The SAS System
1
16:34 Monday, December 8, 2008
Obs y treatid rep day id_M id_pc id_pp tree
1 0 PC
1
42
0
1
0
1
2 0 PC
1
42
0
1
0
2
3 0 PC
1
42
0
1
0
3
4 0 PC
1
42
0
1
0
4
5 0 PC
1
42
0
1
0
5
6 0 PC
1
42
0
1
0
6
7 0 PC
1
42
0
1
0
7
8 0 PC
1
42
0
1
0
8
9 0 PC
1
42
0
1
0
9
10 0 PC
1
42
0
1
0
10
11 0 PC
1
42
0
1
0
11
12 0 PC
1
42
0
1
0
12
13 0 PC
1
42
0
1
0
13
14 0 PC
1
42
0
1
0
14
15 0 PC
1
42
0
1
0
15
16 0 PC
1
42
0
1
0
16
17 0 PC
1
42
0
1
0
17
18 0 PC
1
42
0
1
0
18
19 0 PC
1
42
0
1
0
19
20 0 PC
1
42
0
1
0
20
21 0 PC
1
57
0
1
0
1
22 0 PC
1
57
0
1
0
2
23 0 PC
1
57
0
1
0
3
24 0 PC
1
57
0
1
0
4
25 0 PC
1
57
0
1
0
5
id_pp is a 0/1 identifier variable for treatment PP
2
16:34 Monday, December 8, 2008
Obs treatid rep day p_disease ndisease n_trees id_pp id_pc id_m id_t repid
t
1 M
5
42
0.05
1
20
0
0
1
0 M5
-48
2 M
8
42
0
0
20
0
0
1
0 M8
-48
3 M
11
42
0.1
2
20
0
0
1
0 M11
-48
4 M
16
42
0
0
20
0
0
1
0 M16
-48
5 M
19
42
0.05
1
20
0
0
1
0 M19
-48
6 PC
1
42
0
0
20
0
1
0
0 PC1
-48
7 PC
4
42
0
0
20
0
1
0
0 PC4
-48
8 PC
9
42
0.05
1
20
0
1
0
0 PC9
-48
9 PC
14
42
0
0
20
0
1
0
0 PC14 -48
10 PC
17
42
0
0
20
0
1
0
0 PC17 -48
11 PP
3
42
0
0
20
1
0
0
0 PP3
-48
12 PP
6
42
0
0
20
1
0
0
0 PP6
-48
13 PP
12
42
0
0
20
1
0
0
0 PP12 -48
14 PP
13
42
0
0
20
1
0
0
0 PP13 -48
15 PP
18
42
0
0
20
1
0
0
0 PP18 -48
16 T
2
42
0.05
1
20
0
0
0
1 T2
-48
17 T
7
42
0.1
2
20
0
0
0
1 T7
-48
18 T
10
42
0
0
20
0
0
0
1 T10
-48
19 T
15
42
0.05
1
20
0
0
0
1 T15
-48
20 T
20
42
0.05
1
20
0
0
0
1 T20
-48
21 M
5
57
0.15
3
20
0
0
1
0 M5
-33
22 M
8
57
0.15
3
20
0
0
1
0 M8
-33
23 M
11
57
0.15
3
20
0
0
1
0 M11
-33
24 M
16
57
0.05
1
20
0
0
1
0 M16
-33
25 M
19
57
0.2
4
20
0
0
1
0 M19
-33
p_disease
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
40
50
60
70
80
90
100
110
120
130
day
treatid
M
PC
PP
T
140
150
NLIN Logistic curve fitting
4
16:34 Monday, December 8, 2008
The NLIN Procedure
NOTE: Convergence criterion met.
Estimation Summary
Method
Gauss-Newton
Iterations
8
Subiterations
2
Average Subiterations
0.25
R
3.747E-6
PPC(rm)
0.000055
RPC(rm)
0.000192
Object
9.92E-10
Objective
1.691582
Observations Read
160
Observations Used
160
Observations Missing
Note: An
0
intercept was not specified for this model.
Source
Model
Error
Sum of Mean
Approx
DF Squares Square F Value Pr > F
8 54.1884 6.7736
152
608.65 <.0001
1.6916 0.0111
Uncorrected Total 160 55.8800
Approx
Parameter Estimate Std Error
Approximate
95%
Confidence
Limits
b0
-0.2073
bm
0.3215
0.1517
0.0219
0.6212
bpc
1.7844
0.2593
1.2720
2.2968
bpp
2.3447
0.3276
1.6974
2.9919
-0.0593
0.00578 -0.0708
-0.0479
rm
-0.00231
0.00838 -0.0189
0.0143
rpc
-0.0425
0.0139 -0.0699
-0.0151
rpp
-0.0535
0.0158 -0.0848
-0.0223
r
0.1068 -0.4183 0.00371
NLIN Logistic curve fitting
5
16:34 Monday, December 8, 2008
The NLIN Procedure
Approximate Correlation Matrix
b0
b0
bm
bm
bpc
bpp
1.0000000 -0.7041933 -0.4118170 -0.3259979
r
rm
rpc
rpp
0.1650091 -0.1137911 -0.0688300 -0.0603497
-0.7041933
1.0000000
0.2899988
0.2295655 -0.1161983
0.0223546
0.0484696
0.0424979
bpc -0.4118170
0.2899988
1.0000000
0.1342515 -0.0679535
0.0468611 -0.6503084
0.0248530
bpp -0.3259979
0.2295655
0.1342515
1.0000000 -0.0537926
0.0370956
r
0.1650091 -0.1161983 -0.0679535 -0.0537926
0.0224384 -0.7615598
1.0000000 -0.6896049 -0.4171285 -0.3657357
rm
-0.1137911
0.0223546
0.0468611
0.0370956 -0.6896049
1.0000000
0.2876539
0.2522131
rpc
-0.0688300
0.0484696 -0.6503084
0.0224384 -0.4171285
0.2876539
1.0000000
0.1525588
rpp
-0.0603497
0.0424979
0.0248530 -0.7615598 -0.3657357
0.2522131
0.1525588
1.0000000
pred
1.0
p_disease
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0.0
0
40
50
60
70
80
90
100
110
120
130
140
150
day
treatid
M
PC
PP
T
treatid
M
PC
PP
T
NLIN Gompertz curve fitting
7
16:34 Monday, December 8, 2008
The NLIN Procedure
NOTE: Convergence criterion met.
