I have brain data from two time points coded as 1,2, respectively. I would like to use mgcv::gam to measure the change of each brain region (Y) between time 1 and time 2. Each subject has an ID variable that I would like to factor into the model as well.
I am struggling to write the correct model and plot
#model
mygam <- mgcv::gam(Y ~ (Timepoint) + Sex + s(Age) + Years_Education + s(ID, by = Timepoint),
method = "REML", data = DF_w)
#plot
plot(mygam, residuals = T, pages = 1, shade = T, shade.col = "lightblue", shift = coef(mygam)[1])
Some sample data:
structure(list(ID = c(33714L, 35377L, 38623L, 38806L, 39593L,
39820L, 39951L, 40286L, 40556L, 40798L, 40800L, 40815L, 43762L,
50848L, 52183L, 52461L, 52577L, 53202L, 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, 81727L, 33714L, 35377L, 38623L,
38806L, 39593L, 39820L, 39951L, 40286L, 40556L, 40798L, 40800L,
40815L, 43762L, 50848L, 52183L, 52461L, 52577L, 53202L, 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, 81727L), Age = c(15L,
15L, 42L, 62L, 66L, 57L, 42L, 65L, 9L, 11L, 16L, 9L, 53L, 16L,
16L, 14L, 50L, 43L, 8L, 6L, 61L, 14L, 10L, 15L, 13L, 15L, 8L,
9L, 9L, 8L, 9L, 9L, 13L, 56L, 10L, 7L, 8L, 8L, 6L, 15L, 42L,
8L, 11L, 43L, 69L, 14L, 12L, 10L, 16L, 12L, 10L, 6L, 13L, 66L,
11L, 12L, 13L, 10L, 65L, 13L, 14L, 12L, 43L, 51L, 63L, 17L, 9L,
12L, 44L, 69L, 11L, 10L, 12L, 10L, 10L, 70L, 54L, 45L, 42L, 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, 17L, 15L,
15L, 42L, 62L, 66L, 57L, 42L, 65L, 9L, 11L, 16L, 9L, 53L, 16L,
16L, 14L, 50L, 43L, 8L, 6L, 61L, 14L, 10L, 15L, 13L, 15L, 8L,
9L, 9L, 8L, 9L, 9L, 13L, 56L, 10L, 7L, 8L, 8L, 6L, 15L, 42L,
8L, 11L, 43L, 69L, 14L, 12L, 10L, 16L, 12L, 10L, 6L, 13L, 66L,
11L, 12L, 13L, 10L, 65L, 13L, 14L, 12L, 43L, 51L, 63L, 17L, 9L,
12L, 44L, 69L, 11L, 10L, 12L, 10L, 10L, 70L, 54L, 45L, 42L, 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, 17L), Sex = c("Male",
"Female", "Female", "Female", "Female", "Female", "Male", "Female",
"Male", "Male", "Male", "Male", "Female", "Male", "Male", "Male",
"Female", "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", "Female", "Male", "Female", "Female", "Female",
"Female", "Female", "Male", "Female", "Male", "Male", "Male",
"Male", "Female", "Male", "Male", "Male", "Female", "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", "Female"), Years_Education = c(NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, 16L, NA, NA, NA, 14L, 12L, 16L, NA, NA, NA,
16L, 16L, NA, NA, NA, NA, NA, 18L, 13L, 13L, 16L, 16L, NA, 17L,
14L, NA, NA, 18L, 18L, 16L, 16L, 18L, 16L, 16L, NA, 14L, NA,
NA, 14L, 16L, 14L, 16L, 16L, 12L, 18L, NA, 14L, 12L, NA, 16L,
NA, 16L, 16L, 18L, 16L, 21L, 18L, NA, 16L, 11L, 18L, 14L, 18L,
14L, 18L, 12L, 18L, NA, 18L, 20L, 16L, 12L, 17L, 14L, NA, 16L,
NA, 12L, 12L, NA, NA, 13L, 18L, 18L, 17L, 16L, 12L, NA, 21L,
18L, 18L, NA, 16L, 18L, 18L, NA, 12L, 19L, 16L, 16L, 12L, 18L,
16L, 19L, 15L, NA, NA, 12L, 17L, 12L, 18L, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, 16L, NA, NA, NA, 14L, 12L, 16L, NA, NA,
NA, 16L, 16L, NA, NA, NA, NA, NA, 18L, 13L, 13L, 16L, 16L, NA,
