R 中的 lmer 纵向分析对象内和时间点之间的差异
lmer longitudinal analyses in R for variance within subjects and between timepoints
我有以下纵向（3 Timepoints）数据集：
# A tibble: 504 x 6
ID Age Age_group Sex Timepoint outcome
<int> <int> <fct> <chr> <chr> <dbl>
1 33714 15 Young Male bl 0.00103
2 35377 15 Young Female bl 0.00106
3 38623 45 Older Female bl 0.00103
4 38806 66 Older Female bl 0.00114
5 39593 69 Older Female bl 0.00113
6 39820 60 Older Female bl 0.00113
7 39951 46 Older Male bl 0.000986
8 40286 68 Older Female bl 0.00107
9 40556 9 Young Male bl 0.00114
10 40798 11 Young Male bl 0.00111
# ... with 494 more rows
数据：
39820L, 39951L, 40286L, 40556L, 40798L, 40800L, 40815L, 43762L,
50848L, 52183L, 52461L, 52577L, 53320L, 53873L, 54153L, 54206L,
54581L, 55122L, 55267L, 55462L, 55612L, 55920L, 56022L, 56307L,
56420L, 56679L, 57405L, 57445L, 57480L, 57725L, 57809L, 58004L,
58215L, 58229L, 58503L, 59326L, 59327L, 59344L, 59361L, 59865L,
60099L, 60100L, 60280L, 60384L, 60429L, 60493L, 60503L, 60575L,
60603L, 60664L, 60846L, 61415L, 61656L, 61749L, 61883L, 62081L,
62210L, 62285L, 62937L, 62983L, 63327L, 63329L, 64081L, 64328L,
64418L, 64507L, 64596L, 65178L, 65250L, 65302L, 65478L, 65480L,
65487L, 65572L, 65802L, 65935L, 65974L, 65975L, 65978L, 65991L,
65995L, 66013L, 66154L, 66237L, 66245L, 66389L, 66396L, 66460L,
66572L, 66589L, 67174L, 73230L, 73525L, 73539L, 73677L, 73942L,
73953L, 74034L, 74113L, 74114L, 74427L, 74439L, 74607L, 74641L,
74657L, 74794L, 74800L, 74836L, 74942L, 74952L, 74962L, 74969L,
74977L, 74985L, 74989L, 75220L, 75229L, 75407L, 75653L, 75732L,
75735L, 75757L, 75895L, 75898L, 76381L, 76559L, 76574L, 76594L,
76595L, 76746L, 76751L, 76755L, 76759L, 76775L, 77088L, 77091L,
77099L, 77134L, 77188L, 77203L, 77252L, 77304L, 77413L, 77453L,
77528L, 77556L, 77585L, 77668L, 78262L, 79724L, 79730L, 79850L,
79977L, 80052L, 80819L, 80901L, 80932L, 81064L, 81065L, 81071L,
81098L, 81142L, 81175L, 33714L, 35377L, 38623L, 38806L, 39593L,
39820L, 39951L, 40286L, 40556L, 40798L, 40800L, 40815L, 43762L,
50848L, 52183L, 52461L, 52577L, 53320L, 53873L, 54153L, 54206L,
54581L, 55122L, 55267L, 55462L, 55612L, 55920L, 56022L, 56307L,
56420L, 56679L, 57405L, 57445L, 57480L, 57725L, 57809L, 58004L,
58215L, 58229L, 58503L, 59326L, 59327L, 59344L, 59361L, 59865L,
60099L, 60100L, 60280L, 60384L, 60429L, 60493L, 60503L, 60575L,
60603L, 60664L, 60846L, 61415L, 61656L, 61749L, 61883L, 62081L,
62210L, 62285L, 62937L, 62983L, 63327L, 63329L, 64081L, 64328L,
64418L, 64507L, 64596L, 65178L, 65250L, 65302L, 65478L, 65480L,
65487L, 65572L, 65802L, 65935L, 65974L, 65975L, 65978L, 65991L,
65995L, 66013L, 66154L, 66237L, 66245L, 66389L, 66396L, 66460L,
66572L, 66589L, 67174L, 73230L, 73525L, 73539L, 73677L, 73942L,
73953L, 74034L, 74113L, 74114L, 74427L, 74439L, 74607L, 74641L,
74657L, 74794L, 74800L, 74836L, 74942L, 74952L, 74962L, 74969L,
74977L, 74985L, 74989L, 75220L, 75229L, 75407L, 75653L, 75732L,
75735L, 75757L, 75895L, 75898L, 76381L, 76559L, 76574L, 76594L,
76595L, 76746L, 76751L, 76755L, 76759L, 76775L, 77088L, 77091L,
77099L, 77134L, 77188L, 77203L, 77252L, 77304L, 77413L, 77453L,
77528L, 77556L, 77585L, 77668L, 78262L, 79724L, 79730L, 79850L,
79977L, 80052L, 80819L, 80901L, 80932L, 81064L, 81065L, 81071L,
81098L, 81142L, 81175L, 33714L, 35377L, 38623L, 38806L, 39593L,
39820L, 39951L, 40286L, 40556L, 40798L, 40800L, 40815L, 43762L,
50848L, 52183L, 52461L, 52577L, 53320L, 53873L, 54153L, 54206L,
54581L, 55122L, 55267L, 55462L, 55612L, 55920L, 56022L, 56307L,
56420L, 56679L, 57405L, 57445L, 57480L, 57725L, 57809L, 58004L,
58215L, 58229L, 58503L, 59326L, 59327L, 59344L, 59361L, 59865L,
60099L, 60100L, 60280L, 60384L, 60429L, 60493L, 60503L, 60575L,
60603L, 60664L, 60846L, 61415L, 61656L, 61749L, 61883L, 62081L,
62210L, 62285L, 62937L, 62983L, 63327L, 63329L, 64081L, 64328L,
64418L, 64507L, 64596L, 65178L, 65250L, 65302L, 65478L, 65480L,
65487L, 65572L, 65802L, 65935L, 65974L, 65975L, 65978L, 65991L,
65995L, 66013L, 66154L, 66237L, 66245L, 66389L, 66396L, 66460L,
66572L, 66589L, 67174L, 73230L, 73525L, 73539L, 73677L, 73942L,
73953L, 74034L, 74113L, 74114L, 74427L, 74439L, 74607L, 74641L,
74657L, 74794L, 74800L, 74836L, 74942L, 74952L, 74962L, 74969L,
74977L, 74985L, 74989L, 75220L, 75229L, 75407L, 75653L, 75732L,
75735L, 75757L, 75895L, 75898L, 76381L, 76559L, 76574L, 76594L,
76595L, 76746L, 76751L, 76755L, 76759L, 76775L, 77088L, 77091L,
77099L, 77134L, 77188L, 77203L, 77252L, 77304L, 77413L, 77453L,
77528L, 77556L, 77585L, 77668L, 78262L, 79724L, 79730L, 79850L,
79977L, 80052L, 80819L, 80901L, 80932L, 81064L, 81065L, 81071L,