Estimation Summary
Method
Gauss-Newton
Iterations
11
Subiterations
2
Average Subiterations
0.181818
R
3.426E-6
PPC(rm)
0.000024
RPC(rm)
0.000096
Object
2.12E-10
Objective
1.913087
Observations Read
160
Observations Used
160
Observations Missing
Note: An
0
intercept was not specified for this model.
Source
Model
Error
Sum of Mean
Approx
DF Squares Square F Value Pr > F
8 53.9669 6.7459
152
535.98 <.0001
1.9131 0.0126
Uncorrected Total 160 55.8800
Parameter
Approx
Estimate Std Error
b0
0.6125
bm
-0.2169
0.1138 -0.4418 0.00799
bpc
-1.3102
0.1832 -1.6722
-0.9482
bpp
-1.7687
0.2374 -2.2378
-1.2997
r
0.0404
0.0831
Approximate
95%
Confidence
Limits
0.00400
0.4482
0.7767
0.0325
0.0483
0.00578 -0.0104
0.0124
rm
0.000993
rpc
0.0332
0.0105
0.0124
0.0540
rpp
0.0439
0.0125
0.0192
0.0685
NLIN Gompertz curve fitting
8
16:34 Monday, December 8, 2008
The NLIN Procedure
Approximate Correlation Matrix
b0
b0
bm
bm
bpc
bpp
1.0000000 -0.7303377 -0.4537618 -0.3502025
r
rm
rpc
rpp
0.4152086 -0.2870235 -0.1578921 -0.1329777
-0.7303377
1.0000000
0.3313993
0.2557661 -0.3032425
0.3004333
0.1153146
0.0971186
bpc -0.4537618
0.3313993
1.0000000
0.1589085 -0.1884058
0.1302403 -0.5774270
0.0603402
bpp -0.3502025
0.2557661
0.1589085
1.0000000 -0.1454071
0.1005164
r
0.4152086 -0.3032425 -0.1884058 -0.1454071
0.0552942 -0.7336226
1.0000000 -0.6912754 -0.3802718 -0.3202673
rm
-0.2870235
0.3004333
0.1302403
0.1005164 -0.6912754
1.0000000
0.2628726
0.2213929
rpc
-0.1578921
0.1153146 -0.5774270
0.0552942 -0.3802718
0.2628726
1.0000000
0.1217886
rpp
-0.1329777
0.0971186
0.0603402 -0.7336226 -0.3202673
0.2213929
0.1217886
1.0000000
pred
1.0
p_disease
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0.0
0
40
50
60
70
80
90
100
110
120
130
140
150
day
treatid
M
PC
PP
T
treatid
M
PC
PP
T
1.0
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0.0
0.0
40
50
60
70
80
90
100
110
120
130
140
day
treatid
M
PC
PP
T
treatid
M
PC
PP
T
150
GOMPERTZ
LOGISTIC
1.0
GENOMD Logistic fitting
ndisease/n_trees is response
11
16:34 Monday, December 8, 2008
The GENMOD Procedure
Model Information
Data Set
WORK.OUTMN
Distribution
Binomial
Link Function
Logit
Response Variable (Events)
ndisease
Response Variable (Trials)
n_trees
Number of Observations Read
160
Number of Observations Used
160
Number of Events
1440
Number of Trials
3200
Class Level Information
Class
treatid
Levels Values
4 M PC PP T
Parameter Information
Parameter Effect
treatid
Prm1
Intercept
Prm2
treatid
M
Prm3
treatid
PC
Prm4
treatid
PP
Prm5
treatid
T
Prm6
day
Prm7
day*treatid M
Prm8
day*treatid PC
Prm9
day*treatid PP
Prm10
day*treatid T
Criteria For Assessing Goodness Of Fit
Criterion
DF
Deviance
152
280.1112
1.8428
Scaled Deviance
152
280.1112
1.8428
Pearson Chi-Square 152
289.2850
1.9032
Scaled Pearson X2
289.2850
1.9032
Log Likelihood
152
Value Value/DF
-1129.2014
Algorithm converged.
GENOMD Logistic fitting
ndisease/n_trees is response
12
16:34 Monday, December 8, 2008
The GENMOD Procedure
Analysis Of Parameter Estimates
Standard
DF Estimate
Error
Parameter
Intercept
Note: The
Wald 95%
Confidence
Limits
1
-5.4031
0.3764 -6.1407 -4.6654
Chi-Square Pr > ChiSq
206.08
<.0001
treatid
M
1
-0.4827
0.5497 -1.5601
0.5948
0.77
0.3799
treatid
PC
1
-4.4469
0.7899 -5.9950 -2.8987
31.69
<.0001
treatid
PP
1
-5.8215
0.9027 -7.5908 -4.0522
41.59
<.0001
treatid
T
0
0.0000
0.0000
0.0000
0.0000
.
.
day
1
0.0631
0.0042
0.0549
0.0713
227.82
<.0001
day*treatid M
1
0.0020
0.0060 -0.0097
0.0138
0.11
0.7351
day*treatid PC
1
0.0308
0.0078
0.0155
0.0461
15.57
<.0001
day*treatid PP
1
0.0404
0.0086
0.0235
0.0574
21.87
<.0001
day*treatid T
0
0.0000
0.0000
0.0000
0.0000
.
.
Scale
0
1.0000
0.0000
1.0000
1.0000
scale parameter was held fixed.
