Note: This page has been updated using SAS 9.2 in January 2011.
Showing proc contents for the data file.
proc contents data=imm10 pos; run;
And here are the results.
# Variable Type Len Pos Label
-----------------------------------------------------------------------------------------------
15 cstr Num 8 112
5 homework Num 8 32 Time spent on math homework each week
11 math Num 8 80 Math score
4 meanses Num 8 24 Mean SES for the school
7 parented Num 8 48 Parents highest education level
10 percmin Num 8 72 Percent minority in school
8 public Num 8 56 Public school: 1=public, 0=non-public
13 race Num 8 96 race of student, 1=asian, 2=Hispanic, 3=Black, 4=White, 5=Native American
9 ratio Num 8 64 Student-Teacher ratio
18 region Num 8 136
1 schid Num 8 0 School ID
19 schnum Num 8 144 group(schid)
16 scsize Num 8 120
14 sctype Num 8 104 Type of school, 1=public, 2=catholic, 3=Private
other religious, 4=Private non-r
3 ses Num 8 16 Socioecnonomic Status
12 sex Num 8 88 Sex: 1=male, 2=female
2 stuid Num 8 8 Student ID
17 urban Num 8 128
6 white Num 8 40 Race: 1=white, 0=non-white
Page 48, Table 3.3
proc mixed data=imm10 covtest method=ml;
class schid;
model math = homework / solution ;
random intercept homework / subject=schid type=un;
run;
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) schid 61.8012 29.8685 2.07 0.0193
UN(2,1) schid -28.2571 15.4829 -1.83 0.0680
UN(2,2) schid 19.9766 9.8069 2.04 0.0208
Residual 43.0671 3.9292 10.96 <.0001
Fit Statistics
-2 Log Likelihood 1769.4
AIC (smaller is better) 1781.4
AICC (smaller is better) 1781.7
BIC (smaller is better) 1783.2
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 146.97 <.0001
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 44.7726 2.6031 9 17.20 <.0001
homework 2.0487 1.4722 9 1.39 0.1975
Page 50, table 3.4 equations.
proc mixed data=imm10 covtest method=ml;
class schid;
model math = homework public / solution ;
random intercept homework / subject=schid type=un;
run;
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) schid 40.6657 20.6116 1.97 0.0243
UN(2,1) schid -29.1507 14.4739 -2.01 0.0440
UN(2,2) schid 21.6760 10.5313 2.06 0.0198
Residual 42.9550 3.9104 10.98 <.0001
Fit Statistics
-2 Log Likelihood 1750.8
AIC (smaller is better) 1764.8
AICC (smaller is better) 1765.3
BIC (smaller is better) 1767.0
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 95.17 <.0001
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 58.0556 2.6944 8 21.55 <.0001
homework 1.9409 1.5247 9 1.27 0.2349
public -14.6511 1.8315 240 -8.00 <.0001
Page 51, table 3.5 equations.
proc mixed data=imm10 covtest method=ml; class schid; model math = homework public homework*public / solution ; random intercept homework / subject=schid type=un; run;
Results shown below. Note the interaction is positive but the bottom of page 50 shows the interaction is negative. We think this may be a typographical error.
Covariance Parameter Estimates Standard Z Cov Parm Subject Estimate Error Value Pr Z UN(1,1) schid 40.4919 20.5363 1.97 0.0243 UN(2,1) schid -29.0135 14.4220 -2.01 0.0442 UN(2,2) schid 21.5703 10.4935 2.06 0.0199 Residual 42.9549 3.9104 10.98 <.0001 Fit Statistics -2 Log Likelihood 1750.8 AIC (smaller is better) 1766.8 AICC (smaller is better) 1767.4 BIC (smaller is better) 1769.2 Null Model Likelihood Ratio Test DF Chi-Square Pr > ChiSq 3 92.27 <.0001 Solution for Fixed Effects Standard Effect Estimate Error DF t Value Pr > |t| Intercept 59.2102 6.5967 8 8.98 <.0001 homework 1.0946 4.6679 8 0.23 0.8205 public -15.9419 6.9767 240 -2.29 0.0232 homework*public 0.9473 4.9375 240 0.19 0.8480
Page 52, Table 3.6 and Figure 3.8
proc mixed data= imm10 method=ml; class schid; model math = homework / solution outp=t; random intercept homework / subject=schid type=un g solution; ods output solutionR=randest; run; DATA randest2; set randest; by schid; retain intercept slope; if effect="Intercept" then intercept = 44.772 + estimate; if effect="homework" then slope = 2.0487 + estimate; if last.schid; keep schid intercept slope; run; proc print data=randest2 noobs; var intercept slope; run;
intercept slope 50.2702 -3.14337 48.8855 -2.75398 39.1947 7.56630 35.1560 5.39411 53.0804 -3.73816 48.5853 -1.76515 58.0548 1.33518 37.1518 6.05997 39.1691 5.43043 38.1722 6.10167
proc sgplot data = t; series x = homework y = pred /group=schid; run;
Page 53, Figure 3.8