81098L, 81142L, 81175L), Age = c(15L, 15L, 45L, 66L, 69L, 60L,
46L, 68L, 9L, 11L, 16L, 9L, 56L, 16L, 16L, 14L, 53L, 8L, 6L,
63L, 14L, 10L, 15L, 13L, 15L, 8L, 9L, 9L, 8L, 9L, 9L, 13L, 58L,
10L, 7L, 8L, 8L, 6L, 15L, 43L, 8L, 11L, 44L, 70L, 14L, 12L, 10L,
16L, 12L, 10L, 6L, 13L, 67L, 11L, 12L, 13L, 10L, 66L, 13L, 14L,
12L, 45L, 52L, 64L, 17L, 9L, 12L, 44L, 69L, 11L, 10L, 12L, 10L,
10L, 70L, 54L, 45L, 43L, 54L, 14L, 42L, 44L, 16L, 15L, 43L, 45L,
50L, 53L, 53L, 49L, 69L, 14L, 65L, 14L, 13L, 67L, 59L, 52L, 54L,
44L, 62L, 69L, 10L, 63L, 57L, 12L, 62L, 9L, 53L, 54L, 66L, 49L,
63L, 51L, 9L, 45L, 49L, 49L, 61L, 62L, 57L, 67L, 65L, 45L, 16L,
55L, 64L, 67L, 56L, 52L, 63L, 10L, 62L, 14L, 66L, 68L, 15L, 13L,
43L, 47L, 55L, 69L, 67L, 52L, 15L, 64L, 55L, 44L, 13L, 48L, 71L,
64L, 13L, 50L, 61L, 70L, 57L, 51L, 46L, 57L, 69L, 46L, 8L, 11L,
46L, 71L, 38L, 56L, 16L, 16L, 46L, 67L, 70L, 61L, 47L, 69L, 11L,
13L, 18L, 10L, 57L, 18L, 18L, 15L, 54L, 10L, 8L, 64L, 15L, 12L,
16L, 14L, 16L, 9L, 11L, 11L, 10L, 10L, 11L, 14L, 59L, 12L, 8L,
9L, 9L, 8L, 16L, 44L, 9L, 13L, 45L, 71L, 16L, 13L, 12L, 18L,
13L, 11L, 8L, 14L, 68L, 12L, 13L, 14L, 11L, 67L, 14L, 15L, 14L,
46L, 53L, 65L, 18L, 11L, 14L, 46L, 70L, 12L, 12L, 13L, 11L, 11L,
71L, 55L, 46L, 44L, 55L, 15L, 43L, 45L, 17L, 16L, 44L, 46L, 51L,
55L, 54L, 50L, 70L, 15L, 66L, 15L, 14L, 68L, 60L, 53L, 55L, 46L,
63L, 70L, 11L, 64L, 58L, 13L, 63L, 10L, 54L, 55L, 67L, 50L, 64L,
52L, 11L, 46L, 50L, 50L, 62L, 63L, 58L, 68L, 66L, 46L, 18L, 56L,
65L, 68L, 57L, 53L, 64L, 11L, 63L, 15L, 67L, 69L, 16L, 14L, 44L,
48L, 56L, 70L, 68L, 53L, 17L, 65L, 56L, 45L, 14L, 49L, 73L, 65L,
14L, 50L, 62L, 71L, 58L, 52L, 47L, 58L, 70L, 47L, 9L, 12L, 47L,
72L, 39L, 57L, 18L, 18L, 47L, 68L, 71L, 62L, 48L, 70L, 12L, 14L,
19L, 11L, 58L, 19L, 19L, 16L, 55L, 11L, 9L, 65L, 17L, 13L, 18L,
16L, 18L, 11L, 12L, 12L, 11L, 11L, 12L, 16L, 60L, 13L, 9L, 11L,
10L, 9L, 17L, 45L, 11L, 14L, 46L, 72L, 17L, 14L, 13L, 19L, 15L,
12L, 9L, 15L, 69L, 14L, 14L, 15L, 12L, 68L, 16L, 17L, 15L, 47L,
54L, 66L, 20L, 12L, 15L, 47L, 71L, 13L, 13L, 14L, 12L, 12L, 72L,
56L, 47L, 45L, 56L, 16L, 44L, 46L, 19L, 18L, 44L, 47L, 52L, 56L,
55L, 51L, 71L, 16L, 67L, 16L, 15L, 69L, 60L, 54L, 56L, 46L, 64L,
71L, 12L, 65L, 59L, 14L, 64L, 11L, 55L, 57L, 68L, 51L, 65L, 53L,
11L, 47L, 51L, 51L, 63L, 64L, 59L, 69L, 67L, 48L, 19L, 57L, 66L,
69L, 59L, 54L, 65L, 12L, 64L, 16L, 68L, 70L, 17L, 15L, 45L, 48L,
57L, 71L, 69L, 54L, 18L, 66L, 57L, 50L, 15L, 50L, 74L, 66L, 15L,
51L, 63L, 72L, 59L, 53L, 48L, 59L, 71L, 48L, 10L, 13L, 48L, 73L,
40L, 58L), Age_group = structure(c(1L, 1L, 2L, 2L, 2L, 2L, 2L,
2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L,
1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L,
1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L,
2L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L,
2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L,
2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L,
2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L,
1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L,
2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L,
1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 2L,
2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L,
2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L,
2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L,
2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L,
1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L,
1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L,
2L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L,
2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L,
2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L,
2L), .Label = c("Young", "Older"), class = "factor"), Sex = c("Male",
"Female", "Female", "Female", "Female", "Female", "Male", "Female",
"Male", "Male", "Male", "Male", "Female", "Male", "Male", "Male",
"Female", "Male", "Male", "Male", "Male", "Male", "Male", "Male",
"Male", "Female", "Female", "Male", "Female", "Male", "Female",
"Female", "Female", "Male", "Female", "Female", "Male", "Female",
"Male", "Female", "Male", "Female", "Male", "Male", "Female",
"Male", "Male", "Male", "Female", "Female", "Female", "Male",
"Female", "Male", "Female", "Female", "Male", "Male", "Female",
"Male", "Male", "Female", "Female", "Male", "Male", "Female",
"Female", "Female", "Female", "Female", "Male", "Male", "Male",
"Male", "Female", "Female", "Female", "Female", "Female", "Male",
"Female", "Female", "Male", "Male", "Female", "Male", "Female",
