John Sorkin
2012-Jun-12 14:51 UTC
[R] lme random slope results the same as random slope and intercept model
R 2.15.0
Windows XP
Can someone help me understand why a random intercept model gives the same
results as the random intercept and slope models?
I am rather surprised by the results I am getting from lme. I am running three
models
(1) random intercept
fitRI <- lme(echogen~time,random=~ 1
|subject,data=repeatdata,na.action=na.omit)
(2) random slope> fitRT <- lme(echogen~time,random=~
-1+time|subject,data=repeatdata,na.action=na.omit)
(3) random intercept and slope.
fitRIRT <- lme(echogen~time,random=~
1+time|subject,data=repeatdata,na.action=na.omit)
The results of the (1) random intercept model are different from the (2) random
slope model,not a surprise.
The results of the (1) random intercept model and the (3) random intercept and
slope models are exactly the same, a surprise!
Below I copy the results for each model. Further below I give all my output.
RESULTS FROM EACH MODEL
(1) Random intercept results:
Random effects:
Formula: ~1 | subject
(Intercept) Residual
StdDev: 19.1751 10.44601
Fixed effects: echogen ~ time
Value Std.Error DF t-value p-value
(Intercept) 64.54864 4.258235 32 15.158545 0.0000
time 0.35795 0.227080 32 1.576307 0.1248
Correlation:
(Intr)
time -0.242
(2) Random slope results
Random effects:
Formula: ~-1 + time | subject
time Residual
StdDev: 0.6014915 19.63638
Fixed effects: echogen ~ time
Value Std.Error DF t-value p-value
(Intercept) 65.03691 3.494160 32 18.613032 0.0000
time 0.22688 0.467306 32 0.485503 0.6306
Correlation:
(Intr)
time -0.625
(3) Random intercept and slope results
Random effects:
Formula: ~1 + time | subject
Structure: General positive-definite, Log-Cholesky parametrization
StdDev Corr
(Intercept) 1.917511e+01 (Intr)
time 2.032072e-04 0
Residual 1.044601e+01
Fixed effects: echogen ~ time
Value Std.Error DF t-value p-value
(Intercept) 64.54864 4.258235 32 15.158543 0.0000
time 0.35795 0.227080 32 1.576307 0.1248
Correlation:
(Intr)
time -0.242
COMPLETE OUTPUT> repeatdata
subject time value echogen
1 1 1 22 63
2 1 3 40 60
3 1 NA NA NA
4 1 NA NA NA
5 1 NA NA NA
6 2 1 39 19
7 2 NA NA NA
8 2 NA NA NA
9 2 NA NA NA
10 2 NA NA NA
11 3 1 47 76
12 3 6 43 82
13 3 NA NA NA
14 3 NA NA NA
15 3 NA NA NA
16 4 1 44 44
17 4 3 50 50
18 4 7 67 67
19 4 21 39 39
20 4 NA NA NA
21 5 1 42 58
22 5 3 60 78
23 5 7 86 85
24 5 19 56 60
25 5 35 39 84
26 6 1 57 67
27 6 NA NA NA
28 6 NA NA NA
29 6 NA NA NA
30 6 NA NA NA
31 7 1 71 58
32 7 3 55 67
33 7 10 57 95
34 7 17 62 94
35 7 25 47 73
36 8 1 79 105
37 8 NA NA NA
38 8 NA NA NA
39 8 NA NA NA
40 8 NA NA NA
41 9 1 60 70
42 9 3 64 62
43 9 9 68 65
44 9 NA NA NA
45 9 NA NA NA
46 10 1 47 75
47 10 3 49 73
48 10 9 46 70
49 10 17 48 70
50 10 NA NA NA
51 11 1 57 97
52 11 6 75 108
53 11 NA NA NA
54 11 NA NA NA
55 11 NA NA NA
56 12 1 85 116
57 12 3 77 110
58 12 NA NA NA
59 12 NA NA NA
60 12 NA NA NA
61 13 1 34 51
62 13 NA NA NA
63 13 NA NA NA
64 13 NA NA NA
65 13 NA NA NA