LR Statistics For Type 3 Analysis
Source
DF Chi-Square Pr > ChiSq
treatid
3
81.36
<.0001
day
1
2051.24
<.0001
day*treatid
3
39.85
<.0001
Contrast Results
Contrast
DF Chi-Square Pr > ChiSq Type
PP=PC
1
1.65
0.1983 LR
T=M
1
0.77
0.3794 LR
(PPandPC= TandM)
1
79.57
<.0001 LR
rpc=rpp
1
0.92
0.3369 LR
rm=rt
1
0.11
0.7350 LR
(rpc and rpp) = (rm and rt)
1
39.29
<.0001 LR
ndisease/n_trees is response
Predicted Value
1.0
p_disease
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0.0
0
40
50
60
70
80
90
100
110
120
130
140
day
treatid
M
PC
PP
T
treatid
M
PC
PP
T
150
GENOMD Logistic fitting
ndisease/n_trees is response - overdispersion
14
16:34 Monday, December 8, 2008
The GENMOD Procedure
Model Information
Data Set
WORK.OUTMN
Distribution
Binomial
Link Function
Logit
Response Variable (Events)
ndisease
Response Variable (Trials)
n_trees
Number of Observations Read
160
Number of Observations Used
160
Number of Events
1440
Number of Trials
3200
Class Level Information
Class
Levels Values
treatid
4 M PC PP T
Parameter Information
Parameter Effect
treatid
Prm1
Intercept
Prm2
treatid
M
Prm3
treatid
PC
Prm4
treatid
PP
Prm5
treatid
T
Prm6
day
Prm7
day*treatid M
Prm8
day*treatid PC
Prm9
day*treatid PP
Prm10
day*treatid T
Criteria For Assessing Goodness Of Fit
Criterion
DF
Deviance
152
280.1112
1.8428
Scaled Deviance
152
152.0000
1.0000
Pearson Chi-Square 152
289.2850
1.9032
Scaled Pearson X2
156.9781
1.0328
Log Likelihood
152
Value Value/DF
-612.7516
Algorithm converged.
GENOMD Logistic fitting
ndisease/n_trees is response - overdispersion
15
16:34 Monday, December 8, 2008
The GENMOD Procedure
Analysis Of Parameter Estimates
Parameter
Intercept
Note: The
Wald 95%
Confidence
Limits
Standard
DF Estimate
Error
Chi-Square Pr > ChiSq
1
-5.4031
0.5109 -6.4045 -4.4017
111.83
<.0001
treatid
M
1
-0.4827
0.7463 -1.9453
0.9800
0.42
0.5178
treatid
PC
1
-4.4469
1.0723 -6.5485 -2.3452
17.20
<.0001
treatid
PP
1
-5.8215
1.2254 -8.2233 -3.4197
22.57
<.0001
treatid
T
0
0.0000
0.0000
0.0000
0.0000
.
.
day
1
0.0631
0.0057
0.0520
0.0743
123.63
<.0001
day*treatid M
1
0.0020
0.0081 -0.0139
0.0180
0.06
0.8031
day*treatid PC
1
0.0308
0.0106
0.0100
0.0516
8.45
0.0037
day*treatid PP
1
0.0404
0.0117
0.0174
0.0635
11.87
0.0006
day*treatid T
0
0.0000
0.0000
0.0000
0.0000
.
.
Scale
0
1.3575
0.0000
1.3575
1.3575
scale parameter was estimated by the square root of DEVIANCE/DOF.
LR Statistics For Type 3 Analysis
Source
Num DF Den DF F Value
Pr > F Chi-Square Pr > ChiSq
treatid
3
152
14.72 <.0001
44.15
<.0001
day
1
152 1113.09 <.0001
1113.09
<.0001
day*treatid
3
152
21.62
<.0001
7.21 0.0001
Contrast Results
Contrast
Num DF Den DF F Value
Pr > F Chi-Square Pr > ChiSq Type
PP=PC
1
152
0.90 0.3449
0.90
0.3434 LR
T=M
1
152
0.42 0.5183
0.42
0.5173 LR
(PPandPC= TandM)
1
152
43.18 <.0001
43.18
<.0001 LR
rpc=rpp
1
152
0.50 0.4804
0.50
0.4793 LR
rm=rt
1
152
0.06 0.8034
0.06
0.8031 LR
(rpc and rpp) = (rm and rt)
1
152
21.32 <.0001
21.32
<.0001 LR
ndisease/n_trees is response - overdispersion
Predicted Value
1.0
p_disease
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0.0
0
40
50
60
70
80
90
100
110
120
130
140
day
treatid
M
PC
PP
T
treatid
M
PC
PP
T
150
NLMIXED fitting ndisease is binomial(20, p_i)
separate slope for M , T , PC and PP
separate intercept for M , T , PC and PP
17
16:34 Monday, December 8, 2008
The NLMIXED Procedure
Specifications
Data Set
WORK.OUTMN
Dependent Variable
ndisease
Distribution for Dependent Variable Binomial
Random Effects
u
Distribution for Random Effects
Normal
Subject Variable
repid
Optimization Technique
Dual Quasi-Newton
Integration Method
Adaptive Gaussian Quadrature
Dimensions
Observations Used
160
Observations Not Used
0
Total Observations
160
Subjects
160
Max Obs Per Subject
1
Parameters
9
Quadrature Points
5
Parameters
b0
bm bpc bpp
r
rm
rpc
rpp sigma2 NegLogLike
-1 -0.67 -1.6 -1.1 0.06 0.003 0.04 0.05
1 364.311182
Iteration History
Iter
Calls NegLogLike
Diff MaxGrad
Slope
1
4 355.527044 8.784139 410.3034 -15100.9
2
6 352.818903 2.708141 334.7839 -351.608
3
7 339.490828 13.32807 313.1631 -198.044
4
9 312.246334 27.24449
309.943 -2422.44
5
11 297.354925 14.89141 347.9569 -738.479
6
13 288.796771 8.558154 76.97885 -12.8884
7
16 281.553488 7.243283 298.5461 -3.55676
8
20
9
22 275.830207 1.556702 26.98637 -6.59475
10
24 274.762029 1.068179 85.57418 -0.70916
11
26 274.393768 0.368261 8.607969
12
28 274.177738 0.216031 27.05481 -0.22186
13
29 273.975936 0.201802 38.86522 -0.27645
14
31
277.38691 4.166578 282.9434 -8.30548
-0.8065
273.89652 0.079416 4.230033 -0.16661
NLMIXED fitting ndisease is binomial(20, p_i)
separate slope for M , T , PC and PP
separate intercept for M , T , PC and PP
18
16:34 Monday, December 8, 2008
The NLMIXED Procedure
Iteration History
Iter
Calls NegLogLike
Diff MaxGrad
Slope
15
33 273.893236 0.003283 2.959343 -0.01295
16
35 273.891527
17
37 273.891074 0.000453
18
39 273.890933 0.000141 0.155844 -0.00035
19
41 273.890933
4.4E-7 0.178486 -3.84E-6
20
42 273.890932
6.55E-7 0.030399 -1.37E-6
0.00171 1.507449 -0.00289
1.92073 -0.00043
NOTE: GCONV convergence criterion satisfied.
