2
AIC (smaller is better) 198.2
AICC (smaller is better) 198.4
BIC (smaller is better) 227.9
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 447.61 <.0001
Solution for Fixed Effects
student Standard
Effect gender Estimate Error DF t Value Pr > |t|
Intercept 2.6440 0.08999 197 29.38 <.0001
TIME 0.1040 0.005622 199 18.49 <.0001
JOB -0.1196 0.01746 799 -6.85 <.0001
HIGHGPA 0.08984 0.02647 799 3.39 0.0007
SEX 1 -0.1168 0.03153 799 -3.70 0.0002
SEX 2 0 . . . .
Part 2: Cross level interaction of variable time and sex is included. We first created the interaction term.
proc mixed data = gpachp5 covtest method = ml; class sex; model gpa = time job highgpa sex time*sex/solution; random intercept time /subject = student type=un; run;
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) STUDENT 0.03855 0.006149 6.27 <.0001
UN(2,1) STUDENT -0.00227 0.001506 -1.51 0.1310
UN(2,2) STUDENT 0.003690 0.000624 5.91 <.0001
Residual 0.04178 0.002101 19.89 <.0001
Fit Statistics
-2 Log Likelihood 173.2
AIC (smaller is better) 193.2
AICC (smaller is better) 193.4
BIC (smaller is better) 226.2
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 446.52 <.0001
Solution for Fixed Effects
student Standard
Effect gender Estimate Error DF t Value Pr > |t|
Intercept 2.6273 0.09018 197 29.14 <.0001
TIME 0.1180 0.007614 198 15.49 <.0001
JOB -0.1206 0.01743 799 -6.92 <.0001
HIGHGPA 0.08981 0.02646 799 3.39 0.0007
SEX 1 -0.07680 0.03490 799 -2.20 0.0281
SEX 2 0 . . . .
TIME*SEX 1 -0.02947 0.01104 799 -2.67 0.0077
TIME*SEX 2 0 . . . .
Figure 5.4 on page 84.
proc mixed data = gpachp5 method = ml;
class sex;
model gpa = time job highgpa sex time*sex/solution ;
random intercept time /subject = student type=un;
run;
data fig54;
set gpachp5;
pred = 2.63 + 0.12*time -0.07682*(sex=1) - 0.02947*time*(sex=1);
run;
symbol1 i = join r=2 v=circle;
axis1 order = (2.5 to 3.3 by .1) minor = none label=(a= 90 "Predicted GPA");
axis2 order = (0 to 6 by 1) minor = none label=("Time");
proc gplot data = fig54;
plot pred*time = sex /vaxis = axis1 haxis = axis2;
run;
quit;
Table 5.5 on page 85.
data table55; set gpachp5; t1 = time; t2 = time - 5; t3 = time - 2.5; run;
Part 1: First occasion = 0.
proc mixed data = table55 covtest method = ml; class sex; model gpa = t1 job highgpa sex /solution ; random intercept t1/subject = student type=un; run;
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) STUDENT 0.03897 0.006221 6.26 <.0001
UN(2,1) STUDENT -0.00256 0.001558 -1.65 0.0999
UN(2,2) STUDENT 0.003912 0.000646 6.06 <.0001
Residual 0.04176 0.002099 19.89 <.0001
Fit Statistics
-2 Log Likelihood 180.2
AIC (smaller is better) 198.2
AICC (smaller is better) 198.4
BIC (smaller is better) 227.9
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 447.61 <.0001
Solution for Fixed Effects
student Standard
Effect gender Estimate Error DF t Value Pr > |t|
Intercept 2.6440 0.08999 197 29.38 <.0001
t1 0.1040 0.005622 199 18.49 <.0001
JOB -0.1196 0.01746 799 -6.85 <.0001
HIGHGPA 0.08984 0.02647 799 3.39 0.0007
SEX 1 -0.1168 0.03153 799 -3.70 0.0002
SEX 2 0 . . . .