17L, 14L, NA, NA, 18L, 18L, 16L, 16L, 18L, 16L, 16L, NA, 14L,
NA, NA, 14L, 16L, 14L, 16L, 16L, 12L, 18L, NA, 14L, 12L, NA,
16L, NA, 16L, 16L, 18L, 16L, 21L, 18L, NA, 16L, 11L, 18L, 14L,
18L, 14L, 18L, 12L, 18L, NA, 18L, 20L, 16L, 12L, 17L, 14L, NA,
16L, NA, 12L, 12L, NA, NA, 13L, 18L, 18L, 17L, 16L, 12L, NA,
21L, 18L, 18L, NA, 16L, 18L, 18L, NA, 12L, 19L, 16L, 16L, 12L,
18L, 16L, 19L, 15L, NA, NA, 12L, 17L, 12L, 18L, NA), Timepoint = c(1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L), Y = c(0.316483, 0.3510685, 0.267147, 0.254661, 0.3249415,
0.2461125, 0.3238965, 0.375393, 0.2516335, 0.3038465, 0.3206155,
0.2868495, 0.3346625, 0.297433, 0.2869195, 0.3351975, 0.315691,
0.2660795, 0.3195265, 0.3481915, 0.2785565, 0.3471645, 0.315884,
0.251254, 0.3061215, 0.334314, 0.2758345, 0.3539715, 0.307193,
0.224277, 0.302592, 0.327028, 0.2510545, 0.307193, 0.361899,
0.231769, 0.350601, 0.337318, 0.302148, 0.321019, 0.335075, 0.3318655,
0.3464885, 0.348252, 0.3281445, 0.3341985, 0.3437265, 0.28315,
0.3351165, 0.344683, 0.328796, 0.2996415, 0.329305, 0.294367,
0.3512895, 0.3617735, 0.320697, 0.307166, 0.31381, 0.299173,
0.332073, 0.3212095, 0.2990235, 0.323863, 0.3450765, 0.2904305,
0.3595685, 0.3391065, 0.3245175, 0.3418675, 0.2913055, 0.298335,
0.3394605, 0.344435, 0.284265, 0.3228975, 0.3116815, 0.3157865,
0.31368, 0.286124, 0.3255705, 0.343879, 0.3436655, 0.2713715,
0.3381005, 0.3385825, 0.3190355, 0.3597505, 0.3271475, 0.3115485,
0.3276145, 0.3437875, 0.3158815, 0.3218285, 0.326796, 0.3061665,
0.3555745, 0.3250755, 0.321343, 0.337907, 0.3159475, 0.301024,
0.3316655, 0.3446295, 0.3135155, 0.3220135, 0.3710685, 0.2866515,
0.300246, 0.3141975, 0.332256, 0.3296115, 0.321672, 0.287862,
0.354463, 0.321344, 0.304759, 0.337911, 0.3248345, 0.3188435,
0.3068095, 0.3741625, 0.336544, 0.351038, 0.343052, 0.3070755,
0.3310035, 0.3137875, 0.328222, 0.3308255, 0.309383, 0.3096755,
0.299197, 0.3684665, 0.3453295, 0.3565655, 0.3318945, 0.3180955,
0.356223, 0.331051, 0.2844205, 0.316385, 0.347013, 0.326344,
0.3122595, 0.318758, 0.340933, 0.337239, 0.320081, 0.3142475,
0.34704, 0.2590365, 0.31095, 0.317086, 0.342804, 0.271582, 0.2907645,
0.3033985, 0.3154525, 0.3431455, 0.2930245, 0.321643, 0.3315875,
0.328915, 0.317671, 0.2761495, 0.316245, 0.2994025, 0.318245,
0.321339, 0.2885835, 0.4122365, 0.360488, 0.38055, 0.303596,
0.4333405, 0.3850125, 0.3844505, 0.3769385, 0.355161, 0.3364065,
0.418439, 0.4192125, 0.42794, 0.4094405, 0.4032555, 0.3959455,
0.3589195, 0.324668, 0.385214, 0.4323475, 0.3646705, 0.4504675,
0.359749, 0.372037, 0.3742195, 0.2957245, 0.3762205, 0.400279,
0.361942, 0.379597, 0.3540285, 0.3292105, 0.4370465, 0.404536,
0.355939, 0.3330285, 0.3895195, 0.413656, 0.386604, 0.384212,
0.305916, 0.355114, 0.3440965, 0.3500305, 0.388537, 0.346431,
0.3394215, 0.3871285, 0.3946955, 0.409459, 0.454724, 0.422755,
0.399704, 0.3929715, 0.3473955, 0.359285, 0.4414455, 0.590826,
0.427441, 0.387022, 0.3764, 0.3959585, 0.3014585, 0.487619, 0.454884,
0.4070005, 0.4467275, 0.465484, 0.403643, 0.406269, 0.391375,