Fit Statistics
-2 Log Likelihood
547.8
AIC (smaller is better)
565.8
AICC (smaller is better) 567.0
BIC (smaller is better)
593.5
Parameter Estimates
Parameter
Estimate
Standard
Error
DF t Value Pr > |t| Alpha
Lower
Upper
Gradient
b0
0.3505
0.1498 159
2.34 0.0205
0.05
0.05468
0.6463
-0.0013
bm
-0.2966
0.2102 159
-1.41 0.1602
0.05
-0.7119
0.1186
-0.00035
bpc
-1.7488
0.2503 159
-6.99 <.0001
0.05
-2.2432 -1.2544
-0.00049
bpp
-2.2418
0.2734 159
-8.20 <.0001
0.05
-2.7818 -1.7018 0.000131
r
0.06896 0.005835 159
11.82 <.0001
0.05
0.05744 0.08049 0.030399
0.001911 0.008116 159
0.24 0.8141
0.05 -0.01412 0.01794 0.029448
rm
rpc
0.03107
0.01009 159
3.08 0.0024
0.05
0.01114 0.05099
rpp
0.03934
0.01088 159
3.61 0.0004
0.05
0.01785 0.06083 0.006952
0.3813
0.1122 159
3.40 0.0009
0.05
sigma2
0.1597
Contrasts
Label
Num Den
DF DF F Value
Pr > F
PP=PC
1 159
2.63 0.1065
T=M
1 159
3.77 0.0539
rpc=rpp
1 159
0.44 0.5077
PPandPC = TandM
1 159
79.45 <.0001
slopes: (T,M) = (PP,PC)
1 159
98.96 <.0001
-0.00962
0.6030 0.000135
pred is the fixed predicted value of p=proportion diseased
19
16:34 Monday, December 8, 2008
Obs treatid rep day p_disease ndisease n_trees id_pp id_pc id_m id_t repid
t
Pred
1 M
5
42
0.05
1
20
0
0
1
0 M5
-48 0.033957
2 M
8
42
0
0
20
0
0
1
0 M8
-48 0.033957
3 M
11
42
0.1
2
20
0
0
1
0 M11
-48 0.033957
4 M
16
42
0
0
20
0
0
1
0 M16
-48 0.033957
5 M
19
42
0.05
1
20
0
0
1
0 M19
-48 0.033957
6 PC
1
42
0
0
20
0
1
0
0 PC1
-48 0.002026
7 PC
4
42
0
0
20
0
1
0
0 PC4
-48 0.002026
8 PC
9
42
0.05
1
20
0
1
0
0 PC9
-48 0.002026
9 PC
14
42
0
0
20
0
1
0
0 PC14 -48 0.002026
10 PC
17
42
0
0
20
0
1
0
0 PC17 -48 0.002026
11 PP
3
42
0
0
20
1
0
0
0 PP3
-48 0.000833
12 PP
6
42
0
0
20
1
0
0
0 PP6
-48 0.000833
13 PP
12
42
0
0
20
1
0
0
0 PP12 -48 0.000833
14 PP
13
42
0
0
20
1
0
0
0 PP13 -48 0.000833
15 PP
18
42
0
0
20
1
0
0
0 PP18 -48 0.000833
16 T
2
42
0.05
1
20
0
0
0
1 T2
-48 0.049278
17 T
7
42
0.1
2
20
0
0
0
1 T7
-48 0.049278
18 T
10
42
0
0
20
0
0
0
1 T10
-48 0.049278
19 T
15
42
0.05
1
20
0
0
0
1 T15
-48 0.049278
20 T
20
42
0.05
1
20
0
0
0
1 T20
-48 0.049278
Obs StdErrPred DF
tValue
Probt
Alpha
Lower
Upper
1
0.010300 159 3.29684 0.00121
0.05
0.013615 0.05430
2
0.010300 159 3.29684 0.00121
0.05
0.013615 0.05430
3
0.010300 159 3.29684 0.00121
0.05
0.013615 0.05430
4
0.010300 159 3.29684 0.00121
0.05
0.013615 0.05430
5
0.010300 159 3.29684 0.00121
0.05
0.013615 0.05430
6
0.001080 159 1.87515 0.06261
0.05 -0.000108 0.00416
7
0.001080 159 1.87515 0.06261
0.05 -0.000108 0.00416
8
0.001080 159 1.87515 0.06261
0.05 -0.000108 0.00416
9
0.001080 159 1.87515 0.06261
0.05 -0.000108 0.00416
10
0.001080 159 1.87515 0.06261
0.05 -0.000108 0.00416
11
0.000513 159 1.62286 0.10660
0.05 -0.000181 0.00185
12
0.000513 159 1.62286 0.10660
0.05 -0.000181 0.00185
13
0.000513 159 1.62286 0.10660
0.05 -0.000181 0.00185
14
0.000513 159 1.62286 0.10660
0.05 -0.000181 0.00185
15
0.000513 159 1.62286 0.10660
0.05 -0.000181 0.00185
16
0.013993 159 3.52152 0.00056
0.05
0.021641 0.07692
17
0.013993 159 3.52152 0.00056
0.05
0.021641 0.07692
18
0.013993 159 3.52152 0.00056
0.05
0.021641 0.07692
19
0.013993 159 3.52152 0.00056
0.05
0.021641 0.07692
20
0.013993 159 3.52152 0.00056
0.05
0.021641 0.07692
pred is the fixed predicted value of p=proportion diseased
20
16:34 Monday, December 8, 2008
Obs treatid rep day p_disease ndisease n_trees id_pp id_pc id_m id_t repid
