Minnesota Health Plan Dataset
Example of Poisson GLMM
Number of clinic visits and calls to clinic for 4 nonoverlapping six month periods for each of 121 senior citizens enrolled in a medical plan. From:
These data have been used as an example by multiple authors.
Results from Zipunnikov and Booth (2006):
Term | MCEM | GLIMMIX | WinBUGS |
---|---|---|---|
Intercept | 0.868 (0.096) | 0.961 (0.104) | 0.844 (0.109) |
Event | -0.165 (0.127) | -0.164 (0.106) | -0.160 (0.110) |
Period 1 | -0.091 (0.095) | -0.089 (0.109) | -0.085 (0.111) |
Period 2 | 0.414 (0.098) | 0.394 (0.104) | 0.422 (0.110) |
Period 3 | 0.491 (0.109) | 0.468 (0.103) | 0.498 (0.110) |
E x P 11 | 0.246 (0.097) | 0.240 (0.103) | 0.243 (0.103) |
E x P 12 | 0.104 (0.080) | 0.101 (0.095) | 0.102 (0.097) |
E x P 13 | -0.085 (0.099) | -0.084 (0.096) | -0.088 (0.097) |
sd(Subject) | 0.493 (0.082) | 0.491 (0.081) | 0.511 (0.078) |
sd(E:Subject) | 0.608 (0.056) | 0.578 (0.048) | 0.605 (0.053) |
sd(P:Subject) | 0.625 (0.040) | 0.593 (0.034) | 0.627 (0.038) |
The model fitted:
mod <- glmer(Count ~ Event*Period + (1|Subject) + (1|Subject:Event) + (1|Subject:Period), data=mhp, family=poisson())
Head of data:
record | Count | Subject | Event | Period |
---|---|---|---|---|
1 | 4 | 1 | 1 | 1 |
2 | 0 | 1 | 2 | 1 |
3 | 2 | 1 | 1 | 2 |
4 | 3 | 1 | 2 | 2 |
5 | 3 | 1 | 1 | 3 |
… | ||||
968 | 0 | 121 | 2 | 4 |
mhp <-
structure(list(Count = c(4, 0, 2, 3, 3, 0, 1, 0, 1, 9, 5, 11,
3, 2, 5, 4, 2, 2, 10, 7, 9, 5, 1, 2, 8, 14, 6, 10, 4, 7, 3, 4,
4, 3, 4, 3, 6, 6, 8, 8, 2, 1, 5, 4, 4, 8, 1, 0, 4, 4, 1, 0, 2,
0, 2, 0, 1, 0, 0, 0, 4, 0, 1, 0, 1, 2, 23, 3, 11, 10, 15, 12,
0, 0, 6, 3, 4, 4, 8, 5, 3, 4, 5, 11, 5, 12, 4, 2, 5, 2, 8, 14,
7, 5, 0, 0, 4, 7, 5, 6, 1, 2, 4, 2, 3, 4, 5, 7, 4, 21, 5, 21,
1, 0, 4, 4, 4, 3, 3, 1, 8, 9, 10, 4, 3, 18, 7, 32, 1, 0, 8, 5,
5, 4, 0, 4, 1, 1, 5, 3, 8, 4, 5, 3, 3, 2, 6, 2, 4, 1, 1, 1, 1,
2, 6, 8, 2, 2, 4, 13, 3, 2, 2, 4, 1, 3, 3, 11, 10, 5, 4, 5, 3,
4, 5, 7, 6, 1, 2, 3, 3, 0, 3, 2, 1, 0, 1, 3, 2, 0, 3, 1, 2, 1,
1, 1, 3, 1, 1, 1, 4, 1, 5, 3, 2, 4, 3, 0, 1, 0, 10, 11, 6, 3,
7, 5, 0, 1, 6, 0, 3, 4, 0, 0, 11, 6, 8, 11, 2, 20, 0, 0, 0, 0,
2, 6, 1, 3, 0, 0, 1, 0, 6, 6, 5, 9, 0, 0, 6, 4, 6, 5, 1, 4, 0,
0, 7, 5, 18, 12, 11, 19, 0, 0, 3, 1, 0, 0, 1, 0, 3, 9, 2, 1,
2, 2, 4, 4, 2, 1, 0, 0, 2, 2, 0, 2, 1, 1, 3, 1, 3, 2, 6, 7, 6,
2, 0, 1, 5, 2, 8, 4, 2, 4, 1, 0, 2, 1, 3, 4, 1, 0, 2, 3, 5, 2,
1, 3, 5, 7, 0, 0, 1, 2, 1, 1, 0, 0, 3, 1, 5, 1, 6, 11, 9, 5,
3, 2, 1, 8, 12, 21, 11, 13, 1, 1, 6, 3, 4, 0, 1, 0, 0, 0, 3,
4, 2, 2, 1, 2, 4, 2, 10, 1, 6, 5, 0, 0, 1, 0, 1, 1, 6, 3, 0,
0, 3, 1, 0, 1, 8, 8, 3, 0, 0, 3, 1, 11, 0, 20, 0, 3, 5, 30, 2,
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0, 5, 3, 12, 2, 2, 0, 7, 0, 7, 1, 0, 0, 1, 1, 3, 0, 0, 5, 4,
1, 4, 3, 11, 5, 4, 1, 13, 1, 7, 0, 11, 0, 7, 0, 19, 0, 8, 0,
11, 0, 7, 3, 1, 2, 0, 6, 7, 3, 15, 1, 0, 8, 15, 3, 21, 6, 14,
1, 19, 8, 56, 6, 32, 0, 1, 2, 1, 3, 3, 0, 9, 0, 1, 6, 6, 12,
23, 7, 4, 0, 0, 10, 8, 8, 18, 13, 32, 0, 2, 4, 3, 10, 20, 4,
10, 3, 7, 2, 4, 7, 5, 0, 7, 0, 0, 3, 0, 1, 15, 1, 22, 0, 9, 6,
1, 8, 3, 4, 8, 0, 0, 3, 3, 2, 5, 6, 19, 1, 2, 7, 7, 5, 6, 6,
15, 1, 7, 3, 27, 1, 12, 2, 11, 1, 7, 1, 2, 3, 8, 9, 20, 3, 10,
5, 1, 6, 11, 6, 9, 11, 13, 0, 0, 4, 5, 6, 4, 4, 9, 20, 16, 25,
12, 29, 7, 11, 4, 1, 0, 2, 1, 4, 0, 3, 2, 11, 4, 11, 14, 5, 3,
12, 5, 13, 9, 14, 10, 6, 5, 4, 9, 2, 0, 5, 1, 4, 4, 6, 1, 12,
12, 6, 11, 5, 5, 7, 3, 6, 2, 2, 3, 5, 4, 0, 0, 7, 5, 6, 8, 6,
6, 9, 1, 8, 4, 3, 1, 6, 1, 4, 0, 13, 51, 11, 25, 3, 9, 10, 12,
1, 0, 7, 2, 3, 1, 3, 0, 8, 2, 6, 1, 4, 1, 8, 7, 4, 2, 8, 3, 8,
1, 7, 1, 0, 1, 1, 2, 0, 1, 2, 4, 7, 6, 5, 8, 3, 3, 3, 7, 2, 1,
3, 14, 5, 7, 2, 1, 1, 0, 1, 5, 0, 2, 4, 7, 0, 3, 3, 3, 2, 3,
1, 13, 2, 6, 6, 7, 10, 5, 10, 4, 6, 9, 22, 7, 11, 7, 15, 14,
0, 0, 0, 10, 0, 6, 0, 0, 7, 12, 4, 15, 6, 8, 8, 16, 9, 21, 4,
8, 8, 27, 0, 13, 7, 6, 7, 8, 4, 6, 3, 2, 3, 0, 4, 2, 2, 0, 3,
1, 1, 0, 1, 0, 3, 1, 7, 1, 1, 1, 0, 0, 1, 0, 5, 3, 3, 4, 1, 0,
9, 2, 0, 1, 0, 1, 1, 2, 0, 0, 0, 0, 1, 0, 1, 0, 3, 1, 1, 0, 1,
0, 0, 0, 1, 0, 0, 0, 3, 5, 2, 6, 3, 7, 3, 6, 0, 0, 0, 0, 0, 0,
1, 0, 2, 1, 3, 4, 4, 2, 1, 1, 2, 0, 7, 7, 4, 5, 4, 4, 3, 5, 5,
0, 0, 1, 0, 0, 5, 1, 1, 0, 2, 0, 2, 1, 3, 3, 1, 2, 3, 1, 0, 1,
1, 0, 0, 0, 8, 2, 4, 3, 6, 1, 7, 2, 8, 5, 7, 1, 7, 2, 11, 5,
6, 3, 9, 2, 5, 5, 1, 0, 2, 2, 2, 1, 5, 4, 5, 4, 4, 1, 7, 2, 7,
5, 9, 3, 9, 4, 6, 5, 3, 1, 2, 1, 8, 1, 3, 1, 1, 0, 1, 0, 0, 1,