0.403408, 0.409922, 0.3901505, 0.3131075, 0.405408, 0.4024165,
0.4020865, 0.4253735, 0.433137, 0.4444525, 0.398744, 0.3378935,
0.29192, 0.382819, 0.4414085, 0.484809, 0.432799, 0.3276835,
0.4749325, 0.4284325, 0.320546, 0.4325895, 0.3743695, 0.395499,
0.427603, 0.500991, 0.3820045, 0.3838265, 0.3551735, 0.5114045,
0.433393, 0.378873, 0.435692, 0.4510495, 0.413954, 0.333738,
0.3538425, 0.5222565, 0.5051025, 0.4181785, 0.4526625, 0.346886,
0.453598, 0.4338855, 0.3979005, 0.378339, 0.4218445, 0.459127,
0.376291, 0.457066, 0.419093, 0.324645, 0.4700745, 0.3207305,
0.4078725, 0.466963, 0.425291, 0.480983, 0.365733, 0.52236, 0.3796195,
0.5241235, 0.385068, 0.4372355, 0.4265785, 0.373038, 0.4076305,
0.313645, 0.417434, 0.4494865, 0.4868035, 0.366238, 0.364009,
0.313894, 0.371546, 0.385691, 0.3840595, 0.3589585, 0.4525265,
0.4209155, 0.39987, 0.3591295, 0.4241465, 0.5168695, 0.2102594,
0.405142, 0.391291, 0.386246, 0.3784075, 0.4903315, 0.334801,
0.3767035, 0.4459985, 0.3702205, 0.4718795, 0.34822, 0.3262135,
0.318815)), class = "data.frame", row.names = c(NA, -340L))
There are several issues with the setup you have. The by term is specified incorrectly, in your data id isn't a factor, which it needs to be, and the arguments are reversed. Your model smooths over id by timepoint. In the example below, it's fixed and you can see that mgcv cannot fit id specific smooths over time because there isn't enough data.
library('mgcv')
library('gratia')
library('ggplot2')
# df <- your data
names(df) <- tolower(names(df))
summary(df)
# id age sex years_education timepoint y
# 33714 : 2 Min. : 6.00 Length:340 Min. :11.00 Min. :1.0 Min. :0.2103
# 35377 : 2 1st Qu.:13.00 Class :character 1st Qu.:14.00 1st Qu.:1.0 1st Qu.:0.3188
# 38623 : 2 Median :43.00 Mode :character Median :16.00 Median :1.5 Median :0.3449
# 38806 : 2 Mean :36.38 Mean :15.79 Mean :1.5 Mean :0.3583
# 39593 : 2 3rd Qu.:57.00 3rd Qu.:18.00 3rd Qu.:2.0 3rd Qu.:0.3949
# 39820 : 2 Max. :71.00 Max. :21.00 Max. :2.0 Max. :0.5908
# (Other):328 NA's :180
apply(df, 2, function(x) sum(is.na(x)))
# missing 180 cases of `years_education`
mean(df[df$sex == "Male",]$y)
#[1] 0.3675737
mean(df[df$sex == "Female",]$y)
#[1] 0.3712672
## your model without education
## this smooths over ids which are "integer" and rather should be factor
mygam1 <- mgcv::gam(y ~ (timepoint) + sex + s(age) + s(id, by = timepoint),
method = "REML", data = df)
summary(mygam1)
# Family: gaussian
# Link function: identity
#
# Formula:
# y ~ (timepoint) + sex + s(age) + s(id, by = timepoint)
#
# Parametric coefficients:
# Estimate Std. Error t value Pr(>|t|)
# (Intercept) 0.239312 0.007405 32.318 < 2e-16 ***
# timepoint 0.094749 0.019223 4.929 1.31e-06 ***
# sexMale 0.001933 0.004719 0.410 0.682
# ---
# Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#
# Approximate significance of smooth terms:
# edf Ref.df F p-value
# s(age) 1.001 1.002 9.660 0.00203 **
# s(id):timepoint 3.423 4.257 3.609 0.00828 **
# ---
# Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#
