How can I apply General Additive Mixed Models to my data?

Hello everyone,

I am considering how I could use General Additive Mixed Models to validate the effect of categorical variables (C, V, syllable, etc.) on my data.
The problem is that my continuous variable is a series of values that form a trajectory. I would like to find a statistical way to determine whether the evolution of my trajectories depends on the categorical variables or not.

Here is a small sample of my data

structure(list(syllabe = c("CV", "CV", "VCs", "CV", "CV", "CVs",
"CV", "CV", "CV", "CV"), C = c("w", "w", "l", "w", "w", "l",
"w", "l", "w", "l"), V = c("e", "e", "a", "o", "e", "e", "e",
"e", "e", "e"), F10 = c(1276L, 650L, 637L, 626L, 591L, 1868L,
595L, 555L, 675L, 1787L), F11 = c(1088L, 641L, 633L, 602L, 557L,
1846L, 595L, 581L, 670L, 1932L), F12 = c(568L, 628L, 627L, 578L,
539L, 1825L, 598L, 530L, 665L, 1745L), F13 = c(571L, 604L, 619L,
608L, 528L, 1799L, 542L, 487L, 663L, 1814L), F14 = c(587L, 565L,
610L, 691L, 536L, 1774L, 486L, 490L, 660L, 1768L), F15 = c(660L,
523L, 595L, 715L, 542L, 1190L, 490L, 566L, 658L, 1735L), F16 = c(657L,
503L, 579L, 699L, 547L, 443L, 496L, 589L, 650L, 1715L), F17 = c(558L,
515L, 564L, 650L, 562L, 472L, 489L, 1797L, 641L, 1694L), F18 = c(530L,
547L, 547L, 610L, 584L, 477L, 493L, 1802L, 635L, 1687L), F19 = c(500L,
575L, 525L, 575L, 597L, 499L, 503L, 494L, 629L, 1690L), F110 = c(1771L,
532L, 507L, 585L, 572L, 641L, 530L, 580L, 492L, 504L)), row.names = c(NA,
10L), class = "data.frame")

The values in columns F10 to F110 correspond to the trajectories.

Thank you in advance for any help / suggestion

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