[R] lme random slope results the same as random slope and intercept model

John Sorkin jsorkin at grecc.umaryland.edu
Tue Jun 12 17:25:31 CEST 2012


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) Confidentiality Statement:
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