66 14 1 30 59
67 14 3 NA NA
68 14 NA NA NA
69 14 NA NA NA
70 14 NA NA NA
71 15 1 42 47
72 15 3 50 62
73 15 11 33 75
74 15 NA NA NA
75 15 NA NA NA
76 16 1 NA 83
77 16 7 NA 88
78 16 13 NA 74
79 16 NA NA NA
80 16 NA NA NA
81 17 1 NA 51
82 17 7 NA 62
83 17 NA NA NA
84 17 NA NA NA
85 17 NA NA NA
86 18 1 NA 39
87 18 7 NA 44
88 18 NA NA NA
89 18 NA NA NA
90 18 NA NA NA
91 19 1 NA 45
92 19 7 NA 56
93 19 14 NA NA
94 19 NA NA NA
95 19 NA NA NA
96 20 1 NA 45
97 20 7 NA 57
98 20 NA NA NA
99 20 NA NA NA
100 20 NA NA NA
101 21 1 NA 80
102 21 NA NA NA
103 21 NA NA NA
104 21 NA NA NA
105 21 NA NA NA
106 22 1 NA 42
107 22 7 NA 33
108 22 14 NA 36
109 22 21 NA NA
110 22 NA NA NA
111 23 1 NA 69
112 23 7 NA 68
113 23 NA NA NA
114 23 NA NA NA
115 23 NA NA NA
116 24 1 NA 48
117 24 6 NA 58
118 24 14 NA 82
119 24 NA NA NA
120 24 NA NA NA
121 25 1 NA 67
122 25 NA NA NA
123 25 NA NA NA
124 25 NA NA NA
125 25 NA NA NA>
> library(nlme)
> fitRI <- lme(echogen~time,random=~ 1
|subject,data=repeatdata,na.action=na.omit)
> summary(fitRI)
Linear mixed-effects model fit by REML
Data: repeatdata
AIC BIC logLik
491.097 499.1984 -241.5485
Random effects:
Formula: ~1 | subject
(Intercept) Residual
StdDev: 19.1751 10.44601
Fixed effects: echogen ~ time
Value Std.Error DF t-value p-value
(Intercept) 64.54864 4.258235 32 15.158545 0.0000
time 0.35795 0.227080 32 1.576307 0.1248
Correlation:
(Intr)
time -0.242
Standardized Within-Group Residuals:
Min Q1 Med Q3 Max
-1.61362748 -0.52710871 0.02948022 0.41793307 1.77340062
Number of Observations: 58
Number of Groups: 25 >
> fitRT <- lme(echogen~time,random=~
-1+time|subject,data=repeatdata,na.action=na.omit)
> summary(fitRT)
Linear mixed-effects model fit by REML
Data: repeatdata
AIC BIC logLik
515.2225 523.3239 -253.6112
Random effects:
Formula: ~-1 + time | subject
time Residual
StdDev: 0.6014915 19.63638
Fixed effects: echogen ~ time
Value Std.Error DF t-value p-value
(Intercept) 65.03691 3.494160 32 18.613032 0.0000
time 0.22688 0.467306 32 0.485503 0.6306
Correlation:
(Intr)
time -0.625
Standardized Within-Group Residuals:
Min Q1 Med Q3 Max
-2.35381603 -0.69490411 -0.04299361 0.52973023 2.57509584
Number of Observations: 58
Number of Groups: 25 >
> fitRIRT <- lme(echogen~time,random=~
1+time|subject,data=repeatdata,na.action=na.omit)
> summary(fitRIRT)
Linear mixed-effects model fit by REML
Data: repeatdata
AIC BIC logLik
495.097 507.2491 -241.5485
Random effects:
Formula: ~1 + time | subject
Structure: General positive-definite, Log-Cholesky parametrization
StdDev Corr
(Intercept) 1.917511e+01 (Intr)
time 2.032072e-04 0
Residual 1.044601e+01
Fixed effects: echogen ~ time
Value Std.Error DF t-value p-value
(Intercept) 64.54864 4.258235 32 15.158543 0.0000
time 0.35795 0.227080 32 1.576307 0.1248
Correlation:
(Intr)
time -0.242
Standardized Within-Group Residuals:
Min Q1 Med Q3 Max
-1.61362755 -0.52710871 0.02948008 0.41793322 1.77340082
Number of Observations: 58
Number of Groups: 25 >
John David Sorkin M.D., Ph.D.