t
Pred
21 M
5
57
0.15
3
20
0
0
1
0 M5
-33 0.092373
22 M
8
57
0.15
3
20
0
0
1
0 M8
-33 0.092373
23 M
11
57
0.15
3
20
0
0
1
0 M11
-33 0.092373
24 M
16
57
0.05
1
20
0
0
1
0 M16
-33 0.092373
25 M
19
57
0.2
4
20
0
0
1
0 M19
-33 0.092373
Obs StdErrPred DF
tValue
Probt
Alpha
Lower
Upper
21
0.020088 159 4.59845 0.00001
0.05
0.052699 0.13205
22
0.020088 159 4.59845 0.00001
0.05
0.052699 0.13205
23
0.020088 159 4.59845 0.00001
0.05
0.052699 0.13205
24
0.020088 159 4.59845 0.00001
0.05
0.052699 0.13205
25
0.020088 159 4.59845 0.00001
0.05
0.052699 0.13205
pred is the predicted value of p= fixed + random effects
predicted value for random effect is not zero
21
16:34 Monday, December 8, 2008
Obs treatid rep day p_disease ndisease n_trees id_pp id_pc id_m id_t repid
t
Pred
1 M
5
42
0.05
1
20
0
0
1
0 M5
-48 0.03729
2 M
8
42
0
0
20
0
0
1
0 M8
-48 0.02767
3 M
11
42
0.1
2
20
0
0
1
0 M11
-48 0.04923
4 M
16
42
0
0
20
0
0
1
0 M16
-48 0.02767
5 M
19
42
0.05
1
20
0
0
1
0 M19
-48 0.03729
6 PC
1
42
0
0
20
0
1
0
0 PC1
-48 0.00200
7 PC
4
42
0
0
20
0
1
0
0 PC4
-48 0.00200
8 PC
9
42
0.05
1
20
0
1
0
0 PC9
-48 0.00290
9 PC
14
42
0
0
20
0
1
0
0 PC14 -48 0.00200
10 PC
17
42
0
0
20
0
1
0
0 PC17 -48 0.00200
11 PP
3
42
0
0
20
1
0
0
0 PP3
-48 0.00083
12 PP
6
42
0
0
20
1
0
0
0 PP6
-48 0.00083
13 PP
12
42
0
0
20
1
0
0
0 PP12 -48 0.00083
14 PP
13
42
0
0
20
1
0
0
0 PP13 -48 0.00083
15 PP
18
42
0
0
20
1
0
0
0 PP18 -48 0.00083
16 T
2
42
0.05
1
20
0
0
0
1 T2
-48 0.04947
17 T
7
42
0.1
2
20
0
0
0
1 T7
-48 0.06390
18 T
10
42
0
0
20
0
0
0
1 T10
-48 0.03748
19 T
15
42
0.05
1
20
0
0
0
1 T15
-48 0.04947
20 T
20
42
0.05
1
20
0
0
0
1 T20
-48 0.04947
Obs StdErrPred DF
tValue
Probt
Alpha
Lower
Upper
1
0.021509 159 1.73352 0.08494
0.05 -0.005194 0.07977
2
0.016822 159 1.64513 0.10192
0.05 -0.005549 0.06090
3
0.027129 159 1.81449 0.07149
0.05 -0.004354 0.10280
4
0.016822 159 1.64513 0.10192
0.05 -0.005549 0.06090
5
0.021509 159 1.73352 0.08494
0.05 -0.005194 0.07977
6
0.001610 159 1.23948 0.21700
0.05 -0.001184 0.00517
7
0.001610 159 1.23948 0.21700
0.05 -0.001184 0.00517
8
0.002310 159 1.25482 0.21139
0.05 -0.001664 0.00746
9
0.001610 159 1.23948 0.21700
0.05 -0.001184 0.00517
10
0.001610 159 1.23948 0.21700
0.05 -0.001184 0.00517
11
0.000719 159 1.15198 0.25106
0.05 -0.000591 0.00225
12
0.000719 159 1.15198 0.25106
0.05 -0.000591 0.00225
13
0.000719 159 1.15198 0.25106
0.05 -0.000591 0.00225
14
0.000719 159 1.15198 0.25106
0.05 -0.000591 0.00225
15
0.000719 159 1.15198 0.25106
0.05 -0.000591 0.00225
16
0.026969 159 1.83428 0.06848
0.05 -0.003795 0.10273
17
0.032958 159 1.93883 0.05429
0.05 -0.001192 0.12899
18
0.021736 159 1.72451 0.08656
0.05 -0.005445 0.08041
19
0.026969 159 1.83428 0.06848
0.05 -0.003795 0.10273
20
0.026969 159 1.83428 0.06848
0.05 -0.003795 0.10273
pred is the predicted value of p= fixed + random effects
predicted value for random effect is not zero
22
16:34 Monday, December 8, 2008
Obs treatid rep day p_disease ndisease n_trees id_pp id_pc id_m id_t repid
t
Pred
21 M
5
57
0.15
3
20
0
0
1
0 M5
-33 0.11630
22 M
8
57
0.15
3
20
0
0
1
0 M8
-33 0.11630
23 M
11
57
0.15
3
20
0
0
1
0 M11
-33 0.11630
24 M
16
57
0.05
1
20
0
0
1
0 M16
-33 0.07667
25 M
19
57
0.2
4
20
0
0
1
0 M19
-33 0.13924
Obs StdErrPred DF
tValue
Probt
Alpha
Lower
Upper
21
0.049539 159 2.34763 0.02012
0.05
0.018460 0.21414
22
0.049539 159 2.34763 0.02012
0.05
