The SAS System 16:45 Monday, December 3, 2012 1
The REG Procedure
Model: MODEL1
Dependent Variable: Totbpt
Number of Observations Read 89
Number of Observations Used 26
Number of Observations with Missing Values 63
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 5 1424.43378 284.88676 7.71 0.0004
Error 20 739.41238 36.97062
Corrected Total 25 2163.84615
Root MSE 6.08035 R-Square 0.6583
Dependent Mean 53.07692 Adj R-Sq 0.5729
Coeff Var 11.45573
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 -2.93924 12.00345 -0.24 0.8091
SexP 1 -3.76858 2.80346 -1.34 0.1939
DeptP 1 0.88845 0.20224 4.39 0.0003
AnxtP 1 -0.06422 0.16908 -0.38 0.7081
DeptS 1 -0.35464 0.15540 -2.28 0.0336
AnxtS 1 0.60805 0.16604 3.66 0.0015
The SAS System 16:45 Monday, December 3, 2012 2
The MI Procedure
Model Information
Data Set WORK.MISSING
Method MCMC
Multiple Imputation Chain Single Chain
Initial Estimates for MCMC EM Posterior Mode
Start Starting Value
Prior Jeffreys
Number of Imputations 5
Number of Burn-in Iterations 200
Number of Iterations 100
Seed for random number generator 35399
Missing Data Patterns
----Group
SexP DeptP AnxtP GSItP DeptS AnxtS GSItS SexChild Totbpt Means----
Group Freq Percent SexP
1 X X X X X X X X X 26 29.21 1.730769
2 X X X X X X X . . 26 29.21 1.730769
3 X X X X . . . X X 11 12.36 2.000000
4 X X X X . . . . . 16 17.98 1.875000
5 X . . . X X X . . 1 1.12 2.000000
6 X . . . . . . . . 2 2.25 1.500000
7 . . . . X X X X X 4 4.49 .
8 . . . . X X X . . 3 3.37 .
Missing Data Patterns
--------------------------------------Group Means--------------------------------------
Group DeptP AnxtP GSItP DeptS AnxtS GSItS
1 57.384615 59.153846 58.076923 54.500000 57.038462 55.269231
2 51.153846 52.230769 52.884615 53.923077 52.653846 51.807692
3 60.272727 57.000000 59.454545 . . .
4 52.562500 54.312500 55.375000 . . .
5 . . . 50.000000 55.000000 45.000000
6 . . . . . .
7 . . . 60.750000 57.500000 58.000000
8 . . . 54.000000 59.333333 53.333333
Continued
---------Group Means--------
Group SexChild Totbpt
1 1.461538 53.076923
2 . .
3 1.454545 53.636364
4 . .
5 . .
6 . .
7 1.500000 56.750000
8 . .
EM (Posterior Mode) Estimates
_TYPE_ _NAME_ SexP DeptP AnxtP GSItP DeptS
MEAN 1.790868 54.974278 55.775243 56.221614 54.725422
COV SexP 0.147019 -0.168639 -0.803902 -0.345265 0.080326
COV DeptP -0.168639 85.908921 56.118133 61.326113 24.953762
COV AnxtP -0.803902 56.118133 83.463312 61.694439 8.905795
COV GSItP -0.345265 61.326113 61.694439 65.631490 17.439631
EM (Posterior Mode) Estimates
AnxtS GSItS SexChild Totbpt
55.418508 53.822267 1.477020 50.186358
0.451450 0.115634 -0.017013 -0.387399
17.412712 28.014656 -0.389392 75.423360
12.010188 14.225855 -0.417106 55.223908
17.202091 20.307471 -0.531005 65.339218
The MI Procedure
EM (Posterior Mode) Estimates
_TYPE_ _NAME_ SexP DeptP AnxtP GSItP DeptS
COV DeptS 0.080326 24.953762 8.905795 17.439631 100.677436
COV AnxtS 0.451450 17.412712 12.010188 17.202091 78.883036
COV GSItS 0.115634 28.014656 14.225855 20.307471 83.339906
COV SexChild -0.017013 -0.389392 -0.417106 -0.531005 -0.823657
COV Totbpt -0.387399 75.423360 55.223908 65.339218 37.720915
EM (Posterior Mode) Estimates
AnxtS GSItS SexChild Totbpt
78.883036 83.339906 -0.823657 37.720915
