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Using proc contents to see the names of the variables and the variable labels.
1 schid Num 8 0 School ID
2 stuid Num 8 8 Student ID
3 ses Num 8 16 Socioecnonomic Status
4 meanses Num 8 24 Mean SES for the school
5 homework Num 8 32 Time spent on math homework each week
6 white Num 8 40 Race: 1=white, 0=non-white
7 parented Num 8 48 Parents highest education level
8 public Num 8 56 Public school: 1=public, 0=non-public
9 ratio Num 8 64 Student-Teacher ratio
10 percmin Num 8 72 Percent minority in school
11 math Num 8 80 Math score
12 sex Num 8 88 Sex: 1=male, 2=female
13 race Num 8 96 race of student, 1=asian, 2=Hispanic, 3=Black, 4=White, 5=Native American
14 sctype Num 8 104 Type of school, 1=public, 2=catholic, 3=Private
other religious, 4=Private non-r
15 cstr Num 8 112
16 scsize Num 8 120
17 urban Num 8 128
18 region Num 8 136
Page 64, 4.2.2, The Null Model, Model 0 (SAS Program).
proc mixed data="c:\imm\imm23" covtest; class schid; model math = / solution ; random intercept / subject=schid ; run;
Results from the program (abbreviated).
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
Intercept schid 26.1211 8.9853 2.91 0.0018
Residual 81.2442 5.1539 15.76 <.0001
Fit Statistics
-2 Res Log Likelihood 3798.7
AIC (smaller is better) 3802.7
AICC (smaller is better) 3802.7
BIC (smaller is better) 3804.9
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 50.7589 1.1511 22 44.10 <.0001
Page 65, 4.2.3 'Homework and 'MathAchievement', Model 1, (SAS Program).
proc mixed data="c:\imm\imm23" covtest; class schid; model math = homework / solution ; random intercept / subject=schid ; run;
Results for model 1.
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
Intercept schid 21.3376 7.5722 2.82 0.0024
Residual 71.2842 4.5305 15.73 <.0001
Fit Statistics
-2 Res Log Likelihood 3729.3
AIC (smaller is better) 3733.3
AICC (smaller is better) 3733.3
BIC (smaller is better) 3735.6
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 46.3557 1.1627 22 39.87 <.0001
homework 2.3999 0.2772 495 8.66 <.0001
Pages 66 and 67, 4.2.4 Random slope for 'Homework', model 2 (SAS Program).
proc mixed data="c:\imm\imm23" covtest; class schid; model math = homework / solution ; random intercept homework / subject=schid type=un; run;
Results for model 2.
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) schid 62.4231 21.3807 2.92 0.0018
UN(2,1) schid -27.5930 10.5657 -2.61 0.0090
UN(2,2) schid 17.7260 6.2599 2.83 0.0023
Residual 53.2947 3.4660 15.38 <.0001
Fit Statistics
-2 Res Log Likelihood 3635.6
AIC (smaller is better) 3643.6
AICC (smaller is better) 3643.6
BIC (smaller is better) 3648.1
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 190.19 <.0001
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 46.3256 1.7589 22 26.34 <.0001
homework 1.9802 0.9284 22 2.13 0.0443
Type 3 Tests of Fixed Effects
Num Den
Effect DF DF F Value Pr > F
homework 1 22 4.55 0.0443
Page 69, 4.2.5 Adding 'ParentEducation', model 3 (SAS Program).
proc mixed data="c:\imm\imm23" covtest; class schid; model math = homework parented / solution ; random intercept homework / subject=schid type=un; run;
Results of model 3
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) schid 47.8612 17.0115 2.81 0.0025
UN(2,1) schid -21.9452 8.4985 -2.58 0.0098
UN(2,2) schid 13.8741 5.0365 2.75 0.0029
Residual 50.7789 3.3118 15.33 <.0001
Fit Statistics
-2 Res Log Likelihood 3600.0
AIC (smaller is better) 3608.0
AICC (smaller is better) 3608.1
BIC (smaller is better) 3612.6
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 119.94 <.0001
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 40.8545 1.7901 22 22.82 <.0001
homework 1.8817 0.8301 22 2.27 0.0336
parented 1.8415 0.2959 472 6.22 <.0001
Page 70 and 71, 4.2.6 Traditional regression model.
proc mixed data="c:\imm\imm23" covtest; class schid; model math = homework parented / solution ; run;
Results
Covariance Parameter Estimates
Standard Z
Cov Parm Estimate Error Value Pr Z
Residual 76.1163 4.7388 16.06 <.0001
Fit Statistics
-2 Res Log Likelihood 3720.0
AIC (smaller is better) 3722.0
AICC (smaller is better) 3722.0
BIC (smaller is better) 3726.2
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 37.2392 0.9963 516 37.38 <.0001
homework 2.3354 0.2684 516 8.70 <.0001
parented 3.0040 0.2765 516 10.86 <.0001
Page 73/74, 4.3.2 A model with 'SchoolSize' (Model 2), SAS Program.