0.018460 0.21414
23
0.049539 159 2.34763 0.02012
0.05
0.018460 0.21414
24
0.037105 159 2.06638 0.04041
0.05
0.003391 0.14996
25
0.055957 159 2.48834 0.01386
0.05
0.028725 0.24976
fixed effect plus average of random effect for each treatment and day combination
23
16:34 Monday, December 8, 2008
Obs treatid day _TYPE_ _FREQ_
Pred
var
nobs
mx
mi
1 M
42
3
5 0.03583 0.000079
5 0.04923 0.02767
2 M
57
3
5 0.11296 0.000510
5 0.13924 0.07667
3 M
71
3
5 0.25349 0.002053
5 0.32583 0.20678
4 M
85
3
5 0.36432 0.002859
5 0.44145 0.31342
5 M
99
3
5 0.61765 0.000720
5 0.65604 0.59193
6 M
112
3
5 0.79762 0.003167
5 0.86639 0.73066
7 M
126
3
5 0.93622 0.000240
5 0.95146 0.92049
8 M
143
3
5 0.98118 0.000000
5 0.98118 0.98118
9 PC
42
3
5 0.00218 0.000000
5 0.00290 0.00200
10 PC
57
3
5 0.00917 0.000003
5 0.01201 0.00846
11 PC
71
3
5 0.04990 0.000940
5 0.10228 0.02879
12 PC
85
3
5 0.12264 0.005112
5 0.24714 0.07691
13 PC
99
3
5 0.34340 0.013421
5 0.52276 0.23758
14 PC
112
3
5 0.68388 0.025954
5 0.83888 0.43793
15 PC
126
3
5 0.87294 0.008709
5 0.93634 0.71696
16 PC
143
3
5 0.98264 0.000000
5 0.98264 0.98264
17 PP
42
3
5 0.00083 0.000000
5 0.00083 0.00083
18 PP
57
3
5 0.00445 0.000001
5 0.00589 0.00408
19 PP
71
3
5 0.02433 0.000109
5 0.04206 0.01669
20 PP
85
3
5 0.08168 0.000407
5 0.10794 0.05469
21 PP
99
3
5 0.24084 0.000587
5 0.26415 0.20640
22 PP
112
3
5 0.61854 0.011581
5 0.73240 0.47667
23 PP
126
3
5 0.85386 0.007708
5 0.92801 0.73168
24 PP
143
3
5 0.98179 0.000000
5 0.98179 0.98179
42
3
5 0.04996 0.000088
5 0.06390 0.03748
25 T
Predicted Value
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
40
50
60
70
80
90
100
110
120
130
day
treatid
M
PC
PP
T
140
150
NLMIXED fitting ndisease is binomial(20, p_i)
same slopes fo rM and T and for PC and PP
same intercept fo rM and T and for PC and PP
25
16:34 Monday, December 8, 2008
The NLMIXED Procedure
Specifications
Data Set
WORK.OUTMN
Dependent Variable
ndisease
Distribution for Dependent Variable Binomial
Random Effects
u
Distribution for Random Effects
Normal
Subject Variable
repid
Optimization Technique
Dual Quasi-Newton
Integration Method
Adaptive Gaussian Quadrature
Dimensions
Observations Used
160
Observations Not Used
0
Total Observations
160
Subjects
160
Max Obs Per Subject
1
Parameters
5
Quadrature Points
7
Parameters
b0 bpp
r
rpp sigma2 NegLogLike
-1 -1.1 0.06 0.05
1.5 327.178041
Iteration History
Iter
Calls NegLogLike
Diff MaxGrad
Slope
1
4 321.593152 5.584889 134.3517 -6482.26
2
6 320.766683 0.826469 143.0028 -98.9681
3
8 296.414023 24.35266 140.5357 -46.5202
4
10 289.586657 6.827366 499.9346 -4.04787
5
12 279.882356 9.704302 345.3743 -9.10671
6
14 277.429724 2.452632 58.90003 -9.07967
7
16 276.997446 0.432278
8
17 276.516025 0.481421 30.29399 -1.12744
9
19 276.296732 0.219294 19.91271 -0.29731
10
21 276.261927 0.034805 3.495221 -0.09058
11
23 276.259961 0.001966 3.467253
12
25 276.259642 0.000319 0.672443 -0.00076
13
27 276.259632 0.000011 0.647131 -0.00005
75.7299 -1.18667
-0.0059
NLMIXED fitting ndisease is binomial(20, p_i)
same slopes fo rM and T and for PC and PP
same intercept fo rM and T and for PC and PP
26
16:34 Monday, December 8, 2008
The NLMIXED Procedure
Iteration History
Iter
Calls NegLogLike
Diff MaxGrad
Slope
14
29 276.259625 6.179E-6 0.065643 -0.00001
15
31 276.259625 8.439E-8 0.031938 -3.24E-7
NOTE: GCONV convergence criterion satisfied.