106.325402 85.794731 -0.524820 59.687782
85.794731 92.361142 -0.630447 46.403752
-0.524820 -0.630447 0.198886 -0.606631
59.687782 46.403752 -0.606631 121.815553
Multiple Imputation Variance Information
-----------------Variance-----------------
Variable Between Within Total DF
SexP 0.000063486 0.001853 0.001929 80.084
DeptP 0.071240 1.036767 1.122255 71.287
AnxtP 0.062699 1.072402 1.147641 74.027
GSItP 0.074984 0.838580 0.928561 65.732
DeptS 0.795011 1.410242 2.364255 16.615
AnxtS 0.277218 1.508794 1.841456 44.764
GSItS 0.319711 1.337634 1.721288 36.535
SexChild 0.002398 0.002650 0.005528 10.868
Totbpt 1.139107 1.626534 2.993463 13.603
Multiple Imputation Variance Information
Relative Fraction
Increase Missing Relative
Variable in Variance Information Efficiency
SexP 0.041122 0.040246 0.992015
DeptP 0.082456 0.078844 0.984476
AnxtP 0.070159 0.067561 0.986668
GSItP 0.107302 0.101114 0.980178
DeptS 0.676489 0.446792 0.917972
AnxtS 0.220482 0.193702 0.962705
GSItS 0.286815 0.241497 0.953926
SexChild 1.086179 0.574648 0.896918
Totbpt 0.840394 0.505627 0.908162
Multiple Imputation Parameter Estimates
95% Confidence
Variable Mean Std Error Limits DF Minimum Maximum
SexP 1.783757 0.043918 1.69636 1.87116 80.084 1.774811 1.794053
DeptP 54.846106 1.059365 52.73394 56.95827 71.287 54.516087 55.177821
AnxtP 55.802149 1.071280 53.66759 57.93671 74.027 55.524451 56.166482
GSItP 56.139447 0.963619 54.21537 58.06352 65.732 55.881300 56.467344
DeptS 54.445574 1.537614 51.19576 57.69539 16.615 53.506240 55.812335
AnxtS 54.784346 1.357002 52.05080 57.51789 44.764 53.978757 55.410073
GSItS 53.207082 1.311979 50.54762 55.86655 36.535 52.337055 53.900741
SexChild 1.455977 0.074347 1.29210 1.61986 10.868 1.397642 1.532763
Totbpt 50.215494 1.730163 46.49448 53.93651 13.603 49.166536 51.864690
Multiple Imputation Parameter Estimates
t for H0:
Variable Mu0 Mean=Mu0 Pr > |t|
SexP 0 40.62 <.0001
DeptP 0 51.77 <.0001
AnxtP 0 52.09 <.0001
GSItP 0 58.26 <.0001
DeptS 0 35.41 <.0001
AnxtS 0 40.37 <.0001
GSItS 0 40.55 <.0001
SexChild 0 19.58 <.0001
Totbpt 0 29.02 <.0001
The SAS System 16:45 Monday, December 3, 2012 6
--------------------------------------- Imputation Number=1 ---------------------------------------
The REG Procedure
Model: MODEL1
Dependent Variable: Totbpt
Number of Observations Read 89
Number of Observations Used 89
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 5 9063.26982 1812.65396 32.02 <.0001
Error 83 4699.20289 56.61690
Corrected Total 88 13762
Root MSE 7.52442 R-Square 0.6585
Dependent Mean 51.86469 Adj R-Sq 0.6380
Coeff Var 14.50779
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 -1.66002 7.48508 -0.22 0.8250
SexP 1 -4.87081 2.18862 -2.23 0.0288
DeptP 1 0.89628 0.11073 8.09 <.0001
AnxtP 1 -0.20472 0.11546 -1.77 0.0799
DeptS 1 -0.23504 0.11514 -2.04 0.0444
AnxtS 1 0.69262 0.10555 6.56 <.0001
--------------------------------------- Imputation Number=2 ---------------------------------------
The REG Procedure
Model: MODEL1
Dependent Variable: Totbpt
Number of Observations Read 89
Number of Observations Used 89
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 5 9782.38999 1956.47800 41.27 <.0001
Error 83 3934.83733 47.40768
Corrected Total 88 13717
Root MSE 6.88532 R-Square 0.7131