"Female", "Female", "Female", "Female", "Male", "Male", "Female",
"Female", "Male", "Female", "Female", "Female", "Female", "Female",
"Female", "Female", "Female", "Female", "Female", "Female", "Female",
"Female", "Female", "Male", "Female", "Male", "Female", "Male",
"Female", "Female", "Female", "Female", "Female", "Male", "Male",
"Female", "Female", "Male", "Female", "Male", "Female", "Female",
"Male", "Female", "Female", "Female", "Male", "Female", "Male",
"Male", "Male", "Female", "Female", "Male", "Male", "Male", "Female",
"Female", "Male", "Female", "Female", "Male", "Female", "Female",
"Male", "Female", "Male", "Male", "Male", "Male", "Female", "Male",
"Male", "Female", "Male", "Male", "Male", "Male", "Male", "Male",
"Female", "Male", "Female", "Female", "Female", "Female", "Female",
"Male", "Female", "Male", "Male", "Male", "Male", "Female", "Male",
"Male", "Male", "Female", "Male", "Male", "Male", "Male", "Male",
"Male", "Male", "Male", "Female", "Female", "Male", "Female",
"Male", "Female", "Female", "Female", "Male", "Female", "Female",
"Male", "Female", "Male", "Female", "Male", "Female", "Male",
"Male", "Female", "Male", "Male", "Male", "Female", "Female",
"Female", "Male", "Female", "Male", "Female", "Female", "Male",
"Male", "Female", "Male", "Male", "Female", "Female", "Male",
"Male", "Female", "Female", "Female", "Female", "Female", "Male",
"Male", "Male", "Male", "Female", "Female", "Female", "Female",
"Female", "Male", "Female", "Female", "Male", "Male", "Female",
"Male", "Female", "Female", "Female", "Female", "Female", "Male",
"Male", "Female", "Female", "Male", "Female", "Female", "Female",
"Female", "Female", "Female", "Female", "Female", "Female", "Female",
"Female", "Female", "Female", "Female", "Male", "Female", "Male",
"Female", "Male", "Female", "Female", "Female", "Female", "Female",
"Male", "Male", "Female", "Female", "Male", "Female", "Male",
"Female", "Female", "Male", "Female", "Female", "Female", "Male",
"Female", "Male", "Male", "Male", "Female", "Female", "Male",
"Male", "Male", "Female", "Female", "Male", "Female", "Female",
"Male", "Female", "Female", "Male", "Female", "Male", "Male",
"Male", "Male", "Female", "Male", "Male", "Female", "Male", "Male",
"Male", "Male", "Male", "Male", "Female", "Male", "Female", "Female",
"Female", "Female", "Female", "Male", "Female", "Male", "Male",
"Male", "Male", "Female", "Male", "Male", "Male", "Female", "Male",
"Male", "Male", "Male", "Male", "Male", "Male", "Male", "Female",
"Female", "Male", "Female", "Male", "Female", "Female", "Female",
"Male", "Female", "Female", "Male", "Female", "Male", "Female",
"Male", "Female", "Male", "Male", "Female", "Male", "Male", "Male",
"Female", "Female", "Female", "Male", "Female", "Male", "Female",
"Female", "Male", "Male", "Female", "Male", "Male", "Female",
"Female", "Male", "Male", "Female", "Female", "Female", "Female",
"Female", "Male", "Male", "Male", "Male", "Female", "Female",
"Female", "Female", "Female", "Male", "Female", "Female", "Male",
"Male", "Female", "Male", "Female", "Female", "Female", "Female",
"Female", "Male", "Male", "Female", "Female", "Male", "Female",
"Female", "Female", "Female", "Female", "Female", "Female", "Female",
"Female", "Female", "Female", "Female", "Female", "Female", "Male",
"Female", "Male", "Female", "Male", "Female", "Female", "Female",
"Female", "Female", "Male", "Male", "Female", "Female", "Male",
"Female", "Male", "Female", "Female", "Male", "Female", "Female",
"Female", "Male", "Female", "Male", "Male", "Male", "Female",
"Female", "Male", "Male", "Male", "Female", "Female", "Male",
"Female", "Female", "Male", "Female", "Female", "Male", "Female",
"Male", "Male", "Male", "Male", "Female", "Male", "Male", "Female",
"Male", "Male", "Male", "Male", "Male", "Male", "Female"), Timepoint = c("bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1",
"flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1",
"flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1",
"flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1",
"flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1",
"flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1",
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), class = c("tbl_df", "tbl", "data.frame"))
outcome 是在 timepoint-bl (1)、timepoint-flu1 (2) 和 timepoint-flu2 时对每个受试者 (ID) 进行采样的生理指标(3).每个对象 age、age_group 和 sex 也被记录下来。 Age 是 outcome 的预测变量，sex 用作交互变量。
目标：
我正在尝试估计 outcome 变量 在 Young 和 [= 之间的斜率是否存在显着差异27=] 成人跨越 3 Timepoints.
我正在尝试估计 个人 (ID) outcome 在 timepoints [=47] 之间的方差=]和 age_group.