Chief, Biostatistics and Informatics
University of Maryland School of Medicine Division of Gerontology
Baltimore VA Medical Center
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524
(Phone) 410-605-7119
(Fax) 410-605-7913 (Please call phone number above prior to faxing)
Confidentiality Statement:
This email message, including any attachments, is for the sole use of the
intended recipient(s) and may contain confidential and privileged information.
Any unauthorized use, disclosure or distribution is prohibited. If you are not
the intended recipient, please contact the sender by reply email and destroy all
copies of the original message.
ONKELINX, Thierry
2012-Jun-12 15:14 UTC
[R] lme random slope results the same as random slope and intercept model
Dear John,
R-sig-mixed-models is a better list for this kind of questions.
It looks like the model finds no evidence for a random slope. Notice the very
small variance of the random slope. In the model without random intercept, the
random slope tries to mimic the effect of a random intercept.
Best regards,
Thierry
ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and
Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium
+ 32 2 525 02 51
+ 32 54 43 61 85
Thierry.Onkelinx at inbo.be
www.inbo.be
To call in the statistician after the experiment is done may be no more than
asking him to perform a post-mortem examination: he may be able to say what the
experiment died of.
~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data.
~ Roger Brinner
The combination of some data and an aching desire for an answer does not ensure
that a reasonable answer can be extracted from a given body of data.
~ John Tukey
-----Oorspronkelijk bericht-----
Van: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
Namens John Sorkin
Verzonden: dinsdag 12 juni 2012 16:52
Aan: r-help at r-project.org
Onderwerp: [R] lme random slope results the same as random slope and intercept
model
R 2.15.0
Windows XP
Can someone help me understand why a random intercept model gives the same
results as the random intercept and slope models?
I am rather surprised by the results I am getting from lme. I am running three
models
(1) random intercept
fitRI <- lme(echogen~time,random=~ 1
|subject,data=repeatdata,na.action=na.omit)
(2) random slope> fitRT <- lme(echogen~time,random=~
-1+time|subject,data=repeatdata,na.action=na.omit)
(3) random intercept and slope.
fitRIRT <- lme(echogen~time,random=~
1+time|subject,data=repeatdata,na.action=na.omit)
The results of the (1) random intercept model are different from the (2) random
slope model,not a surprise.
The results of the (1) random intercept model and the (3) random intercept and
slope models are exactly the same, a surprise!
Below I copy the results for each model. Further below I give all my output.
RESULTS FROM EACH MODEL
(1) Random intercept results:
Random effects:
Formula: ~1 | subject
(Intercept) Residual
StdDev: 19.1751 10.44601
Fixed effects: echogen ~ time
Value Std.Error DF t-value p-value
(Intercept) 64.54864 4.258235 32 15.158545 0.0000
time 0.35795 0.227080 32 1.576307 0.1248
Correlation:
(Intr)
time -0.242
(2) Random slope results
Random effects:
Formula: ~-1 + time | subject
time Residual
StdDev: 0.6014915 19.63638
Fixed effects: echogen ~ time
Value Std.Error DF t-value p-value
(Intercept) 65.03691 3.494160 32 18.613032 0.0000
time 0.22688 0.467306 32 0.485503 0.6306
Correlation:
(Intr)
time -0.625
