rlme4r-lavaanstructural-equation-model
lmer longitudinal analyses in R for variance within subjects and between timepoints
I have the following longitudinal (3 Timepoints) data set:
# 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
data:
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 is a physiological measure that was sampled per subject (ID) at timepoint-bl (1), timepoint-flu1 (2) and timepoint-flu2 (3). Each subject age, age_group and sex are recorded as well. Age is a predictor of outcome and sex is used as an interaction variable.
Aims:
I am trying to estimate if there is a significant difference in slope of the
outcomevariable betweenYoungandOlderadults across the 3Timepoints.I am trying to estimate the individual (
ID) variance ofoutcomebetweentimepointsandage_group.
Is this the correct way to model for my aims? The plot doesn't look accurate to me. I am new to linear mixed models so any advice is appreciated.
#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
Solution
Below, I walk through suggestions for (1) preparing your data, (2) specifying the model, and (3) examining model results.
In addition to tidyverse packages and lme4, I'll use broom.mixed::glance() and tidy() to inspect model parameters, and ggeffects::ggpredict() to generate model predictions for plotting.
library(tidyverse)
library(lme4)
library(broom.mixed)
library(ggeffects)
Data Prep & Variable Selection
Timepoint is a character, and will be treated as as an unordered category in the model, which likely isn't what you want. It's often better to use the actual time elapsed since baseline rather than a generic "timepoint," especially if distance between timepoints is variable. For this answer, I computed an alternate Timepoint_yrs based on each subject's change in age from baseline; but if you have a more precise record of time, you may want to use that instead.
Also, outcome consists of a small range of values, on the order of 1e-4 - 1e-3; this can cause lmer to misbehave, so I scaled this.
DF <- DF %>%
group_by(ID) %>%
mutate(Timepoint_yrs = Age - min(Age)) %>%
ungroup() %>%
mutate(outcome_scaled = as.numeric(scale(outcome)))
Including both Age and Age_group in the model will cause issues with multicollinearity, as one is a function of the other. Given the extreme bimodal distribution of Age, I just used Age_group. And as above, change in age is now accounted for by Timepoint_yrs.
Model Specification
"I am trying to estimate if there is a significant difference in slope of the outcome variable between Young and Older adults across the 3 Timepoints" -- i.e., an Age_group by Timepoint_yrs interaction. You also wrote that "sex is used as an interaction variable." So putting this together, you're looking at a 3-way Age_group by Sex by Timepoint_yrs interaction. Because Age_group and Sex only vary between subjects, we'll specify this at the level of fixed effects:
outcome_scaled ~ Age_group * Sex * Timepoint_yrs
Because you have multiple measurements per person (ID), we'll include random intercepts for ID:
outcome_scaled ~ Age_group * Sex * Timepoint_yrs + (1 | ID)
We can also allow the slope of Timepoint_yrs to vary within individuals. From your post, I don't see a strong theoretical reason for whether or not to include random slopes -- so we'll do both and see which model fits best.
# 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)
Model Results
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
Looking at AIC and BIC, the random intercepts model seems a better / more parsimonious fit; absent any theoretical reason to prefer the random slopes model, we'll stick with that one.
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
Finally, we can plot predicted values from the model. Your original code predicted a datapoint for every row in your original data, then basically traced a line between each of these, which as you noted isn't very informative. Instead, we want to base the plot on just one predicted outcome value (+/- error) for each unique combination of your predictors. ggeffects::ggpredict() is a nice shortcut for this; emmeans::emmeans() would be another option.
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()
Based on your model coefficients, you may also want to look at just Age_group across Timepoint_yrs, as well as the main effect of Timepoint_yrs collapsed across other variables. You can do this by changing the terms argument to ggpredict() and modifying the ggplot spec accordingly.