proc mixed data="c:\imm\imm23" covtest; class schid; model math = homework scsize / solution ; random intercept homework / subject=schid type=un; run;
And the results are
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) schid 66.4271 23.3302 2.85 0.0022
UN(2,1) schid -28.7509 11.0714 -2.60 0.0094
UN(2,2) schid 17.7846 6.2816 2.83 0.0023
Residual 53.3058 3.4673 15.37 <.0001
Fit Statistics
-2 Res Log Likelihood 3634.2
AIC (smaller is better) 3642.2
AICC (smaller is better) 3642.3
BIC (smaller is better) 3646.8
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 189.33 <.0001
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 44.9720 2.7109 21 16.59 <.0001
homework 1.9812 0.9298 22 2.13 0.0445
scsize 0.4259 0.6410 473 0.66 0.5067
Page 74/75, 4.3.3 Changing 'SchoolSize' to 'Public' (Model 3), SAS Program.
proc mixed data="c:\imm\imm23" covtest; class schid; model math = homework public / solution ; random intercept homework / subject=schid type=un; run;
And the results are
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) schid 60.1538 20.8873 2.88 0.0020
UN(2,1) schid -27.4478 10.3743 -2.65 0.0082
UN(2,2) schid 17.3031 6.1085 2.83 0.0023
Residual 53.3443 3.4716 15.37 <.0001
Fit Statistics
-2 Res Log Likelihood 3628.4
AIC (smaller is better) 3636.4
AICC (smaller is better) 3636.5
BIC (smaller is better) 3640.9
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 157.64 <.0001
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 49.0504 2.1847 21 22.45 <.0001
homework 1.9753 0.9182 22 2.15 0.0427
public -4.0611 1.9779 473 -2.05 0.0406
Page 77, 4.3.4 Adding a cross level interaction with 'Public', (Model 4), SAS Program.
proc mixed data="c:\imm\imm23" covtest; class schid; model math = homework public homework*public / solution ; random intercept homework / subject=schid type=un; run;
And the results are
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) schid 62.5515 22.0536 2.84 0.0023
UN(2,1) schid -28.9502 11.0801 -2.61 0.0090
UN(2,2) schid 18.2497 6.5507 2.79 0.0027
Residual 53.3329 3.4702 15.37 <.0001
Fit Statistics
-2 Res Log Likelihood 3625.2
AIC (smaller is better) 3633.2
AICC (smaller is better) 3633.2
BIC (smaller is better) 3637.7
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 159.63 <.0001
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 48.5289 3.0160 21 16.09 <.0001
homework 2.2928 1.5913 21 1.44 0.1644
public -3.2620 3.7145 473 -0.88 0.3803
homework*public -0.4957 1.9727 473 -0.25 0.8017
Page 80, 4.3.5 Model 4 will full NELS-88 data (we don't have these data, so this is omitted).
Page 80/82, 4.3.6 Deleting 'HomePublic' and adding 'White' (Model 5), SAS Program.
proc mixed data="c:\imm\imm23" covtest; class schid; model math = homework public white / solution ; random intercept homework / subject=schid type=un; run;
And the results are
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) schid 56.0169 19.6224 2.85 0.0022
UN(2,1) schid -26.8055 9.9968 -2.68 0.0073
UN(2,2) schid 16.7698 5.9278 2.83 0.0023
Residual 52.7291 3.4370 15.34 <.0001
Fit Statistics
-2 Res Log Likelihood 3615.5
AIC (smaller is better) 3623.5
AICC (smaller is better) 3623.5
BIC (smaller is better) 3628.0
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 133.03 <.0001
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 46.6283 2.1921 21 21.27 <.0001
homework 1.8992 0.9049 22 2.10 0.0475
public -3.8825 1.7987 472 -2.16 0.0314
white 3.3095 0.9699 472 3.41 0.0007
Page 82/83, 4.3.7 Adding a random part for 'White' (Model 6), SAS Program.
proc mixed data="c:\imm\imm23" covtest; class schid; model math = homework public white / solution ; random intercept homework white / subject=schid type=un; run;
And the results are
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) schid 69.1398 31.1837 2.22 0.0133
UN(2,1) schid -28.5298 12.2476 -2.33 0.0198
UN(2,2) schid 16.6238 5.8694 2.83 0.0023
UN(3,1) schid -22.0770 20.9222 -1.06 0.2913
UN(3,2) schid 2.9197 7.9180 0.37 0.7123
UN(3,3) schid 26.4989 22.5376 1.18 0.1198
Residual 51.1580 3.3848 15.11 <.0001
Fit Statistics
-2 Res Log Likelihood 3610.5
AIC (smaller is better) 3624.5
AICC (smaller is better) 3624.7
BIC (smaller is better) 3632.4
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 48.2276 2.3398 21 20.61 <.0001
homework 1.9401 0.9003 22 2.16 0.0424
public -4.9292 1.6507 457 -2.99 0.0030
white 2.5982 1.5538 15 1.67 0.1152
Page 85, 4.3.8 Making the coefficient of 'White' fixed and adding 'MeanSES' (Model 7), SAS Program.