0, 0, 12, 9, 10, 4, 1, 2, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0), Subject = structure(c(1L,
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1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 1L), .Label = c("2", "1"), class = "factor"),
Period = structure(c(2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L,
2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L,
2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L,
1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L,
1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L,
4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L,
4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L,
3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L,
3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L,
2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L,
2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L,
1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L,
1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L,
4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L,
4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L,
3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L,
3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L,
2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L,
2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L,
1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L,
1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L,
4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L,
4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L,
3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L,
3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L,
2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L,
2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L,
1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L,
1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L,
4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L,
4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L,
3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L,
3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L,
2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L,
2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L,
1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L,
1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L,
4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L,
4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L,
3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L,
3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L,
2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L,
2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L,
1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L,
1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L,
4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L,
4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L,
3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L,
3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L,
2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L,
2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L,
1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L,
1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L,
4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L,
4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L,
3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L,
3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L,
2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L,
2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L,
1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L,
1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L,
4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L,
4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L,
3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L,
3L, 3L, 4L, 4L, 1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 1L, 1L), .Label = c("4",
"1", "2", "3"), class = "factor")), .Names = c("Count", "Subject",
"Event", "Period"), row.names = c(NA, -968L), class = "data.frame")
library(lme4)
mod <- glmer(Count ~ Event*Period + (1|Subject) + (1|Subject:Event) + (1|Subject:Period), data=mhp,
family=poisson())
page revision: 6, last edited: 25 Jun 2012 06:03