这是为我的目标建模的正确方法吗？情节对我来说看起来不准确。我是线性混合模型的新手，因此不胜感激任何建议。
#mixed
DF_mixed <- lmer(outcome ~ Age* Sex + (1 + Age| Age_group:Timepoint) + (1|ID), data = DF)
# identify age*sex interactions to predict outcome value between timepoints, nested in age_group that have random slope and intercepts
#plot
ggplot(DF, aes(x = Age, y = outcome, color = Timepoint)) +
geom_point(alpha = 0.7) +
theme_classic() +
geom_line(data = cbind(DF, pred = predict(DF_mixed)), aes(y = pred), size = 1) # adding predicted line from mixed model
下面，我将介绍以下建议：(1) 准备数据，(2) 指定模型，以及 (3) 检查模型结果。
除了 tidyverse 包和 lme4，我将使用 broom.mixed::glance() 和 tidy() 检查模型参数，并使用 ggeffects::ggpredict() 生成模型绘图预测。
library(tidyverse)
library(lme4)
library(broom.mixed)
library(ggeffects)
数据准备和变量选择
Timepoint 是一个字符，将被视为模型中的无序类别，这可能不是您想要的。通常最好使用自基线以来经过的实际时间而不是通用的“时间点”，尤其是在时间点之间的距离可变的情况下。对于这个答案，我根据每个受试者相对于基线的年龄变化计算了一个替代 Timepoint_yrs；但是如果你有更精确的时间记录，你可能想用它来代替。
此外，outcome 由一小部分值组成，大约为 1e-4 - 1e-3；这可能会导致 lmer 行为异常，因此我对其进行了缩放。
DF <- DF %>%
group_by(ID) %>%
mutate(Timepoint_yrs = Age - min(Age)) %>%
ungroup() %>%
mutate(outcome_scaled = as.numeric(scale(outcome)))
在模型中包含 Age 和 Age_group 会导致多重共线性问题，因为一个是另一个的函数。鉴于 Age 的极端双峰分布，我只使用了 Age_group。如上所述，年龄的变化现在由 Timepoint_yrs.
解释
型号规格
“我正在尝试估计 3 Timepoints 中 Young 和 Older 成年人的结果变量斜率是否存在显着差异” -- 即 Age_group 通过 Timepoint_yrs 交互。您还写道，"sex 用作交互变量。" 因此，将其放在一起，您正在查看 [= 的 3 向 Age_group 38=] 通过 Timepoint_yrs 互动。因为 Age_group 和 Sex 仅在受试者之间有所不同，我们将在固定效应级别指定：
outcome_scaled ~ Age_group * Sex * Timepoint_yrs
因为每个人有多个测量值 (ID)，我们将包括 ID:
的随机截距
outcome_scaled ~ Age_group * Sex * Timepoint_yrs + (1 | ID)
我们还可以允许 Timepoint_yrs 的斜率因人而异。从你的 post 来看，我没有看到是否包含随机斜率的强有力的理论依据——所以我们将两者都做，看看哪个模型最合适。
# model 1 - random intercepts
rnd_intercept <- lmer(outcome_scaled ~ Age_group * Sex * Timepoint_yrs + (1 | ID), data = DF)
# model 2 - random intercepts and slopes
rnd_int_slope <- lmer(outcome_scaled ~ Age_group * Sex * Timepoint_yrs + (Timepoint_yrs | ID), data = DF)
模型结果
glance(rnd_intercept)
# # A tibble: 1 x 6
# sigma logLik AIC BIC REMLcrit df.residual
# <dbl> <dbl> <dbl> <dbl> <dbl> <int>
# 1 0.510 -575. 1170. 1212. 1150. 494
glance(rnd_int_slopes)
# A tibble: 1 x 6
# sigma logLik AIC BIC REMLcrit df.residual
# <dbl> <dbl> <dbl> <dbl> <dbl> <int>
# 1 0.487 -575. 1173. 1224. 1149. 492
查看 AIC 和 BIC，随机截距模型似乎更好/更简约；由于没有任何理论上的理由更喜欢随机斜率模型，我们将坚持使用该模型。
tidy(rnd_intercept, conf.int = TRUE)
# # A tibble: 10 x 8
# effect group term estimate std.error statistic conf.low conf.high
# <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 fixed NA (Intercept) -0.123 0.122 -1.01 -0.361 0.116
# 2 fixed NA Age_groupYoung -0.0142 0.221 -0.0643 -0.448 0.419
# 3 fixed NA SexMale 0.248 0.214 1.16 -0.171 0.667
# 4 fixed NA Timepoint_yrs 0.131 0.0407 3.21 0.0509 0.210
# 5 fixed NA Age_groupYoung:Se~ -0.0704 0.317 -0.222 -0.692 0.551
# 6 fixed NA Age_groupYoung:Ti~ -0.152 0.0654 -2.32 -0.280 -0.0234
# 7 fixed NA SexMale:Timepoint~ -0.0547 0.0771 -0.709 -0.206 0.0964
# 8 fixed NA Age_groupYoung:Se~ 0.0192 0.101 0.190 -0.178 0.217
# 9 ran_pars ID sd__(Intercept) 0.862 NA NA NA NA
# 10 ran_pars Residual sd__Observation 0.510 NA NA NA NA
最后，我们可以绘制模型的预测值。您的原始代码为原始数据中的每一行预测了一个数据点，然后基本上在每行之间追踪了一条线，正如您所指出的，这不是很有用。相反，对于您的预测变量的每个独特组合，我们只想将绘图基于一个预测结果值（+/- 误差）。 ggeffects::ggpredict() 是一个很好的捷径； emmeans::emmeans() 是另一种选择。
plot_data <- ggpredict(rnd_intercept, terms = c("Timepoint_yrs", "Age_group", "Sex"))
# col names: x = Timepoint_yrs, group = Age_group, facet = Sex, predicted = observed_scaled
ggplot(plot_data, aes(x, predicted)) +
geom_line(aes(color = group)) +
geom_ribbon(aes(ymin = conf.low, ymax = conf.high, fill = group), alpha = .1) +
facet_wrap(vars(facet)) +
labs(x = "Years Since Baseline", y = "Outcome\n(scaled, model-predicted)") +
theme_classic()
根据您的模型系数，您可能还想查看跨 Timepoint_yrs 的 Age_group，以及跨其他变量折叠的 Timepoint_yrs 的主要影响。您可以通过将 terms 参数更改为 ggpredict() 并相应地修改 ggplot 规范来做到这一点。
我有以下纵向（3 Timepoints）数据集：
# A tibble: 504 x 6
ID Age Age_group Sex Timepoint outcome
<int> <int> <fct> <chr> <chr> <dbl>
1 33714 15 Young Male bl 0.00103
2 35377 15 Young Female bl 0.00106
3 38623 45 Older Female bl 0.00103
4 38806 66 Older Female bl 0.00114
5 39593 69 Older Female bl 0.00113
6 39820 60 Older Female bl 0.00113
7 39951 46 Older Male bl 0.000986
8 40286 68 Older Female bl 0.00107
9 40556 9 Young Male bl 0.00114
10 40798 11 Young Male bl 0.00111
# ... with 494 more rows
数据：
39820L, 39951L, 40286L, 40556L, 40798L, 40800L, 40815L, 43762L,
50848L, 52183L, 52461L, 52577L, 53320L, 53873L, 54153L, 54206L,
54581L, 55122L, 55267L, 55462L, 55612L, 55920L, 56022L, 56307L,
56420L, 56679L, 57405L, 57445L, 57480L, 57725L, 57809L, 58004L,
58215L, 58229L, 58503L, 59326L, 59327L, 59344L, 59361L, 59865L,
60099L, 60100L, 60280L, 60384L, 60429L, 60493L, 60503L, 60575L,
60603L, 60664L, 60846L, 61415L, 61656L, 61749L, 61883L, 62081L,
62210L, 62285L, 62937L, 62983L, 63327L, 63329L, 64081L, 64328L,