(3) Random intercept and slope results
Random effects:
Formula: ~1 + time | subject
Structure: General positive-definite, Log-Cholesky parametrization
StdDev Corr
(Intercept) 1.917511e+01 (Intr)
time 2.032072e-04 0
Residual 1.044601e+01
Fixed effects: echogen ~ time
Value Std.Error DF t-value p-value
(Intercept) 64.54864 4.258235 32 15.158543 0.0000
time 0.35795 0.227080 32 1.576307 0.1248
Correlation:
(Intr)
time -0.242
COMPLETE OUTPUT> repeatdata
subject time value echogen
1 1 1 22 63
2 1 3 40 60
3 1 NA NA NA
4 1 NA NA NA
5 1 NA NA NA
6 2 1 39 19
7 2 NA NA NA
8 2 NA NA NA
9 2 NA NA NA
10 2 NA NA NA
11 3 1 47 76
12 3 6 43 82
13 3 NA NA NA
14 3 NA NA NA
15 3 NA NA NA
16 4 1 44 44
17 4 3 50 50
18 4 7 67 67
19 4 21 39 39
20 4 NA NA NA
21 5 1 42 58
22 5 3 60 78
23 5 7 86 85
24 5 19 56 60
25 5 35 39 84
26 6 1 57 67
27 6 NA NA NA
28 6 NA NA NA
29 6 NA NA NA
30 6 NA NA NA
31 7 1 71 58
32 7 3 55 67
33 7 10 57 95
34 7 17 62 94
35 7 25 47 73
36 8 1 79 105
37 8 NA NA NA
38 8 NA NA NA
39 8 NA NA NA
40 8 NA NA NA
41 9 1 60 70
42 9 3 64 62
43 9 9 68 65
44 9 NA NA NA
45 9 NA NA NA
46 10 1 47 75
47 10 3 49 73
48 10 9 46 70
49 10 17 48 70
50 10 NA NA NA
51 11 1 57 97
52 11 6 75 108
53 11 NA NA NA
54 11 NA NA NA
55 11 NA NA NA
56 12 1 85 116
57 12 3 77 110
58 12 NA NA NA
59 12 NA NA NA
60 12 NA NA NA
61 13 1 34 51
62 13 NA NA NA
63 13 NA NA NA
64 13 NA NA NA
65 13 NA NA NA
66 14 1 30 59
67 14 3 NA NA
68 14 NA NA NA
69 14 NA NA NA
70 14 NA NA NA
71 15 1 42 47
72 15 3 50 62
73 15 11 33 75
74 15 NA NA NA
75 15 NA NA NA
76 16 1 NA 83
77 16 7 NA 88
78 16 13 NA 74
79 16 NA NA NA
80 16 NA NA NA
81 17 1 NA 51
82 17 7 NA 62
83 17 NA NA NA
84 17 NA NA NA
85 17 NA NA NA
86 18 1 NA 39
87 18 7 NA 44
88 18 NA NA NA
89 18 NA NA NA
90 18 NA NA NA
91 19 1 NA 45
92 19 7 NA 56
93 19 14 NA NA
94 19 NA NA NA
95 19 NA NA NA
96 20 1 NA 45
97 20 7 NA 57
98 20 NA NA NA
99 20 NA NA NA
100 20 NA NA NA
101 21 1 NA 80
102 21 NA NA NA
103 21 NA NA NA
104 21 NA NA NA
105 21 NA NA NA
106 22 1 NA 42
107 22 7 NA 33
108 22 14 NA 36
109 22 21 NA NA
110 22 NA NA NA
111 23 1 NA 69
112 23 7 NA 68
113 23 NA NA NA
114 23 NA NA NA
115 23 NA NA NA
116 24 1 NA 48
117 24 6 NA 58
118 24 14 NA 82
119 24 NA NA NA
120 24 NA NA NA
121 25 1 NA 67
122 25 NA NA NA
123 25 NA NA NA
124 25 NA NA NA
125 25 NA NA NA>
> library(nlme)
> fitRI <- lme(echogen~time,random=~ 1
|subject,data=repeatdata,na.action=na.omit)
> summary(fitRI)
Linear mixed-effects model fit by REML
Data: repeatdata
AIC BIC logLik
491.097 499.1984 -241.5485
Random effects:
Formula: ~1 | subject
(Intercept) Residual
StdDev: 19.1751 10.44601
Fixed effects: echogen ~ time
Value Std.Error DF t-value p-value
(Intercept) 64.54864 4.258235 32 15.158545 0.0000
time 0.35795 0.227080 32 1.576307 0.1248
Correlation:
(Intr)
time -0.242
Standardized Within-Group Residuals:
Min Q1 Med Q3 Max
-1.61362748 -0.52710871 0.02948022 0.41793307 1.77340062
Number of Observations: 58
Number of Groups: 25>
> fitRT <- lme(echogen~time,random=~
-1+time|subject,data=repeatdata,na.action=na.omit)
> summary(fitRT)
Linear mixed-effects model fit by REML
Data: repeatdata
AIC BIC logLik
515.2225 523.3239 -253.6112
Random effects:
Formula: ~-1 + time | subject
time Residual
StdDev: 0.6014915 19.63638
Fixed effects: echogen ~ time
Value Std.Error DF t-value p-value
(Intercept) 65.03691 3.494160 32 18.613032 0.0000
time 0.22688 0.467306 32 0.485503 0.6306
Correlation:
(Intr)
time -0.625
Standardized Within-Group Residuals:
Min Q1 Med Q3 Max
-2.35381603 -0.69490411 -0.04299361 0.52973023 2.57509584
Number of Observations: 58
Number of Groups: 25>
> fitRIRT <- lme(echogen~time,random=~
> 1+time|subject,data=repeatdata,na.action=na.omit)
> summary(fitRIRT)
Linear mixed-effects model fit by REML
Data: repeatdata
AIC BIC logLik
495.097 507.2491 -241.5485
Random effects:
Formula: ~1 + time | subject
Structure: General positive-definite, Log-Cholesky parametrization
StdDev Corr
(Intercept) 1.917511e+01 (Intr)
time 2.032072e-04 0
Residual 1.044601e+01
Fixed effects: echogen ~ time
Value Std.Error DF t-value p-value
(Intercept) 64.54864 4.258235 32 15.158543 0.0000
time 0.35795 0.227080 32 1.576307 0.1248
Correlation:
(Intr)
time -0.242
Standardized Within-Group Residuals:
Min Q1 Med Q3 Max
-1.61362755 -0.52710871 0.02948008 0.41793322 1.77340082
Number of Observations: 58
Number of Groups: 25>
John David Sorkin M.D., Ph.D.
Chief, Biostatistics and Informatics
University of Maryland School of Medicine Division of Gerontology Baltimore VA
Medical Center
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524
(Phone) 410-605-7119
(Fax) 410-605-7913 (Please call phone number above prior to faxing)
Confidentiality Statement:
This email message, including any attachments, is for th...{{dropped:13}}
John Sorkin
2012-Jun-12 15:25 UTC
[R] lme random slope results the same as random slope and intercept model
Thierry,
Thank you for your thoughts. I agree with your analysis, but am still surprised
that the results are not approximately, but exactly the same to the limit of the
precision of the printed results. The exact comparability of the results makes
me wonder if something else is going on that I have missed.
Thanks,
John
John David Sorkin M.D., Ph.D.
Chief, Biostatistics and Informatics
University of Maryland School of Medicine Division of Gerontology
Baltimore VA Medical Center
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524
(Phone) 410-605-7119
(Fax) 410-605-7913 (Please call phone number above prior to faxing)>>>
"ONKELINX, Thierry" <Thierry.ONKELINX at inbo.be> 6/12/2012
11:14 AM >>>
Dear John,
R-sig-mixed-models is a better list for this kind of questions.
It looks like the model finds no evidence for a random slope. Notice the very
small variance of the random slope. In the model without random intercept, the
random slope tries to mimic the effect of a random intercept.
Best regards,
Thierry
ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and
Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium
+ 32 2 525 02 51
+ 32 54 43 61 85
Thierry.Onkelinx at inbo.be
www.inbo.be
To call in the statistician after the experiment is done may be no more than
asking him to perform a post-mortem examination: he may be able to say what the
experiment died of.
~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data.
~ Roger Brinner
The combination of some data and an aching desire for an answer does not ensure
that a reasonable answer can be extracted from a given body of data.
~ John Tukey
-----Oorspronkelijk bericht-----
Van: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
Namens John Sorkin
Verzonden: dinsdag 12 juni 2012 16:52
Aan: r-help at r-project.org
Onderwerp: [R] lme random slope results the same as random slope and intercept
model
R 2.15.0
Windows XP
Can someone help me understand why a random intercept model gives the same
results as the random intercept and slope models?