proc mixed data="c:\imm\imm23" covtest; class schid; model math = homework public white meanses / solution ; random intercept homework / subject=schid type=un; run;
And the results are
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) schid 54.1137 19.0857 2.84 0.0023
UN(2,1) schid -27.0176 9.8916 -2.73 0.0063
UN(2,2) schid 16.4294 5.8132 2.83 0.0024
Residual 52.7965 3.4449 15.33 <.0001
Fit Statistics
-2 Res Log Likelihood 3606.5
AIC (smaller is better) 3614.5
AICC (smaller is better) 3614.6
BIC (smaller is better) 3619.1
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 44.6158 2.2348 20 19.96 <.0001
homework 1.9243 0.8961 22 2.15 0.0430
public 0.1603 2.2708 472 0.07 0.9437
white 3.0971 0.9631 472 3.22 0.0014
meanses 4.9776 1.9507 472 2.55 0.0110
Page 86, 4.3.9 Deleting the school characteristic 'Public' (Model 8), SAS Program.
proc mixed data="c:\imm\imm23" covtest; class schid; model math = homework white meanses / solution ; random intercept homework / subject=schid type=un; run;
And the results are
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) schid 53.5511 18.8970 2.83 0.0023
UN(2,1) schid -26.9812 9.8535 -2.74 0.0062
UN(2,2) schid 16.3851 5.7957 2.83 0.0023
Residual 52.7925 3.4444 15.33 <.0001
Fit Statistics
-2 Res Log Likelihood 3610.0
AIC (smaller is better) 3618.0
AICC (smaller is better) 3618.1
BIC (smaller is better) 3622.5
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 44.7021 1.7870 21 25.02 <.0001
homework 1.9252 0.8948 22 2.15 0.0427
white 3.1151 0.9570 472 3.25 0.0012
meanses 4.8928 1.3405 472 3.65 0.0003
Page 87/88, 4.3.10 Adding an interaction between 'HomeWork' and 'MeanSES' (Model 9), SAS Program.
proc mixed data="c:\imm\imm23" covtest; class schid; model math = homework white meanses homework*meanses / solution ; random intercept homework / subject=schid type=un; run;
And the results are
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) schid 55.8829 20.0177 2.79 0.0026
UN(2,1) schid -28.3876 10.5226 -2.70 0.0070
UN(2,2) schid 17.2368 6.2097 2.78 0.0028
Residual 52.7811 3.4431 15.33 <.0001
Fit Statistics
-2 Res Log Likelihood 3607.1
AIC (smaller is better) 3615.1
AICC (smaller is better) 3615.1
BIC (smaller is better) 3619.6
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 44.6113 1.8361 21 24.30 <.0001
homework 1.9747 0.9291 21 2.13 0.0456
white 3.1150 0.9571 472 3.25 0.0012
meanses 3.9776 3.0226 472 1.32 0.1888
homework*meanses 0.5531 1.6457 472 0.34 0.7369
Page 88/89, 4.3.11 Adding another student-level variable (Model 10), SAS Program.
proc mixed data="c:\imm\imm23" covtest; class schid; model math = homework white meanses ses / solution ; random intercept homework / subject=schid type=un; run;
And the results are
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) schid 49.8879 17.7280 2.81 0.0024
UN(2,1) schid -24.3721 9.0424 -2.70 0.0070
UN(2,2) schid 14.6440 5.2441 2.79 0.0026
Residual 51.2969 3.3506 15.31 <.0001
Fit Statistics
-2 Res Log Likelihood 3592.8
AIC (smaller is better) 3600.8
AICC (smaller is better) 3600.8
BIC (smaller is better) 3605.3
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 45.6748 1.7519 21 26.07 <.0001
homework 1.8257 0.8503 22 2.15 0.0431
white 2.1708 0.9733 471 2.23 0.0262
meanses 2.9453 1.4280 471 2.06 0.0397
ses 2.2058 0.5356 471 4.12 <.0001
Page 88/89, 4.3.12: Analyses with NELS-88 (we don't have these data, so these analyses are omitted).