64418L, 64507L, 64596L, 65178L, 65250L, 65302L, 65478L, 65480L,
65487L, 65572L, 65802L, 65935L, 65974L, 65975L, 65978L, 65991L,
65995L, 66013L, 66154L, 66237L, 66245L, 66389L, 66396L, 66460L,
66572L, 66589L, 67174L, 73230L, 73525L, 73539L, 73677L, 73942L,
73953L, 74034L, 74113L, 74114L, 74427L, 74439L, 74607L, 74641L,
74657L, 74794L, 74800L, 74836L, 74942L, 74952L, 74962L, 74969L,
74977L, 74985L, 74989L, 75220L, 75229L, 75407L, 75653L, 75732L,
75735L, 75757L, 75895L, 75898L, 76381L, 76559L, 76574L, 76594L,
76595L, 76746L, 76751L, 76755L, 76759L, 76775L, 77088L, 77091L,
77099L, 77134L, 77188L, 77203L, 77252L, 77304L, 77413L, 77453L,
77528L, 77556L, 77585L, 77668L, 78262L, 79724L, 79730L, 79850L,
79977L, 80052L, 80819L, 80901L, 80932L, 81064L, 81065L, 81071L,
81098L, 81142L, 81175L, 33714L, 35377L, 38623L, 38806L, 39593L,
39820L, 39951L, 40286L, 40556L, 40798L, 40800L, 40815L, 43762L,
50848L, 52183L, 52461L, 52577L, 53320L, 53873L, 54153L, 54206L,
54581L, 55122L, 55267L, 55462L, 55612L, 55920L, 56022L, 56307L,
56420L, 56679L, 57405L, 57445L, 57480L, 57725L, 57809L, 58004L,
58215L, 58229L, 58503L, 59326L, 59327L, 59344L, 59361L, 59865L,
60099L, 60100L, 60280L, 60384L, 60429L, 60493L, 60503L, 60575L,
60603L, 60664L, 60846L, 61415L, 61656L, 61749L, 61883L, 62081L,
62210L, 62285L, 62937L, 62983L, 63327L, 63329L, 64081L, 64328L,
64418L, 64507L, 64596L, 65178L, 65250L, 65302L, 65478L, 65480L,
65487L, 65572L, 65802L, 65935L, 65974L, 65975L, 65978L, 65991L,
65995L, 66013L, 66154L, 66237L, 66245L, 66389L, 66396L, 66460L,
66572L, 66589L, 67174L, 73230L, 73525L, 73539L, 73677L, 73942L,
73953L, 74034L, 74113L, 74114L, 74427L, 74439L, 74607L, 74641L,
74657L, 74794L, 74800L, 74836L, 74942L, 74952L, 74962L, 74969L,
74977L, 74985L, 74989L, 75220L, 75229L, 75407L, 75653L, 75732L,
75735L, 75757L, 75895L, 75898L, 76381L, 76559L, 76574L, 76594L,
76595L, 76746L, 76751L, 76755L, 76759L, 76775L, 77088L, 77091L,
77099L, 77134L, 77188L, 77203L, 77252L, 77304L, 77413L, 77453L,
77528L, 77556L, 77585L, 77668L, 78262L, 79724L, 79730L, 79850L,
79977L, 80052L, 80819L, 80901L, 80932L, 81064L, 81065L, 81071L,
81098L, 81142L, 81175L, 33714L, 35377L, 38623L, 38806L, 39593L,
39820L, 39951L, 40286L, 40556L, 40798L, 40800L, 40815L, 43762L,
50848L, 52183L, 52461L, 52577L, 53320L, 53873L, 54153L, 54206L,
54581L, 55122L, 55267L, 55462L, 55612L, 55920L, 56022L, 56307L,
56420L, 56679L, 57405L, 57445L, 57480L, 57725L, 57809L, 58004L,
58215L, 58229L, 58503L, 59326L, 59327L, 59344L, 59361L, 59865L,
60099L, 60100L, 60280L, 60384L, 60429L, 60493L, 60503L, 60575L,
60603L, 60664L, 60846L, 61415L, 61656L, 61749L, 61883L, 62081L,
62210L, 62285L, 62937L, 62983L, 63327L, 63329L, 64081L, 64328L,
64418L, 64507L, 64596L, 65178L, 65250L, 65302L, 65478L, 65480L,
65487L, 65572L, 65802L, 65935L, 65974L, 65975L, 65978L, 65991L,
65995L, 66013L, 66154L, 66237L, 66245L, 66389L, 66396L, 66460L,
66572L, 66589L, 67174L, 73230L, 73525L, 73539L, 73677L, 73942L,
73953L, 74034L, 74113L, 74114L, 74427L, 74439L, 74607L, 74641L,
74657L, 74794L, 74800L, 74836L, 74942L, 74952L, 74962L, 74969L,
74977L, 74985L, 74989L, 75220L, 75229L, 75407L, 75653L, 75732L,
75735L, 75757L, 75895L, 75898L, 76381L, 76559L, 76574L, 76594L,
76595L, 76746L, 76751L, 76755L, 76759L, 76775L, 77088L, 77091L,
77099L, 77134L, 77188L, 77203L, 77252L, 77304L, 77413L, 77453L,
77528L, 77556L, 77585L, 77668L, 78262L, 79724L, 79730L, 79850L,
79977L, 80052L, 80819L, 80901L, 80932L, 81064L, 81065L, 81071L,
81098L, 81142L, 81175L), Age = c(15L, 15L, 45L, 66L, 69L, 60L,
46L, 68L, 9L, 11L, 16L, 9L, 56L, 16L, 16L, 14L, 53L, 8L, 6L,
63L, 14L, 10L, 15L, 13L, 15L, 8L, 9L, 9L, 8L, 9L, 9L, 13L, 58L,
10L, 7L, 8L, 8L, 6L, 15L, 43L, 8L, 11L, 44L, 70L, 14L, 12L, 10L,
16L, 12L, 10L, 6L, 13L, 67L, 11L, 12L, 13L, 10L, 66L, 13L, 14L,
12L, 45L, 52L, 64L, 17L, 9L, 12L, 44L, 69L, 11L, 10L, 12L, 10L,
10L, 70L, 54L, 45L, 43L, 54L, 14L, 42L, 44L, 16L, 15L, 43L, 45L,
50L, 53L, 53L, 49L, 69L, 14L, 65L, 14L, 13L, 67L, 59L, 52L, 54L,
44L, 62L, 69L, 10L, 63L, 57L, 12L, 62L, 9L, 53L, 54L, 66L, 49L,
63L, 51L, 9L, 45L, 49L, 49L, 61L, 62L, 57L, 67L, 65L, 45L, 16L,
55L, 64L, 67L, 56L, 52L, 63L, 10L, 62L, 14L, 66L, 68L, 15L, 13L,
43L, 47L, 55L, 69L, 67L, 52L, 15L, 64L, 55L, 44L, 13L, 48L, 71L,
64L, 13L, 50L, 61L, 70L, 57L, 51L, 46L, 57L, 69L, 46L, 8L, 11L,
46L, 71L, 38L, 56L, 16L, 16L, 46L, 67L, 70L, 61L, 47L, 69L, 11L,
13L, 18L, 10L, 57L, 18L, 18L, 15L, 54L, 10L, 8L, 64L, 15L, 12L,
16L, 14L, 16L, 9L, 11L, 11L, 10L, 10L, 11L, 14L, 59L, 12L, 8L,
9L, 9L, 8L, 16L, 44L, 9L, 13L, 45L, 71L, 16L, 13L, 12L, 18L,
13L, 11L, 8L, 14L, 68L, 12L, 13L, 14L, 11L, 67L, 14L, 15L, 14L,
46L, 53L, 65L, 18L, 11L, 14L, 46L, 70L, 12L, 12L, 13L, 11L, 11L,
71L, 55L, 46L, 44L, 55L, 15L, 43L, 45L, 17L, 16L, 44L, 46L, 51L,
55L, 54L, 50L, 70L, 15L, 66L, 15L, 14L, 68L, 60L, 53L, 55L, 46L,
63L, 70L, 11L, 64L, 58L, 13L, 63L, 10L, 54L, 55L, 67L, 50L, 64L,
52L, 11L, 46L, 50L, 50L, 62L, 63L, 58L, 68L, 66L, 46L, 18L, 56L,