Part 2: The variable time has been recoded as -5, …,-1, 0, …with the last occasion coded as zero. This is variable t2.
proc mixed data = table55 covtest method = ml; class sex; model gpa = t2 job highgpa sex /solution ; random intercept t2/subject = student type=un; run;
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) STUDENT 0.1111 0.01373 8.09 <.0001
UN(2,1) STUDENT 0.01700 0.002676 6.35 <.0001
UN(2,2) STUDENT 0.003912 0.000646 6.06 <.0001
Residual 0.04176 0.002099 19.89 <.0001
Fit Statistics
-2 Log Likelihood 180.2
AIC (smaller is better) 198.2
AICC (smaller is better) 198.4
BIC (smaller is better) 227.9
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 447.61 <.0001
Solution for Fixed Effects
student Standard
Effect gender Estimate Error DF t Value Pr > |t|
Intercept 3.1639 0.09127 197 34.67 <.0001
t2 0.1040 0.005622 199 18.49 <.0001
JOB -0.1196 0.01746 799 -6.85 <.0001
HIGHGPA 0.08984 0.02647 799 3.39 0.0007
SEX 1 -0.1168 0.03153 799 -3.70 0.0002
SEX 2 0 . . . .
Part 3: The variable time is recoded centered around its mean and is included as a fixed effect. This is variable t3.
proc mixed data = table55 covtest method = ml; class sex; model gpa = t3 job highgpa sex /solution ; random intercept t3/subject = student type=un; run;
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) STUDENT 0.05060 0.005885 8.60 <.0001
UN(2,1) STUDENT 0.007217 0.001480 4.88 <.0001
UN(2,2) STUDENT 0.003912 0.000646 6.06 <.0001
Residual 0.04176 0.002099 19.89 <.0001
Fit Statistics
-2 Log Likelihood 180.2
AIC (smaller is better) 198.2
AICC (smaller is better) 198.4
BIC (smaller is better) 227.9
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 447.61 <.0001
Solution for Fixed Effects
student Standard
Effect gender Estimate Error DF t Value Pr > |t|
Intercept 2.9040 0.08953 197 32.44 <.0001
t3 0.1040 0.005622 199 18.49 <.0001
JOB -0.1196 0.01746 799 -6.85 <.0001
HIGHGPA 0.08984 0.02647 799 3.39 0.0007
SEX 1 -0.1168 0.03153 799 -3.70 0.0002
SEX 2 0 . . . .
Table 5.6 using data file vocagrwt.
proc freq data = vocagrwt ; tables age /nopercent nocum ; run;
The FREQ Procedure AGE Frequency ---------------- 12 22 14 5 16 22 18 11 20 22 22 11 24 22 26 11
Table 5.7 on page 89. We will create all the variables needed for this table in the following data step.
data voca; set in.vocagrwt; sdummy = study - .5; agec = age - 18.889; agec2 = agec*agec; run;
Part 1: Intercept only model.
proc mixed data = voca covtest method = ml; model vocab = sdummy /solution; random intercept /subject = child type = un; run;
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) CHILD 2400.41 2147.95 1.12 0.1319
Residual 31076 4201.58 7.40 <.0001
Fit Statistics
-2 Log Likelihood 1668.9
AIC (smaller is better) 1676.9
AICC (smaller is better) 1677.2
BIC (smaller is better) 1681.3
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 132.07 19.5083 20 6.77 <.0001
sdummy -110.91 39.0165 104 -2.84 0.005
Part 2: The variable age is grand mean centered and is included as a fixed effect. This is variable agec.
proc mixed data = voca covtest method = ml; model vocab = sdummy agec/solution; random intercept /subject = child type = un; run;
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) CHILD 4882.74 1937.08 2.52 0.0059
Residual 10377 1421.19 7.30 <.0001
Fit Statistics
-2 Log Likelihood 1550.9
AIC (smaller is better) 1560.9
AICC (smaller is better) 1561.4
BIC (smaller is better) 1566.4
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 137.78 17.6864 20 7.79 <.0001
sdummy -69.7926 35.4737 103 -1.97 0.0518
agec 29.5553 2.0138 103 14.68 <.0001
Part 3: The squared term of agec is included as a fixed effect.
proc mixed data = voca covtest method = ml; model vocab = sdummy agec agec2/solution; random intercept /subject = child type = un; run;
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) CHILD 5166.25 1902.71 2.72 0.0033
Residual 7721.24 1060.15 7.28 <.0001
Fit Statistics
-2 Log Likelihood 1519.5
AIC (smaller is better) 1531.5
AICC (smaller is better) 1532.2
BIC (smaller is better) 1538.0
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 84.7951 19.4698 20 4.36 0.0003
sdummy -68.2509 34.8592 102 -1.96 0.0530
agec 30.6225 1.7460 102 17.54 <.0001
agec2 2.5573 0.4227 102 6.05 <.0001
Part 4: Centered variable agec is included as a random effect.
