Martijn Wieling

University of Groningen

- Introduction
- Generalized additive modeling
- Articulography
- Using articulography to study L2 pronunciation differences

- Design
- Methods:
`R`

code - Results
- Discussion

*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)

- 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

- Choosing a smoothing basis
- Single predictor or isotropic predictors: thin plate regression spline (this lecture)
- Efficient approximation of the optimal (thin plate) spline

- Combining non-isotropic predictors: tensor product spline

- Single predictor or isotropic predictors: thin plate regression spline (this lecture)
- Generalized Additive Mixed Modeling:
- Random effects can be treated as smooths as well (Wood, 2008)
`R`

:`gam`

and`bam`

(package`mgcv`

)

- For more (mathematical) details, see Wood (2006) and Wood (2017)

- 19 native Dutch speakers from Groningen
- 22 native Standard Southern British English speakers from London
- Material: 10 minimal pairs [t]:[θ] repeated twice:
- 'tent'-'tenth', 'fate'-'faith', 'forth'-'fort', 'kit'-'kith', 'mitt'-'myth'
- 'tank'-'thank', 'team'-'theme', 'tick'-'thick', 'ties'-'thighs', 'tongs'-'thongs'
- Note that the sound [θ] does not exist in the Dutch language

- Goal: compare distinction between this sound contrast for both groups
- Preprocessing:
- Articulatory segmentation: gestural onset to offset (within /ə/ context)
- Positions \(z\)-transformed per axis and time normalized (from 0 to 1) per speaker