65L, 68L, 57L, 53L, 64L, 11L, 63L, 15L, 67L, 69L, 16L, 14L, 44L,
48L, 56L, 70L, 68L, 53L, 17L, 65L, 56L, 45L, 14L, 49L, 73L, 65L,
14L, 50L, 62L, 71L, 58L, 52L, 47L, 58L, 70L, 47L, 9L, 12L, 47L,
72L, 39L, 57L, 18L, 18L, 47L, 68L, 71L, 62L, 48L, 70L, 12L, 14L,
19L, 11L, 58L, 19L, 19L, 16L, 55L, 11L, 9L, 65L, 17L, 13L, 18L,
16L, 18L, 11L, 12L, 12L, 11L, 11L, 12L, 16L, 60L, 13L, 9L, 11L,
10L, 9L, 17L, 45L, 11L, 14L, 46L, 72L, 17L, 14L, 13L, 19L, 15L,
12L, 9L, 15L, 69L, 14L, 14L, 15L, 12L, 68L, 16L, 17L, 15L, 47L,
54L, 66L, 20L, 12L, 15L, 47L, 71L, 13L, 13L, 14L, 12L, 12L, 72L,
56L, 47L, 45L, 56L, 16L, 44L, 46L, 19L, 18L, 44L, 47L, 52L, 56L,
55L, 51L, 71L, 16L, 67L, 16L, 15L, 69L, 60L, 54L, 56L, 46L, 64L,
71L, 12L, 65L, 59L, 14L, 64L, 11L, 55L, 57L, 68L, 51L, 65L, 53L,
11L, 47L, 51L, 51L, 63L, 64L, 59L, 69L, 67L, 48L, 19L, 57L, 66L,
69L, 59L, 54L, 65L, 12L, 64L, 16L, 68L, 70L, 17L, 15L, 45L, 48L,
57L, 71L, 69L, 54L, 18L, 66L, 57L, 50L, 15L, 50L, 74L, 66L, 15L,
51L, 63L, 72L, 59L, 53L, 48L, 59L, 71L, 48L, 10L, 13L, 48L, 73L,
40L, 58L), Age_group = structure(c(1L, 1L, 2L, 2L, 2L, 2L, 2L,
2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L,
1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L,
1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L,
2L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L,
2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L,
2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L,
2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L,
1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L,
2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L,
1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 2L,
2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L,
2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L,
2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L,
2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L,
1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L,
1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L,
2L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L,
2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L,
2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L,
2L), .Label = c("Young", "Older"), class = "factor"), Sex = c("Male",
"Female", "Female", "Female", "Female", "Female", "Male", "Female",
"Male", "Male", "Male", "Male", "Female", "Male", "Male", "Male",
"Female", "Male", "Male", "Male", "Male", "Male", "Male", "Male",
"Male", "Female", "Female", "Male", "Female", "Male", "Female",
"Female", "Female", "Male", "Female", "Female", "Male", "Female",
"Male", "Female", "Male", "Female", "Male", "Male", "Female",
"Male", "Male", "Male", "Female", "Female", "Female", "Male",
"Female", "Male", "Female", "Female", "Male", "Male", "Female",
"Male", "Male", "Female", "Female", "Male", "Male", "Female",
"Female", "Female", "Female", "Female", "Male", "Male", "Male",
"Male", "Female", "Female", "Female", "Female", "Female", "Male",
"Female", "Female", "Male", "Male", "Female", "Male", "Female",
"Female", "Female", "Female", "Female", "Male", "Male", "Female",
"Female", "Male", "Female", "Female", "Female", "Female", "Female",
"Female", "Female", "Female", "Female", "Female", "Female", "Female",
"Female", "Female", "Male", "Female", "Male", "Female", "Male",
"Female", "Female", "Female", "Female", "Female", "Male", "Male",
"Female", "Female", "Male", "Female", "Male", "Female", "Female",
"Male", "Female", "Female", "Female", "Male", "Female", "Male",
"Male", "Male", "Female", "Female", "Male", "Male", "Male", "Female",
"Female", "Male", "Female", "Female", "Male", "Female", "Female",
"Male", "Female", "Male", "Male", "Male", "Male", "Female", "Male",
"Male", "Female", "Male", "Male", "Male", "Male", "Male", "Male",
"Female", "Male", "Female", "Female", "Female", "Female", "Female",
"Male", "Female", "Male", "Male", "Male", "Male", "Female", "Male",
"Male", "Male", "Female", "Male", "Male", "Male", "Male", "Male",
"Male", "Male", "Male", "Female", "Female", "Male", "Female",
"Male", "Female", "Female", "Female", "Male", "Female", "Female",
"Male", "Female", "Male", "Female", "Male", "Female", "Male",
"Male", "Female", "Male", "Male", "Male", "Female", "Female",
"Female", "Male", "Female", "Male", "Female", "Female", "Male",
"Male", "Female", "Male", "Male", "Female", "Female", "Male",
"Male", "Female", "Female", "Female", "Female", "Female", "Male",
"Male", "Male", "Male", "Female", "Female", "Female", "Female",
"Female", "Male", "Female", "Female", "Male", "Male", "Female",
"Male", "Female", "Female", "Female", "Female", "Female", "Male",
"Male", "Female", "Female", "Male", "Female", "Female", "Female",
"Female", "Female", "Female", "Female", "Female", "Female", "Female",
"Female", "Female", "Female", "Female", "Male", "Female", "Male",
"Female", "Male", "Female", "Female", "Female", "Female", "Female",