proc mixed data = voca covtest method = ml; model vocab = sdummy agec agec2/solution; random intercept agec/subject = child type = un; run;
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) CHILD 6453.59 1999.97 3.23 0.0006
UN(2,1) CHILD 1267.44 384.64 3.30 0.0010
UN(2,2) CHILD 240.39 74.6448 3.22 0.0006
Residual 941.02 135.58 6.94 <.0001
Fit Statistics
-2 Log Likelihood 1290.0
AIC (smaller is better) 1306.0
AICC (smaller is better) 1307.2
BIC (smaller is better) 1314.7
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 88.0805 17.6336 20 5.00 <.0001
sdummy -3.6132 5.3738 81 -0.67 0.5033
agec 28.1058 3.3675 21 8.35 <.0001
agec2 2.1792 0.1518 81 14.36 <.0001
Table 5.8 on page 91.
Part 1: Intercept only model.
proc mixed data = voca covtest method = ml; model vocab = sdummy/solution; random intercept /subject = child type = un; run;
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) CHILD 2400.41 2147.95 1.12 0.1319
Residual 31076 4201.58 7.40 <.0001
Fit Statistics
-2 Log Likelihood 1668.9
AIC (smaller is better) 1676.9
AICC (smaller is better) 1677.2
BIC (smaller is better) 1681.3
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 132.07 19.5083 20 6.77 <.0001
sdummy -110.91 39.0165 104 -2.84 0.0054
Part 2: The variable age is centered on 12 months and is included as a fixed effect.
proc mixed data = voca covtest method = ml; model vocab = sdummy age12/solution; random intercept /subject = child type = un; run;
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) CHILD 4882.74 1937.08 2.52 0.0059
Residual 10377 1421.19 7.30 <.0001
Fit Statistics
-2 Log Likelihood 1550.9
AIC (smaller is better) 1560.9
AICC (smaller is better) 1561.4
BIC (smaller is better) 1566.4
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept -65.8220 22.2324 20 -2.96 0.0077
sdummy -69.7926 35.4737 103 -1.97 0.0518
AGE12 29.5553 2.0138 103 14.68 <.0001
Part 3: The variable age12sq is included as a fixed effect.
proc mixed data = voca covtest method = ml; model vocab = sdummy age12 age12sq/solution; random intercept /subject = child type = un; run;
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) CHILD 5166.25 1902.71 2.72 0.0033
Residual 7721.24 1060.15 7.28 <.0001
Fit Statistics
-2 Log Likelihood 1519.5
AIC (smaller is better) 1531.5
AICC (smaller is better) 1532.2
BIC (smaller is better) 1538.0
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept -4.7972 23.2299 20 -0.21 0.8385
sdummy -68.2509 34.8592 102 -1.96 0.0530
AGE12 -4.6122 5.9106 102 -0.78 0.4370
AGE12SQ 2.5573 0.4227 102 6.05 <.0001
Part 4: The variable age12 is a random effect.
proc mixed data = voca covtest method = ml; model vocab = sdummy age12 age12sq/solution; random intercept age12 /subject = child type = un; run;
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) CHILD 399.28 271.79 1.47 0.0709
UN(2,1) CHILD -388.63 136.43 -2.85 0.0044
UN(2,2) CHILD 240.41 74.6570 3.22 0.0006
Residual 941.01 135.57 6.94 <.0001
Fit Statistics
-2 Log Likelihood 1290.0
AIC (smaller is better) 1306.0
AICC (smaller is better) 1307.2
BIC (smaller is better) 1314.7
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept -2.1174 7.3727 20 -0.29 0.7769
sdummy -3.6130 5.3738 81 -0.67 0.5033
AGE12 -1.9198 3.9040 21 -0.49 0.6280
AGE12SQ 2.1792 0.1518 81 14.36 <.0001
Table 5.9 on page 92 is created using HLM. We omit it here.
Table 5.10 on page 101 using data file gpa4chp5.