I am rather surprised by the results I am getting from lme. I am running three
models
(1) random intercept
fitRI <- lme(echogen~time,random=~ 1
|subject,data=repeatdata,na.action=na.omit)
(2) random slope> fitRT <- lme(echogen~time,random=~
-1+time|subject,data=repeatdata,na.action=na.omit)
(3) random intercept and slope.
fitRIRT <- lme(echogen~time,random=~
1+time|subject,data=repeatdata,na.action=na.omit)
The results of the (1) random intercept model are different from the (2) random
slope model,not a surprise.
The results of the (1) random intercept model and the (3) random intercept and
slope models are exactly the same, a surprise!
Below I copy the results for each model. Further below I give all my output.
RESULTS FROM EACH MODEL
(1) Random intercept results:
Random effects:
Formula: ~1 | subject
(Intercept) Residual
StdDev: 19.1751 10.44601
Fixed effects: echogen ~ time
Value Std.Error DF t-value p-value
(Intercept) 64.54864 4.258235 32 15.158545 0.0000
time 0.35795 0.227080 32 1.576307 0.1248
Correlation:
(Intr)
time -0.242
(2) Random slope results
Random effects:
Formula: ~-1 + time | subject
time Residual
StdDev: 0.6014915 19.63638
Fixed effects: echogen ~ time
Value Std.Error DF t-value p-value
(Intercept) 65.03691 3.494160 32 18.613032 0.0000
time 0.22688 0.467306 32 0.485503 0.6306
Correlation:
(Intr)
time -0.625
(3) Random intercept and slope results
Random effects:
Formula: ~1 + time | subject
Structure: General positive-definite, Log-Cholesky parametrization
StdDev Corr
(Intercept) 1.917511e+01 (Intr)
time 2.032072e-04 0
Residual 1.044601e+01
Fixed effects: echogen ~ time
Value Std.Error DF t-value p-value
(Intercept) 64.54864 4.258235 32 15.158543 0.0000
time 0.35795 0.227080 32 1.576307 0.1248
Correlation:
(Intr)
time -0.242
COMPLETE OUTPUT> repeatdata
subject time value echogen
1 1 1 22 63
2 1 3 40 60
3 1 NA NA NA
4 1 NA NA NA
5 1 NA NA NA
6 2 1 39 19
7 2 NA NA NA
8 2 NA NA NA
9 2 NA NA NA
10 2 NA NA NA
11 3 1 47 76
12 3 6 43 82
13 3 NA NA NA
14 3 NA NA NA
15 3 NA NA NA
16 4 1 44 44
17 4 3 50 50
18 4 7 67 67
19 4 21 39 39
20 4 NA NA NA
21 5 1 42 58
22 5 3 60 78
23 5 7 86 85
24 5 19 56 60
25 5 35 39 84
26 6 1 57 67
27 6 NA NA NA
28 6 NA NA NA
29 6 NA NA NA
30 6 NA NA NA
31 7 1 71 58
32 7 3 55 67
33 7 10 57 95
34 7 17 62 94
35 7 25 47 73
36 8 1 79 105
37 8 NA NA NA
38 8 NA NA NA
39 8 NA NA NA
40 8 NA NA NA
41 9 1 60 70
42 9 3 64 62
43 9 9 68 65
44 9 NA NA NA
45 9 NA NA NA
46 10 1 47 75
47 10 3 49 73
48 10 9 46 70
49 10 17 48 70
50 10 NA NA NA
51 11 1 57 97
52 11 6 75 108
53 11 NA NA NA
54 11 NA NA NA
55 11 NA NA NA
56 12 1 85 116
57 12 3 77 110
58 12 NA NA NA
59 12 NA NA NA
60 12 NA NA NA
61 13 1 34 51
62 13 NA NA NA
63 13 NA NA NA
64 13 NA NA NA
65 13 NA NA NA
66 14 1 30 59
67 14 3 NA NA
68 14 NA NA NA
69 14 NA NA NA
70 14 NA NA NA
71 15 1 42 47
72 15 3 50 62
73 15 11 33 75
74 15 NA NA NA
75 15 NA NA NA
76 16 1 NA 83
77 16 7 NA 88
78 16 13 NA 74
79 16 NA NA NA
80 16 NA NA NA
81 17 1 NA 51
82 17 7 NA 62
83 17 NA NA NA
84 17 NA NA NA
85 17 NA NA NA