"Male", "Male", "Female", "Female", "Male", "Female", "Male",
"Female", "Female", "Male", "Female", "Female", "Female", "Male",
"Female", "Male", "Male", "Male", "Female", "Female", "Male",
"Male", "Male", "Female", "Female", "Male", "Female", "Female",
"Male", "Female", "Female", "Male", "Female", "Male", "Male",
"Male", "Male", "Female", "Male", "Male", "Female", "Male", "Male",
"Male", "Male", "Male", "Male", "Female", "Male", "Female", "Female",
"Female", "Female", "Female", "Male", "Female", "Male", "Male",
"Male", "Male", "Female", "Male", "Male", "Male", "Female", "Male",
"Male", "Male", "Male", "Male", "Male", "Male", "Male", "Female",
"Female", "Male", "Female", "Male", "Female", "Female", "Female",
"Male", "Female", "Female", "Male", "Female", "Male", "Female",
"Male", "Female", "Male", "Male", "Female", "Male", "Male", "Male",
"Female", "Female", "Female", "Male", "Female", "Male", "Female",
"Female", "Male", "Male", "Female", "Male", "Male", "Female",
"Female", "Male", "Male", "Female", "Female", "Female", "Female",
"Female", "Male", "Male", "Male", "Male", "Female", "Female",
"Female", "Female", "Female", "Male", "Female", "Female", "Male",
"Male", "Female", "Male", "Female", "Female", "Female", "Female",
"Female", "Male", "Male", "Female", "Female", "Male", "Female",
"Female", "Female", "Female", "Female", "Female", "Female", "Female",
"Female", "Female", "Female", "Female", "Female", "Female", "Male",
"Female", "Male", "Female", "Male", "Female", "Female", "Female",
"Female", "Female", "Male", "Male", "Female", "Female", "Male",
"Female", "Male", "Female", "Female", "Male", "Female", "Female",
"Female", "Male", "Female", "Male", "Male", "Male", "Female",
"Female", "Male", "Male", "Male", "Female", "Female", "Male",
"Female", "Female", "Male", "Female", "Female", "Male", "Female",
"Male", "Male", "Male", "Male", "Female", "Male", "Male", "Female",
"Male", "Male", "Male", "Male", "Male", "Male", "Female"), Timepoint = c("bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl", "bl",
"bl", "bl", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1",
"flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1",
"flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1",
"flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1",
"flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1",
"flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1",
"flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1",
"flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1",
"flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1",
"flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1",
"flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1",
"flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1",
"flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1",
"flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1",
"flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1",
"flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1",
"flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1",
"flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1",
"flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1",
"flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1",
"flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1", "flu1",
"flu1", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2",
"flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2",
"flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2",
"flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2",
"flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2",
"flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2",
"flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2",
"flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2",
"flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2",
"flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2",
"flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2",
"flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2",
"flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2",
"flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2",
"flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2",
"flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2",
"flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2",
"flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2",
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"flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2", "flu2",
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), class = c("tbl_df", "tbl", "data.frame"))
outcome 是在 timepoint-bl (1)、timepoint-flu1 (2) 和 timepoint-flu2 时对每个受试者 (ID) 进行采样的生理指标(3).每个对象 age、age_group 和 sex 也被记录下来。 Age 是 outcome 的预测变量，sex 用作交互变量。
目标：
我正在尝试估计
outcome变量 在Young和 [= 之间的斜率是否存在显着差异27=] 成人跨越 3Timepoints.我正在尝试估计 个人 (
ID)outcome在timepoints[=47] 之间的方差=]和age_group.
