Using articulography to study L2 pronunciation differences
Design
Methods: R code
Results
Discussion
Generalized additive modeling (1)
Generalized additive model (GAM): relaxing assumption of linear relation between dependent variable and predictor
Relationship between individual predictors and (possibly transformed) dependent variable is estimated by a non-linear smooth function: \(g(y) = s(x_1) +s(x_2,x_3) + \beta_4x_4 + ...\)
Multiple predictors can be combined in a (hyper)surface smooth (other lecture)
Question 1
Generalized additive modeling (2)
Advantage of GAM over manual specification of non-linearities: the optimal shape of the non-linearity is determined automatically
Appropriate degree of smoothness is automatically determined by minimizing combined error and "wigglyness" (no overfitting)
Maximum number of basis functions limits the maximum amount of non-linearity
First ten basis functions
Generalized additive modeling (3)
Choosing a smoothing basis
Single predictor or isotropic predictors: thin plate regression spline (this lecture)
Efficient approximation of the optimal (thin plate) spline