Fit Statistics
-2 Log Likelihood
552.5
AIC (smaller is better)
562.5
AICC (smaller is better) 562.9
BIC (smaller is better)
577.9
Parameter Estimates
Parameter Estimate
Standard
Error
DF t Value Pr > |t| Alpha
Lower
Upper
Gradient
0.05 -0.00730
0.4226
-0.00242
b0
0.2077
0.1088 159
1.91 0.0582
bpp
-1.8373
0.1883 159
-9.75 <.0001
0.05
-2.2093 -1.4653
-0.0008
r
0.07018 0.004330 159
16.21 <.0001
0.05
0.06163 0.07873
-0.03194
rpp
0.03384 0.007520 159
4.50 <.0001
0.05
0.01899 0.04869
-0.02421
3.56 0.0005
0.05
sigma2
0.4212
0.1183 159
0.1876
0.6548 0.000523
pred is the predicted value of p= fixed effects
predicted value for random effect is zero
27
16:34 Monday, December 8, 2008
Obs treatid rep day p_disease ndisease n_trees id_pp id_pc id_m id_t repid
t
Pred
1 M
5
42
0.05
1
20
0
0
1
0 M5
-48 0.04067
2 M
8
42
0
0
20
0
0
1
0 M8
-48 0.04067
3 M
11
42
0.1
2
20
0
0
1
0 M11
-48 0.04067
4 M
16
42
0
0
20
0
0
1
0 M16
-48 0.04067
5 M
19
42
0.05
1
20
0
0
1
0 M19
-48 0.04067
6 PC
1
42
0
0
20
0
1
0
0 PC1
-48 0.00133
7 PC
4
42
0
0
20
0
1
0
0 PC4
-48 0.00133
8 PC
9
42
0.05
1
20
0
1
0
0 PC9
-48 0.00133
9 PC
14
42
0
0
20
0
1
0
0 PC14 -48 0.00133
10 PC
17
42
0
0
20
0
1
0
0 PC17 -48 0.00133
11 PP
3
42
0
0
20
1
0
0
0 PP3
-48 0.00133
12 PP
6
42
0
0
20
1
0
0
0 PP6
-48 0.00133
13 PP
12
42
0
0
20
1
0
0
0 PP12 -48 0.00133
14 PP
13
42
0
0
20
1
0
0
0 PP13 -48 0.00133
15 PP
18
42
0
0
20
1
0
0
0 PP18 -48 0.00133
16 T
2
42
0.05
1
20
0
0
0
1 T2
-48 0.04067
17 T
7
42
0.1
2
20
0
0
0
1 T7
-48 0.04067
18 T
10
42
0
0
20
0
0
0
1 T10
-48 0.04067
19 T
15
42
0.05
1
20
0
0
0
1 T15
-48 0.04067
20 T
20
42
0.05
1
20
0
0
0
1 T20
-48 0.04067
Obs StdErrPred DF
tValue
Probt
Alpha
Lower
Upper
1
0.008721 159 4.66305 0.000007
0.05 0.023443 0.05789
2
0.008721 159 4.66305 0.000007
0.05 0.023443 0.05789
3
0.008721 159 4.66305 0.000007
0.05 0.023443 0.05789
4
0.008721 159 4.66305 0.000007
0.05 0.023443 0.05789
5
0.008721 159 4.66305 0.000007
0.05 0.023443 0.05789
6
0.000549 159 2.41776 0.016747
0.05 0.000243 0.00241
7
0.000549 159 2.41776 0.016747
0.05 0.000243 0.00241
8
0.000549 159 2.41776 0.016747
0.05 0.000243 0.00241
9
0.000549 159 2.41776 0.016747
0.05 0.000243 0.00241
10
0.000549 159 2.41776 0.016747
0.05 0.000243 0.00241
11
0.000549 159 2.41776 0.016747
0.05 0.000243 0.00241
12
0.000549 159 2.41776 0.016747
0.05 0.000243 0.00241
13
0.000549 159 2.41776 0.016747
0.05 0.000243 0.00241
14
0.000549 159 2.41776 0.016747
0.05 0.000243 0.00241
15
0.000549 159 2.41776 0.016747
0.05 0.000243 0.00241
16
0.008721 159 4.66305 0.000007
0.05 0.023443 0.05789
17
0.008721 159 4.66305 0.000007
0.05 0.023443 0.05789
18
0.008721 159 4.66305 0.000007
0.05 0.023443 0.05789
19
0.008721 159 4.66305 0.000007
0.05 0.023443 0.05789
20
0.008721 159 4.66305 0.000007
0.05 0.023443 0.05789
pred is the predicted value of p= fixed effects
predicted value for random effect is zero
28
16:34 Monday, December 8, 2008
Obs treatid rep day p_disease ndisease n_trees id_pp id_pc id_m id_t repid
t
Pred
21 M
5
57
0.15
3
20
0
0
1
0 M5
-33 0.10831
22 M
8
57
0.15
3
20
0
0
1
0 M8
-33 0.10831
23 M
11
57
0.15
3
20
0
0
1
0 M11
-33 0.10831
24 M
16
57
0.05
1
20
0
0
1
0 M16
-33 0.10831
25 M
19
57
0.2
4
20
0
0
1
0 M19
-33 0.10831
Obs StdErrPred DF
tValue
Probt
Alpha
Lower
Upper
21
0.016383 159 6.61085 0.000000
0.05 0.075950 0.14066
22
0.016383 159 6.61085 0.000000
0.05 0.075950 0.14066
23
0.016383 159 6.61085 0.000000
0.05 0.075950 0.14066
24
0.016383 159 6.61085 0.000000
0.05 0.075950 0.14066
25
0.016383 159 6.61085 0.000000
0.05 0.075950 0.14066
pred is the predicted value of p= fixed + random effects
predicted value for random effect is not zero
29
16:34 Monday, December 8, 2008
Obs treatid rep day p_disease ndisease n_trees id_pp id_pc id_m id_t repid
t
Pred
1 M
5
42
0.05
1
20
0
0
1
0 M5
-48 0.04302
2 M
8
42
0
0
20
0
0
1
0 M8
-48 0.03149
3 M
11
42
0.1
2
20
0
0
1
0 M11
-48 0.05728
4 M
16
42
0
0
20
0
0
1
0 M16
-48 0.03149
5 M
19
42
0.05
1
20
0
0
1
0 M19
-48 0.04302
6 PC
1
42
0
0
20
0
1
0
0 PC1
-48 0.00131
7 PC
4
