Introduction to Generalized Additive Models R. Harald Baayen Seminar für Sprachwissenschaft Universität Tübingen & Department of Linguistics University of Alberta October 17, 2013 / NWAV Pittsburgh 1 | R. H. Baayen GAMs Seminar für Sprachwissenschaft Universität T
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Introduction to Generalized Additive Modelswieling/NWAV/presentations/NWAV-Part-I-Harald.pdfIntroduction to Generalized Additive Models R. Harald Baayen Seminar für Sprachwissenschaft
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Introduction to Generalized Additive Models
R. Harald Baayen
Seminar für SprachwissenschaftUniversität Tübingen & Department of Linguistics
University of Alberta
October 17, 2013 / NWAV Pittsburgh
1 | R. H. Baayen GAMs Seminar für Sprachwissenschaft Universität Tübingen & Department of Linguistics University of Alberta
linear regressionGalton
2 | R. H. Baayen GAMs Seminar für Sprachwissenschaft Universität Tübingen & Department of Linguistics University of Alberta
but . . . how linear were his data?
3 | R. H. Baayen GAMs Seminar für Sprachwissenschaft Universität Tübingen & Department of Linguistics University of Alberta
wiggly lines: regression splines
I restricted cubic splines
I thin plate regression splines
4 | R. H. Baayen GAMs Seminar für Sprachwissenschaft Universität Tübingen & Department of Linguistics University of Alberta
restricted cubic splines(pupil dilation curve)
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0 500 1000 1500 2000 2500
−10
00
100
200
300
400
500
Time (ms)
Pup
il D
ilatio
n (0
.001
mm
)
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0 500 1000 1500 2000 2500−
100
010
020
030
040
050
0
Time (ms)
Pup
il D
ilatio
n (0
.001
mm
)
5 | R. H. Baayen GAMs Seminar für Sprachwissenschaft Universität Tübingen & Department of Linguistics University of Alberta
thin plate regression splines
0 20 40 60 80 100
010
2030
4050
x
f1(x
)
0 20 40 60 80 100
−50
−30
−10
0
x
f2(x
)
0 20 40 60 80 100
−40
020
40
x
f3(x
)
0 20 40 60 80 100
−10
0−
60−
2020
x
f1(x
) +
2 *
f2(x
) +
3/5
* f3
(x)
6 | R. H. Baayen GAMs Seminar für Sprachwissenschaft Universität Tübingen & Department of Linguistics University of Alberta
stress on triconstituent compounds in English
left-branching stress left háy fever treatmentleft-branching stress right science fíction bookright-branching stress left business crédit cardright-branching stress right family Christmas dínner
7 | R. H. Baayen GAMs Seminar für Sprachwissenschaft Universität Tübingen & Department of Linguistics University of Alberta
Pitch(Hz)
100
300
Pitch(Hz)
100
300
300
Pitch(Hz)
100
she read about a gene therapy technology last night
Time (s)0 2.996
8 | R. H. Baayen GAMs Seminar für Sprachwissenschaft Universität Tübingen & Department of Linguistics University of Alberta