GAM

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

See

• QCBS R Workshop Series
• 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:

  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).

• 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

• checkgam
• k.check https://rdrr.io/cran/mgcv/man/k.check.html
• knots in mgcv
• scam if monotonic

#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')