42
0
0
20
0
1
0
0 PC4
-48 0.00131
8 PC
9
42
0.05
1
20
0
1
0
0 PC9
-48 0.00199
9 PC
14
42
0
0
20
0
1
0
0 PC14 -48 0.00131
10 PC
17
42
0
0
20
0
1
0
0 PC17 -48 0.00131
11 PP
3
42
0
0
20
1
0
0
0 PP3
-48 0.00131
12 PP
6
42
0
0
20
1
0
0
0 PP6
-48 0.00131
13 PP
12
42
0
0
20
1
0
0
0 PP12 -48 0.00131
14 PP
13
42
0
0
20
1
0
0
0 PP13 -48 0.00131
15 PP
18
42
0
0
20
1
0
0
0 PP18 -48 0.00131
16 T
2
42
0.05
1
20
0
0
0
1 T2
-48 0.04302
17 T
7
42
0.1
2
20
0
0
0
1 T7
-48 0.05728
18 T
10
42
0
0
20
0
0
0
1 T10
-48 0.03149
19 T
15
42
0.05
1
20
0
0
0
1 T15
-48 0.04302
20 T
20
42
0.05
1
20
0
0
0
1 T20
-48 0.04302
Obs StdErrPred DF
tValue
Probt
Alpha
Lower
Upper
1
0.023994 159 1.79313 0.07485
0.05 -0.004364 0.09041
2
0.018668 159 1.68686 0.09359
0.05 -0.005379 0.06836
3
0.030234 159 1.89443 0.05998
0.05 -0.002436 0.11699
4
0.018668 159 1.68686 0.09359
0.05 -0.005379 0.06836
5
0.023994 159 1.79313 0.07485
0.05 -0.004364 0.09041
6
0.001004 159 1.30919 0.19236
0.05 -0.000668 0.00330
7
0.001004 159 1.30919 0.19236
0.05 -0.000668 0.00330
8
0.001504 159 1.32313 0.18769
0.05 -0.000980 0.00496
9
0.001004 159 1.30919 0.19236
0.05 -0.000668 0.00330
10
0.001004 159 1.30919 0.19236
0.05 -0.000668 0.00330
11
0.001004 159 1.30919 0.19236
0.05 -0.000668 0.00330
12
0.001004 159 1.30919 0.19236
0.05 -0.000668 0.00330
13
0.001004 159 1.30919 0.19236
0.05 -0.000668 0.00330
14
0.001004 159 1.30919 0.19236
0.05 -0.000668 0.00330
15
0.001004 159 1.30919 0.19236
0.05 -0.000668 0.00330
16
0.023994 159 1.79313 0.07485
0.05 -0.004364 0.09041
17
0.030234 159 1.89443 0.05998
0.05 -0.002436 0.11699
18
0.018668 159 1.68686 0.09359
0.05 -0.005379 0.06836
19
0.023994 159 1.79313 0.07485
0.05 -0.004364 0.09041
20
0.023994 159 1.79313 0.07485
0.05 -0.004364 0.09041
pred is the predicted value of p= fixed + random effects
predicted value for random effect is not zero
30
16:34 Monday, December 8, 2008
Obs treatid rep day p_disease ndisease n_trees id_pp id_pc id_m id_t repid
t
Pred
21 M
5
57
0.15
3
20
0
0
1
0 M5
-33 0.12777
22 M
8
57
0.15
3
20
0
0
1
0 M8
-33 0.12777
23 M
11
57
0.15
3
20
0
0
1
0 M11
-33 0.12777
24 M
16
57
0.05
1
20
0
0
1
0 M16
-33 0.08375
25 M
19
57
0.2
4
20
0
0
1
0 M19
-33 0.15294
Obs StdErrPred DF
tValue
Probt
Alpha
Lower
Upper
21
0.052848 159 2.41762 0.01675
0.05
0.023392 0.23214
22
0.052848 159 2.41762 0.01675
0.05
0.023392 0.23214
23
0.052848 159 2.41762 0.01675
0.05
0.023392 0.23214
24
0.039903 159 2.09877 0.03742
0.05
0.004939 0.16256
25
0.059287 159 2.57968 0.01079
0.05
0.035850 0.27004
fixed effect plus average of random effect for each treatment and day combination
31
16:34 Monday, December 8, 2008
Obs treatid day _TYPE_ _FREQ_
Pred
var
nobs
mx
mi
1 M
42
3
5 0.04126 0.000113
5 0.05728 0.03149
2 M
57
3
5 0.12400 0.000625
5 0.15294 0.08375
3 M
71
3
5 0.26729 0.002274
5 0.34335 0.21800
4 M
85
3
5 0.37452 0.003087
5 0.45461 0.32160
5 M
99
3
5 0.62753 0.000766
5 0.66711 0.60100
6 M
112
3
5 0.80519 0.003360
5 0.87592 0.73613
7 M
126
3
5 0.94142 0.000246
5 0.95681 0.92549
8 M
143
3
5 0.98319 0.000000
5 0.98319 0.98319
9 PC
42
3
5 0.00145 0.000000
5 0.00199 0.00131
10 PC
57
3
5 0.00656 0.000002
5 0.00887 0.00598
11 PC
71
3
5 0.04201 0.000873
5 0.09272 0.02206
12 PC
85
3
5 0.10935 0.005185
5 0.23496 0.06376
13 PC
99
3
5 0.32733 0.014197
5 0.51199 0.21877
14 PC
112
3
5 0.67330 0.028176
5 0.83539 0.41765
15 PC
126
3
5 0.86681 0.009959
5 0.93486 0.70030
16 PC
143
3
5 0.98254 0.000000
5 0.98254 0.98254
17 PP
42
3
5 0.00131 0.000000
5 0.00131 0.00131
18 PP
57
3
5 0.00656 0.000002
5 0.00887 0.00598
19 PP
71
3
5 0.03247 0.000199
5 0.05639 0.02206
20 PP
85
3
5 0.09517 0.000546
5 0.12539 0.06376
21 PP
99
3
5 0.25523 0.000656
5 0.27987 0.21877
22 PP
112
3
5 0.63149 0.012290
5 0.74865 0.48522
23 PP
126
3
5 0.85841 0.008252
5 0.93486 0.73186
24 PP
143
3
5 0.98254 0.000000
5 0.98254 0.98254
42
3
5 0.04357 0.000084
5 0.05728 0.03149
25 T
Predicted Value
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
40
50
60
70
80
90
100
110
120
130
day
treatid
M
PC
PP
T
140
150