这是为我的目标建模的正确方法吗？情节对我来说看起来不准确。我是线性混合模型的新手，因此不胜感激任何建议。
#mixed
DF_mixed <- lmer(outcome ~ Age* Sex + (1 + Age| Age_group:Timepoint) + (1|ID), data = DF)
# identify age*sex interactions to predict outcome value between timepoints, nested in age_group that have random slope and intercepts
#plot
ggplot(DF, aes(x = Age, y = outcome, color = Timepoint)) +
geom_point(alpha = 0.7) +
theme_classic() +
geom_line(data = cbind(DF, pred = predict(DF_mixed)), aes(y = pred), size = 1) # adding predicted line from mixed model
下面，我将介绍以下建议：(1) 准备数据，(2) 指定模型，以及 (3) 检查模型结果。
除了 tidyverse 包和 lme4，我将使用 broom.mixed::glance() 和 tidy() 检查模型参数，并使用 ggeffects::ggpredict() 生成模型绘图预测。
library(tidyverse)
library(lme4)
library(broom.mixed)
library(ggeffects)
数据准备和变量选择
Timepoint 是一个字符，将被视为模型中的无序类别，这可能不是您想要的。通常最好使用自基线以来经过的实际时间而不是通用的“时间点”，尤其是在时间点之间的距离可变的情况下。对于这个答案，我根据每个受试者相对于基线的年龄变化计算了一个替代 Timepoint_yrs；但是如果你有更精确的时间记录，你可能想用它来代替。
此外，outcome 由一小部分值组成，大约为 1e-4 - 1e-3；这可能会导致 lmer 行为异常，因此我对其进行了缩放。
DF <- DF %>%
group_by(ID) %>%
mutate(Timepoint_yrs = Age - min(Age)) %>%
ungroup() %>%
mutate(outcome_scaled = as.numeric(scale(outcome)))
在模型中包含 Age 和 Age_group 会导致多重共线性问题，因为一个是另一个的函数。鉴于 Age 的极端双峰分布，我只使用了 Age_group。如上所述，年龄的变化现在由 Timepoint_yrs.
型号规格
“我正在尝试估计 3 Timepoints 中 Young 和 Older 成年人的结果变量斜率是否存在显着差异” -- 即 Age_group 通过 Timepoint_yrs 交互。您还写道，"sex 用作交互变量。" 因此，将其放在一起，您正在查看 [= 的 3 向 Age_group 38=] 通过 Timepoint_yrs 互动。因为 Age_group 和 Sex 仅在受试者之间有所不同，我们将在固定效应级别指定：
outcome_scaled ~ Age_group * Sex * Timepoint_yrs
因为每个人有多个测量值 (ID)，我们将包括 ID:
outcome_scaled ~ Age_group * Sex * Timepoint_yrs + (1 | ID)
我们还可以允许 Timepoint_yrs 的斜率因人而异。从你的 post 来看，我没有看到是否包含随机斜率的强有力的理论依据——所以我们将两者都做，看看哪个模型最合适。
# model 1 - random intercepts
rnd_intercept <- lmer(outcome_scaled ~ Age_group * Sex * Timepoint_yrs + (1 | ID), data = DF)
# model 2 - random intercepts and slopes
rnd_int_slope <- lmer(outcome_scaled ~ Age_group * Sex * Timepoint_yrs + (Timepoint_yrs | ID), data = DF)
模型结果
glance(rnd_intercept)
# # A tibble: 1 x 6
# sigma logLik AIC BIC REMLcrit df.residual
# <dbl> <dbl> <dbl> <dbl> <dbl> <int>
# 1 0.510 -575. 1170. 1212. 1150. 494
glance(rnd_int_slopes)
# A tibble: 1 x 6
# sigma logLik AIC BIC REMLcrit df.residual
# <dbl> <dbl> <dbl> <dbl> <dbl> <int>
# 1 0.487 -575. 1173. 1224. 1149. 492
查看 AIC 和 BIC，随机截距模型似乎更好/更简约；由于没有任何理论上的理由更喜欢随机斜率模型，我们将坚持使用该模型。
tidy(rnd_intercept, conf.int = TRUE)
# # A tibble: 10 x 8
# effect group term estimate std.error statistic conf.low conf.high
# <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 fixed NA (Intercept) -0.123 0.122 -1.01 -0.361 0.116
# 2 fixed NA Age_groupYoung -0.0142 0.221 -0.0643 -0.448 0.419
# 3 fixed NA SexMale 0.248 0.214 1.16 -0.171 0.667
# 4 fixed NA Timepoint_yrs 0.131 0.0407 3.21 0.0509 0.210
# 5 fixed NA Age_groupYoung:Se~ -0.0704 0.317 -0.222 -0.692 0.551
# 6 fixed NA Age_groupYoung:Ti~ -0.152 0.0654 -2.32 -0.280 -0.0234
# 7 fixed NA SexMale:Timepoint~ -0.0547 0.0771 -0.709 -0.206 0.0964
# 8 fixed NA Age_groupYoung:Se~ 0.0192 0.101 0.190 -0.178 0.217
# 9 ran_pars ID sd__(Intercept) 0.862 NA NA NA NA
# 10 ran_pars Residual sd__Observation 0.510 NA NA NA NA
最后，我们可以绘制模型的预测值。您的原始代码为原始数据中的每一行预测了一个数据点，然后基本上在每行之间追踪了一条线，正如您所指出的，这不是很有用。相反，对于您的预测变量的每个独特组合，我们只想将绘图基于一个预测结果值（+/- 误差）。 ggeffects::ggpredict() 是一个很好的捷径； emmeans::emmeans() 是另一种选择。
plot_data <- ggpredict(rnd_intercept, terms = c("Timepoint_yrs", "Age_group", "Sex"))
# col names: x = Timepoint_yrs, group = Age_group, facet = Sex, predicted = observed_scaled
ggplot(plot_data, aes(x, predicted)) +
geom_line(aes(color = group)) +
geom_ribbon(aes(ymin = conf.low, ymax = conf.high, fill = group), alpha = .1) +
facet_wrap(vars(facet)) +
labs(x = "Years Since Baseline", y = "Outcome\n(scaled, model-predicted)") +
theme_classic()
根据您的模型系数，您可能还想查看跨 Timepoint_yrs 的 Age_group，以及跨其他变量折叠的 Timepoint_yrs 的主要影响。您可以通过将 terms 参数更改为 ggpredict() 并相应地修改 ggplot 规范来做到这一点。