[R] lme random slope results the same as random slope and intercept model
John Sorkin
jsorkin at grecc.umaryland.edu
Tue Jun 12 16:51:46 CEST 2012
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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