# Rank: 21/22
# R-sq.(adj) = 0.499 Deviance explained = 50.8%
# -REML = -573.51 Scale est. = 0.001709 n = 340
# this plot doesnt make sense
plot(mygam, residuals = T, pages = 1, shade = T, shade.col = "lightblue", shift = coef(mygam)[1])
# an alterantive which proposes what you desired in mygam1, can't be done, you dont have enough timepoints
df$id <- as.factor(df$id)
mygam2 <- mgcv::gam(y ~ (timepoint) + sex + s(age) + s(timepoint, by = id),
method = "REML", data = df)
# Error in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots) :
# A term has fewer unique covariate combinations than specified maximum degrees of freedom
Given the aims, it seems a random effect over id may be all you need, then you can test a difference in means by time point conditional on those effects. This is implemented below with the s(var, bs = "re") term. I've also changed the likelihood to beta, which has the correct support for y. For plotting the estimated functions, I'd encourage you to check out the gratia package, which makes it much easier and is pretty customizable. I use draw in the examples below (you may also want to use estimate_smooth).
mygam_alt <- mgcv::gam(y ~ as.factor(timepoint) + sex + s(age, bs = "tp") + s(id, bs = "re"),
method = "REML", data = df, family = betar)
summary(mygam_alt)
# Family: Beta regression(129.815)
# Link function: logit
#
# Formula:
# y ~ as.factor(timepoint) + sex + s(age, bs = "tp") + s(id, bs = "re")
#
# Parametric coefficients:
# Estimate Std. Error z value Pr(>|z|)
# (Intercept) -0.842034 0.055622 -15.138 <2e-16 ***
# as.factor(timepoint)2 0.338984 0.019852 17.076 <2e-16 ***
# sexMale -0.004194 0.020406 -0.206 0.837
# ---
# Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#
# Approximate significance of smooth terms:
# edf Ref.df Chi.sq p-value
# s(age) 1.001 1.001 10.048 0.00153 **
# s(id) 0.734 1.000 2.762 0.05242 .
# ---
# Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#
# R-sq.(adj) = 0.483 Deviance explained = 48.3%
# -REML = -585.63 Scale est. = 1 n = 340
gam.check(mygam_alt)
# Method: REML Optimizer: outer newton
# full convergence after 8 iterations.
# Gradient range [-0.0002248251,0.0001459622]
# (score -585.6282 & scale 1).
# Hessian positive definite, eigenvalue range [0.0002246851,168.796].
# Model rank = 13 / 13
#
# Basis dimension (k) checking results. Low p-value (k-index<1) may
# indicate that k is too low, especially if edf is close to k'.
# *** You can see here, it might not be worth including these smooths either ***
# k' edf k-index p-value
# s(age) 9.000 1.001 0.95 0.15
# s(id) 1.000 0.734 0.99 0.42
x <- draw(mygam_alt)
x
For completeness, you dont have enough observations for a factor smooth either (this holds for any choice of k, then number of basis functions.
mygam_alt_fs <- mgcv::gam(y ~ timepoint + sex + s(age, bs = "tp") + s(timepoint,id, bs = "fs"),
method = "REML", data = df, family = betar)
# Error in smooth.construct.tp.smooth.spec(object, data, knots) :
# A term has fewer unique covariate combinations than specified maximum degrees of freedom