[R-sig-ME] problem fitting a mixed model due to between subject variation

Tue Jul 27 16:00:39 CEST 2010

Dear all,

I have a problem with an mixed analysis. All though residual plots and a
fixed analysis suggest that (at least) 
a random intercept should be incorporated in the model, I keep getting a
zero variance (or almost zero variance) for the random intercept, 
I guess because of the huge between subject differences. The data and
some commands for visualizing and analyzing 
the data are given below. These are performed using package nlme, but I
found identical results for packages lme4 and lmm, 
and also for SAS, SPSS and MlWin.
I could use the fixed analysis, but I rather would like not to do that,
since that implies that the number of parameters 
increases with the number of subjects. I could center all predictor
scores around the subject means, but that would 
(almost) be the same so I also would not want to do that. Does anybody
have a suggestion how to proceed?

Best regards
Rogier

_______________________________________________________

Rogier Donders, PhD, Biostatistician
Department of Epidemiology, Biostatistics and HTA, EBH 133
Radboud University Nijmegen Medical Centre
P.O. Box 9101
6500 HB Nijmegen
The Netherlands
_______________________________________________________

strangedat <- 
structure(list(subject = structure(c(1L, 1L, 1L, 2L, 2L, 2L, 
2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 
5L, 5L, 6L, 6L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 7L, 8L, 8L, 
8L, 8L, 8L, 8L, 9L, 9L, 9L, 10L, 10L, 10L, 10L, 10L, 11L, 11L, 
11L, 11L, 11L, 11L, 12L, 12L, 12L, 12L, 13L, 13L, 13L, 13L, 14L, 
14L, 14L, 14L, 14L, 14L, 15L, 15L, 15L, 15L, 15L, 15L, 16L, 16L, 
16L, 16L, 16L, 16L, 17L, 17L, 17L, 17L, 17L, 17L, 18L, 18L, 18L, 
19L, 19L, 19L, 19L, 19L, 19L, 20L, 20L, 20L, 20L, 20L, 20L, 21L, 
21L, 21L, 21L, 22L, 22L, 22L, 22L, 22L, 22L, 23L, 23L, 23L, 23L, 
23L, 24L, 24L, 24L, 24L, 24L, 24L, 25L, 25L, 25L, 25L, 25L, 25L, 
26L, 26L, 26L, 27L, 27L, 27L, 27L, 27L, 27L, 28L, 28L, 28L, 28L, 
28L, 28L, 29L, 29L, 29L, 29L, 29L, 30L, 30L, 30L, 30L, 30L, 30L, 
31L, 31L, 31L, 31L, 32L, 32L, 32L, 32L, 32L, 32L, 33L, 33L, 33L, 
33L, 33L, 33L, 34L, 34L, 34L, 34L, 34L, 34L, 35L, 35L, 35L, 35L, 
35L, 35L, 36L, 36L, 36L, 36L, 36L, 37L, 37L, 37L, 37L, 37L, 37L, 
38L, 38L, 38L, 38L, 38L, 38L, 39L, 39L, 39L, 39L, 39L, 40L, 40L, 
40L, 40L, 40L, 41L, 41L, 41L, 41L, 41L, 42L, 42L, 42L, 42L, 43L, 
43L, 43L, 43L, 43L, 43L, 44L, 44L, 44L, 44L, 44L, 44L, 45L, 45L, 
45L, 45L, 45L, 45L, 46L, 46L, 46L, 46L, 47L, 47L, 47L, 47L, 47L, 
47L, 48L, 48L, 48L, 48L, 48L, 48L, 49L, 49L, 49L, 50L, 50L, 50L, 
50L, 50L, 51L, 51L, 51L, 51L, 51L, 51L, 52L, 52L, 52L, 52L, 52L, 
52L, 53L, 53L, 53L, 53L, 53L, 53L, 54L, 54L, 54L, 54L, 54L, 54L, 
55L, 55L, 55L, 56L, 56L, 56L, 56L, 56L, 56L, 57L, 57L, 57L, 57L, 
57L, 58L, 58L, 58L, 58L, 58L, 58L, 59L, 59L, 59L, 59L, 60L, 60L, 
60L, 60L, 60L, 60L, 61L, 61L, 61L, 61L, 62L, 62L, 62L, 62L, 62L, 
62L, 63L, 63L, 63L, 63L, 63L, 64L, 64L, 64L, 64L, 64L, 65L, 65L, 
65L, 65L, 65L, 65L, 66L, 66L, 66L, 66L, 66L, 66L, 67L, 67L, 67L, 
67L, 67L, 67L, 68L, 68L, 68L, 68L, 69L, 69L, 69L, 69L, 69L, 69L, 
70L, 70L, 70L, 70L, 70L, 70L, 71L, 71L, 71L, 71L, 71L, 72L, 72L, 
72L, 72L, 72L, 73L, 73L, 73L, 73L, 73L, 73L, 74L, 74L, 74L, 74L, 
74L, 75L, 75L, 75L, 76L, 76L, 76L, 76L, 76L, 76L, 77L, 77L, 77L, 
77L, 77L, 77L, 78L, 78L, 78L, 78L, 78L, 79L, 79L, 79L, 80L, 80L, 
80L), .Label = c("5002", "5004", "5005", "5008", "5009", "5010", 
"5012", "5013", "5014", "5016", "5019", "5022", "5023", "5025", 
"5026", "5027", "5028", "5030", "5031", "5032", "5033", "5034", 
"5035", "5038", "5041", "5042", "5044", "5045", "5046", "5051", 
"5052", "5053", "5056", "5060", "5061", "5062", "5064", "5066", 
"5067", "5069", "5072", "5073", "5075", "5077", "5078", "5079", 
"5080", "5081", "5084", "5087", "5089", "5090", "5092", "5093", 
"5095", "5096", "5097", "5098", "5100", "5102", "5103", "5104", 
"5105", "5107", "5108", "5109", "5110", "5111", "5112", "5114", 
"5117", "5118", "5119", "5120", "5121", "5122", "5123", "5124", 
"5126", "5128"), class = "factor"), outcome = c(1.04380405217311, 
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2.05284085988266, 1.59736533119983, 2.12226153886276, 2.31451366385932, 
3.85418200573830, 3.54961738678043, 3.56189799235315, 3.67630067190708, 
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0.598836501088704, 0.887891257352457, 1.11185751541813,
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require(nlme)
require(lattice)

xyplot(outcome ~ pred, data = strangedat, type = c('p','r'))

# Note a clear positive relation over subjects

xyplot(outcome ~ pred|subject, data = strangedat, type = c('p','r'))

# Note that within subjects there does not appear to be a relation

# fixed effect models confirm this
fixedmod1 <- lm(outcome ~ pred, data = strangedat)
summary(fixedmod1)

fixedmod2 <- lm(outcome ~ pred + subject, data = strangedat)
summary(fixedmod2)
# Note that the effect for pred has now disappeared 

anova(fixedmod1, fixedmod2)
# and the model with the individual intercepts fits better

randommod <- lme(outcome ~ pred, data = strangedat, random = ~
1|subject)
summary(randommod)
# but almost no variation for the random intercept

plot(randommod,resid(.) ~ pred|subject, type = c('p','r'))
# however it is clear that the residuals do NOT behave correctly

Het UMC St Radboud staat geregistreerd bij de Kamer van Koophandel in het handelsregister onder nummer 41055629.
The Radboud University Nijmegen Medical Centre is listed in the Commercial Register of the Chamber of Commerce under file number 41055629.