====== GAM ======
Generalized Additive Models (and Generalized Additive *Mixed* Models) for non-linear relationships.

See
  * [[https://r.qcbs.ca/workshop08/book-en/learning-objectives.html|QCBS R Workshop Series]] 
  * [[https://www.sciencedirect.com/science/article/pii/S1053811920310818|A recipe for accurate estimation of lifespan brain trajectories, distinguishing longitudinal and cohort effects]] for "various ways of formulating GAMMs for estimation of lifespan trajectories of 12 brain regions, using a large longitudinal dataset"
  * [[https://peerj.com/articles/6876/]] from Dan: <code>Hierarchical GAMs. Relevant for some of our nested designs choices
 where we look at ROI x Age interactions across some brain measure (ROI nested in person).</code>
===== R: gam vs gamm vs bam =====
  * ''gam'' slower but ''gamm'' gives ''lm'' and ''gam'' part.
  * marginal effects doesn't work with ''gamm'' (need ''gam'')
  * https://github.com/LabNeuroCogDevel/LNCDR/blob/master/R/growthrate_gam.R


===== Knots =====
  * ''checkgam''
  * k.check https://rdrr.io/cran/mgcv/man/k.check.html
  *  [[https://stats.stackexchange.com/questions/301364/gam-optimization-methods-in-mgcv-r-package-which-to-choose|knots in mgcv]]
  * ''scam'' if monotonic

===== Random effects in GAM =====

<code=R>
#In gamm4
gamm4::gamm4(myelin ~ s(age, k = 4, fx = F) + sex, 
             REML = TRUE,
             random=~(1|subject_id), #random intercept
             family = gaussian(link = "identity"), 
             data = df) 

#In mgcv:gamm
mgcv::gamm(myelin ~ s(age, k = 4, fx = F) + sex, 
           method = c("REML"),
           random = list(subject_id=~1), #random intercept
           family = gaussian(link = "identity"),
           data = df)

#In mgcv:gam
mgcv:gam(myelin ~ s(age, k = 4, fx = F) + sex + 
         method = c("REML"),
         s(subject_id, bs = 're'), #random intercept, subject_id *must* be a factor
         family = gaussian(link = "identity"),
         data = df)

#### Random intercept + slopes in GAM ####

#In mgcv:gamm 
mgcv::gamm(myelin ~ s(age, k = 4, fx = F) + sex, 
           method = c("REML"),
           random=list(subject_id=~1, subject_id=~0+age), #uncorrelated random intercepts and slopes
           family = gaussian(link = "identity"),
           data = df)

mgcv::gamm(myelin ~ s(age, k = 4, fx = F) + sex, 
           method = c("REML"),
           random=list(subject_id=~1+age), #correlated random intercepts and slopes
           family = gaussian(link = "identity"),
           data = df)

#In mgcv:gam 
mgcv:gam(myelin ~ s(age, k = 4, fx = F) + sex,
      s(subject_id, bs = 're') +
      s(subject_id, age, bs = 're'),
    data = myelin.glasser.7T$projfrac0.3, method = 'REML')
</code>