Dependent Mean 49.61395 Adj R-Sq 0.6959
Coeff Var 13.87780
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 -3.10217 6.51851 -0.48 0.6354
SexP 1 -3.68446 1.90398 -1.94 0.0564
DeptP 1 0.81093 0.10819 7.50 <.0001
AnxtP 1 -0.13401 0.10442 -1.28 0.2029
DeptS 1 -0.57784 0.10477 -5.52 <.0001
AnxtS 1 0.97745 0.10477 9.33 <.0001
--------------------------------------- Imputation Number=3 ---------------------------------------
The REG Procedure
Model: MODEL1
Dependent Variable: Totbpt
Number of Observations Read 89
Number of Observations Used 89
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 5 9383.05807 1876.61161 39.74 <.0001
Error 83 3919.03172 47.21725
Corrected Total 88 13302
Root MSE 6.87148 R-Square 0.7054
Dependent Mean 49.16654 Adj R-Sq 0.6876
Coeff Var 13.97593
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 -12.77419 7.19739 -1.77 0.0796
SexP 1 -4.02550 1.91987 -2.10 0.0391
DeptP 1 0.76927 0.10647 7.23 <.0001
AnxtP 1 0.10668 0.10888 0.98 0.3300
DeptS 1 -0.39213 0.09683 -4.05 0.0001
AnxtS 1 0.76526 0.09856 7.76 <.0001
--------------------------------------- Imputation Number=4 ---------------------------------------
The REG Procedure
Model: MODEL1
Dependent Variable: Totbpt
Number of Observations Read 89
Number of Observations Used 89
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 5 6999.25428 1399.85086 21.41 <.0001
Error 83 5426.30573 65.37718
Corrected Total 88 12426
Root MSE 8.08562 R-Square 0.5633
Dependent Mean 49.78348 Adj R-Sq 0.5370
Coeff Var 16.24156
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 -6.25011 7.57147 -0.83 0.4115
SexP 1 1.29085 2.19074 0.59 0.5573
DeptP 1 0.73950 0.12129 6.10 <.0001
AnxtP 1 0.13852 0.12051 1.15 0.2537
DeptS 1 -0.29757 0.11170 -2.66 0.0093
AnxtS 1 0.39837 0.10460 3.81 0.0003
The SAS System 16:45 Monday, December 3, 2012 10
--------------------------------------- Imputation Number=5 ---------------------------------------
The REG Procedure
Model: MODEL1
Dependent Variable: Totbpt
Number of Observations Read 89
Number of Observations Used 89
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 5 6977.05267 1395.41053 32.99 <.0001
Error 83 3510.66509 42.29717
Corrected Total 88 10488
Root MSE 6.50363 R-Square 0.6653
Dependent Mean 50.64882 Adj R-Sq 0.6451
Coeff Var 12.84063
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 -4.28616 6.50083 -0.66 0.5115
SexP 1 -5.64106 1.80881 -3.12 0.0025
DeptP 1 0.61804 0.10197 6.06 <.0001
AnxtP 1 0.20884 0.09750 2.14 0.0351
DeptS 1 -0.20440 0.09827 -2.08 0.0406
AnxtS 1 0.55903 0.09614 5.81 <.0001
Parameter estimates from imputed data sets 11
Obs _Imputation_ _TYPE_ _NAME_ Intercept SexP DeptP AnxtP DeptS AnxtS
1 1 PARMS -1.6600 -4.87081 0.89628 -0.20472 -0.23504 0.69262
2 1 COV Intercept 56.0264 -9.64186 -0.13715 -0.39310 -0.20572 0.04259
3 1 COV SexP -9.6419 4.79006 -0.04305 0.08158 0.04204 -0.06257
4 1 COV DeptP -0.1372 -0.04305 0.01226 -0.00813 -0.00188 0.00186
5 1 COV AnxtP -0.3931 0.08158 -0.00813 0.01333 0.00094 -0.00195
6 1 COV DeptS -0.2057 0.04204 -0.00188 0.00094 0.01326 -0.00980
7 1 COV AnxtS 0.0426 -0.06257 0.00186 -0.00195 -0.00980 0.01114
8 2 PARMS -3.1022 -3.68446 0.81093 -0.13401 -0.57784 0.97745
9 2 COV Intercept 42.4909 -7.22724 -0.02316 -0.27716 -0.12657 -0.09915