Part 1: The variable time is a fixed effect. We have built the model at the beginning of this chapter. We will use it here.
proc mixed data = gpachp5 covtest method = ml; model gpa = time job highgpa sex /solution; random intercept /subject = student type=un; run;
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) STUDENT 0.04576 0.005606 8.16 <.0001
Residual 0.05562 0.002495 22.29 <.0001
Fit Statistics
-2 Log Likelihood 294.5
AIC (smaller is better) 308.5
AICC (smaller is better) 308.6
BIC (smaller is better) 331.6
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 2.4651 0.1113 197 22.15 <.0001
TIME 0.1031 0.004002 998 25.77 <.0001
JOB -0.1618 0.01830 998 -8.84 <.0001
HIGHGPA 0.08584 0.02798 998 3.07 0.0022
SEX 0.1484 0.03331 998 4.45 <.0001
Part 2: The variable time is included as random effect.
proc mixed data = gpachp5 covest method = ml; model gpa = time job highgpa sex /solution; random intercept time /subject = student type=un; run;
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) STUDENT 0.03897 0.006221 6.26 <.0001
UN(2,1) STUDENT -0.00256 0.001558 -1.65 0.0999
UN(2,2) STUDENT 0.003912 0.000646 6.06 <.0001
Residual 0.04176 0.002099 19.89 <.0001
Fit Statistics
-2 Log Likelihood 180.2
AIC (smaller is better) 198.2
AICC (smaller is better) 198.4
BIC (smaller is better) 227.9
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 2.4105 0.1051 197 22.94 <.0001
TIME 0.1040 0.005622 199 18.49 <.0001
JOB -0.1196 0.01746 799 -6.85 <.0001
HIGHGPA 0.08984 0.02647 799 3.39 0.0007
SEX 0.1168 0.03153 799 3.70 0.0002
Part 3: The variable time is a fixed effect, MANOVA.
proc mixed data = gpachp5 dfbw covtest method = ml noitprint; class occas; model gpa = time job highgpa sex / solution; repeated occas / subject=student type= un ; run;
The Mixed Procedure
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) STUDENT 0.09208 0.009261 9.94 <.0001
UN(2,1) STUDENT 0.03072 0.007211 4.26 <.0001
UN(2,2) STUDENT 0.1020 0.01027 9.93 <.0001
UN(3,1) STUDENT 0.02018 0.007249 2.78 0.0054
UN(3,2) STUDENT 0.03878 0.008013 4.84 <.0001
UN(3,3) STUDENT 0.1094 0.01098 9.96 <.0001
UN(4,1) STUDENT 0.01380 0.007127 1.94 0.0528
UN(4,2) STUDENT 0.04121 0.008046 5.12 <.0001
UN(4,3) STUDENT 0.06847 0.009147 7.49 <.0001
UN(4,4) STUDENT 0.1078 0.01090 9.89 <.0001
UN(5,1) STUDENT 0.01571 0.007035 2.23 0.0256
UN(5,2) STUDENT 0.04632 0.008063 5.74 <.0001
UN(5,3) STUDENT 0.07114 0.009208 7.73 <.0001
UN(5,4) STUDENT 0.08566 0.009831 8.71 <.0001
UN(5,5) STUDENT 0.1042 0.01062 9.81 <.0001
UN(6,1) STUDENT 0.01774 0.007470 2.38 0.0175
UN(6,2) STUDENT 0.04027 0.008311 4.85 <.0001
UN(6,3) STUDENT 0.07210 0.009591 7.52 <.0001
UN(6,4) STUDENT 0.08961 0.01039 8.63 <.0001
UN(6,5) STUDENT 0.09486 0.01055 8.99 <.0001
UN(6,6) STUDENT 0.1170 0.01194 9.80 <.0001
Fit Statistics
-2 Log Likelihood -4.1
AIC (smaller is better) 47.9
AICC (smaller is better) 49.1
BIC (smaller is better) 133.7
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 2.3640 0.1025 197 23.06 <.0001
TIME 0.1047 0.004835 197 21.65 <.0001
JOB -0.09300 0.01429 197 -6.51 <.0001
HIGHGPA 0.08442 0.02650 197 3.19 0.0017
SEX 0.1193 0.03156 197 3.78 0.0002