86 18 1 NA 39
87 18 7 NA 44
88 18 NA NA NA
89 18 NA NA NA
90 18 NA NA NA
91 19 1 NA 45
92 19 7 NA 56
93 19 14 NA NA
94 19 NA NA NA
95 19 NA NA NA
96 20 1 NA 45
97 20 7 NA 57
98 20 NA NA NA
99 20 NA NA NA
100 20 NA NA NA
101 21 1 NA 80
102 21 NA NA NA
103 21 NA NA NA
104 21 NA NA NA
105 21 NA NA NA
106 22 1 NA 42
107 22 7 NA 33
108 22 14 NA 36
109 22 21 NA NA
110 22 NA NA NA
111 23 1 NA 69
112 23 7 NA 68
113 23 NA NA NA
114 23 NA NA NA
115 23 NA NA NA
116 24 1 NA 48
117 24 6 NA 58
118 24 14 NA 82
119 24 NA NA NA
120 24 NA NA NA
121 25 1 NA 67
122 25 NA NA NA
123 25 NA NA NA
124 25 NA NA NA
125 25 NA NA NA>
> library(nlme)
> fitRI <- lme(echogen~time,random=~ 1
|subject,data=repeatdata,na.action=na.omit)
> summary(fitRI)
Linear mixed-effects model fit by REML
Data: repeatdata
AIC BIC logLik
491.097 499.1984 -241.5485
Random effects:
Formula: ~1 | subject
(Intercept) Residual
StdDev: 19.1751 10.44601
Fixed effects: echogen ~ time
Value Std.Error DF t-value p-value
(Intercept) 64.54864 4.258235 32 15.158545 0.0000
time 0.35795 0.227080 32 1.576307 0.1248
Correlation:
(Intr)
time -0.242
Standardized Within-Group Residuals:
Min Q1 Med Q3 Max
-1.61362748 -0.52710871 0.02948022 0.41793307 1.77340062
Number of Observations: 58
Number of Groups: 25>
> fitRT <- lme(echogen~time,random=~
-1+time|subject,data=repeatdata,na.action=na.omit)
> summary(fitRT)
Linear mixed-effects model fit by REML
Data: repeatdata
AIC BIC logLik
515.2225 523.3239 -253.6112
Random effects:
Formula: ~-1 + time | subject
time Residual
StdDev: 0.6014915 19.63638
Fixed effects: echogen ~ time
Value Std.Error DF t-value p-value
(Intercept) 65.03691 3.494160 32 18.613032 0.0000
time 0.22688 0.467306 32 0.485503 0.6306
Correlation:
(Intr)
time -0.625
Standardized Within-Group Residuals:
Min Q1 Med Q3 Max
-2.35381603 -0.69490411 -0.04299361 0.52973023 2.57509584
Number of Observations: 58
Number of Groups: 25>
> fitRIRT <- lme(echogen~time,random=~
> 1+time|subject,data=repeatdata,na.action=na.omit)
> summary(fitRIRT)
Linear mixed-effects model fit by REML
Data: repeatdata
AIC BIC logLik
495.097 507.2491 -241.5485
Random effects:
Formula: ~1 + time | subject
Structure: General positive-definite, Log-Cholesky parametrization
StdDev Corr
(Intercept) 1.917511e+01 (Intr)
time 2.032072e-04 0
Residual 1.044601e+01
Fixed effects: echogen ~ time
Value Std.Error DF t-value p-value
(Intercept) 64.54864 4.258235 32 15.158543 0.0000
time 0.35795 0.227080 32 1.576307 0.1248
Correlation:
(Intr)
time -0.242
Standardized Within-Group Residuals:
Min Q1 Med Q3 Max
-1.61362755 -0.52710871 0.02948008 0.41793322 1.77340082
Number of Observations: 58
Number of Groups: 25>
John David Sorkin M.D., Ph.D.
Chief, Biostatistics and Informatics
University of Maryland School of Medicine Division of Gerontology Baltimore VA
Medical Center
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524
(Phone) 410-605-7119
(Fax) 410-605-7913 (Please call phone number above prior to faxing)
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