10 2 COV SexP -7.2272 3.62512 -0.03268 0.05662 0.01810 -0.02870
11 2 COV DeptP -0.0232 -0.03268 0.01170 -0.00816 -0.00268 0.00074
12 2 COV AnxtP -0.2772 0.05662 -0.00816 0.01090 0.00139 -0.00113
13 2 COV DeptS -0.1266 0.01810 -0.00268 0.00139 0.01098 -0.00789
14 2 COV AnxtS -0.0991 -0.02870 0.00074 -0.00113 -0.00789 0.01098
15 3 PARMS -12.7742 -4.02550 0.76927 0.10668 -0.39213 0.76526
16 3 COV Intercept 51.8024 -7.84627 -0.05065 -0.36289 -0.18050 -0.08111
17 3 COV SexP -7.8463 3.68591 -0.03246 0.05610 0.02813 -0.02956
18 3 COV DeptP -0.0507 -0.03246 0.01134 -0.00779 -0.00282 0.00128
19 3 COV AnxtP -0.3629 0.05610 -0.00779 0.01185 0.00259 -0.00197
20 3 COV DeptS -0.1805 0.02813 -0.00282 0.00259 0.00938 -0.00664
21 3 COV AnxtS -0.0811 -0.02956 0.00128 -0.00197 -0.00664 0.00971
22 4 PARMS -6.2501 1.29085 0.73950 0.13852 -0.29757 0.39837
23 4 COV Intercept 57.3272 -9.39822 -0.11582 -0.43125 -0.19111 0.02210
24 4 COV SexP -9.3982 4.79932 -0.04821 0.09150 0.01215 -0.04164
25 4 COV DeptP -0.1158 -0.04821 0.01471 -0.00869 -0.00278 0.00062
26 4 COV AnxtP -0.4312 0.09150 -0.00869 0.01452 0.00131 -0.00247
27 4 COV DeptS -0.1911 0.01215 -0.00278 0.00131 0.01248 -0.00807
28 4 COV AnxtS 0.0221 -0.04164 0.00062 -0.00247 -0.00807 0.01094
29 5 PARMS -4.2862 -5.64106 0.61804 0.20884 -0.20440 0.55903
30 5 COV Intercept 42.2608 -6.11563 -0.12586 -0.24990 -0.10572 -0.07948
31 5 COV SexP -6.1156 3.27181 -0.02777 0.04622 0.01418 -0.02766
32 5 COV DeptP -0.1259 -0.02777 0.01040 -0.00642 -0.00345 0.00276
33 5 COV AnxtP -0.2499 0.04622 -0.00642 0.00951 0.00238 -0.00253
34 5 COV DeptS -0.1057 0.01418 -0.00345 0.00238 0.00966 -0.00712
35 5 COV AnxtS -0.0795 -0.02766 0.00276 -0.00253 -0.00712 0.00924
The MIANALYZE Procedure
Model Information
Data Set WORK.OUTREG
Number of Imputations 5
Multiple Imputation Variance Information
-----------------Variance-----------------
Parameter Between Within Total DF
SexP 7.415234 4.034445 12.932726 8.4494
DeptP 0.010399 0.012082 0.024561 15.496
AnxtP 0.032848 0.012024 0.051441 6.8124
DeptS 0.022620 0.011149 0.038293 7.9608
AnxtS 0.047462 0.010403 0.067357 5.5947
intercept 18.844848 49.981542 72.595359 41.222
Multiple Imputation Variance Information
Relative Fraction
Increase Missing Relative
Parameter in Variance Information Efficiency
SexP 2.205577 0.742537 0.870695
DeptP 1.032786 0.561258 0.899077
AnxtP 3.278345 0.813905 0.860007
DeptS 2.434579 0.761970 0.867759
AnxtS 5.474739 0.881493 0.850124
intercept 0.452443 0.342643 0.935866
Multiple Imputation Parameter Estimates
95% Confidence
Parameter Estimate Std Error Limits DF Minimum Maximum
SexP -3.386193 3.596210 -11.6029 4.83052 8.4494 -5.641059 1.290854
DeptP 0.766804 0.156718 0.4337 1.09991 15.496 0.618039 0.896283
AnxtP 0.023061 0.226807 -0.5163 0.56238 6.8124 -0.204718 0.208842
DeptS -0.341397 0.195687 -0.7930 0.11024 7.9608 -0.577840 -0.204401
AnxtS 0.678545 0.259533 0.0322 1.32492 5.5947 0.398366 0.977451
intercept -5.614531 8.520291 -22.8188 11.58973 41.222 -12.774191 -1.660016
Multiple Imputation Parameter Estimates
t for H0:
Parameter Theta0 Parameter=Theta0 Pr > |t|
SexP 0 -0.94 0.3725
DeptP 0 4.89 0.0002
AnxtP 0 0.10 0.9219
DeptS 0 -1.74 0.1194
AnxtS 0 2.61 0.0426
intercept 0 -0.66 0.5136