Page 91, 4.4.1 'SES' as a student-level explanatory variable (Model 1), SAS Program.
proc mixed data="c:\imm\imm23" covtest; class schid; model math = ses / solution ; random intercept / subject=schid ; run;
And the results are
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
Intercept schid 12.6312 5.0151 2.52 0.0059
Residual 75.3279 4.7872 15.74 <.0001
Fit Statistics
-2 Res Log Likelihood 3746.2
AIC (smaller is better) 3750.2
AICC (smaller is better) 3750.2
BIC (smaller is better) 3752.4
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 51.2009 0.8507 22 60.19 <.0001
ses 4.3323 0.5663 495 7.65 <.0001
Page 92, 4.4.2 Adding a random slope (Model 2), SAS Program.
proc mixed data="c:\imm\imm23" covtest; class schid; model math = ses / solution ; random intercept ses / subject=schid type=un ; run;
And the results are
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) schid 12.9434 5.0950 2.54 0.0055
UN(2,1) schid -1.4471 3.1449 -0.46 0.6454
UN(2,2) schid 0 . . .
Residual 75.2360 4.7748 15.76 <.0001
Fit Statistics
-2 Res Log Likelihood 3746.0
AIC (smaller is better) 3752.0
AICC (smaller is better) 3752.0
BIC (smaller is better) 3755.4
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 51.2578 0.8556 22 59.91 <.0001
ses 4.3173 0.5613 22 7.69 <.0001
Page 93, 4.4.3 Adding 'PercentMinorities' (Model 3), SAS Program.
proc mixed data="c:\imm\imm23" covtest; class schid; model math = ses percmin / solution ; random intercept / subject=schid type=un ; run;
And the results are
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) schid 10.6974 4.3367 2.47 0.0068
Residual 75.1727 4.7693 15.76 <.0001
Fit Statistics
-2 Res Log Likelihood 3741.6
AIC (smaller is better) 3745.6
AICC (smaller is better) 3745.6
BIC (smaller is better) 3747.9
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 53.1266 1.1780 21 45.10 <.0001
ses 4.2988 0.5618 495 7.65 <.0001
percmin -0.8094 0.3647 495 -2.22 0.0269
Page 95, 4.4.4 Adding 'MeanSES' (Model 4), SAS Program.
proc mixed data="c:\imm\imm23" covtest; class schid; model math = ses percmin meanses / solution ; random intercept / subject=schid type=un ; run;
And the results are
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) schid 8.8432 3.9345 2.25 0.0123
Residual 75.2413 4.7777 15.75 <.0001
Fit Statistics
-2 Res Log Likelihood 3735.6
AIC (smaller is better) 3739.6
AICC (smaller is better) 3739.6
BIC (smaller is better) 3741.9
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 53.0969 1.1025 20 48.16 <.0001
ses 3.8848 0.6098 495 6.37 <.0001
percmin -0.6922 0.3456 495 -2.00 0.0458
meanses 2.8052 1.4792 495 1.90 0.0585
Page 95, 4.4.5 Analyses with NELS-88, models 2 and 3 (we do not have these data, so these analyses are omitted).
Page 99, 4.5.1 Analysis with class size and a cross level interaction (Model 1), SAS Program.
proc mixed data="c:\imm\imm23" covtest; class schid; model math = homework ratio / solution ; random intercept homework / subject=schid type=un ; run;
And the results are
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) schid 63.4439 21.7601 2.92 0.0018
UN(2,1) schid -27.6790 10.6264 -2.60 0.0092
UN(2,2) schid 17.7255 6.2584 2.83 0.0023
Residual 53.3063 3.4673 15.37 <.0001
Fit Statistics
-2 Res Log Likelihood 3636.6
AIC (smaller is better) 3644.6
AICC (smaller is better) 3644.7
BIC (smaller is better) 3649.2
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 47.9615 4.0831 21 11.75 <.0001
homework 1.9794 0.9285 22 2.13 0.0444
ratio -0.09442 0.2124 473 -0.44 0.6568
Page 100, 4.5.2 Interaction between 'Ratio' and 'HomeWork' (Model 2), SAS Program.
proc mixed data="c:\imm\imm23" covtest; class schid; model math = homework homework*ratio / solution ; random intercept homework / subject=schid type=un ; run;
And the results are
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) schid 62.5534 21.4199 2.92 0.0017
UN(2,1) schid -27.7993 10.6543 -2.61 0.0091
UN(2,2) schid 18.0944 6.3898 2.83 0.0023
Residual 53.2978 3.4664 15.38 <.0001
Fit Statistics
-2 Res Log Likelihood 3637.9
AIC (smaller is better) 3645.9
AICC (smaller is better) 3646.0
BIC (smaller is better) 3650.4
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 46.3306 1.7606 22 26.32 <.0001
homework 2.8841 2.1568 21 1.34 0.1955
homework*ratio -0.05259 0.1123 473 -0.47 0.6398
Page 100, 4.5.3 Reporting the modeling session with NELS-88 (we do not have these data, so these analyses are omitted).
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