biostatistics-lecture 14 generalized additive models ruibin xi peking university school of...
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- Slide 1
- Biostatistics-Lecture 14 Generalized Additive Models Ruibin Xi Peking University School of Mathematical Sciences
- Slide 2
- Generalized Additive models Gillibrand et al. (2007) studied the bioluminescence-depth relationship
- Slide 3
- Generalized Additive models Gillibrand et al. (2007) studied the bioluminescence-depth relationship We may first consider the model
- Slide 4
- Generalized Additive models Gillibrand et al. (2007) studied the bioluminescence-depth relationship We may first consider the model
- Slide 5
- Generalized Additive models Gillibrand et al. (2007) studied the bioluminescence-depth relationship We may first consider the model
- Slide 6
- Generalized Additive models LOESS (locally weighted scatterplot smoothing)-based
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- Generalized Additive models LOESS (locally weighted scatterplot smoothing)-based
- Slide 8
- Generalized Additive models LOESS (locally weighted scatterplot smoothing)-based
- Slide 9
- Generalized Additive models LOESS (locally weighted scatterplot smoothing)-based
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- Generalized Additive models LOESS (locally weighted scatterplot smoothing)-based Spline-based
- Slide 11
- Generalized Additive models LOESS (locally weighted scatterplot smoothing)-based Spline-based
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- Generalized Additive models Suppose that the model is As discussed before, we may approximate the unknown function f with polynomials But the problem is this representation is not very flexible
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- Generalized Additive models
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- What if the data looks like
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- Generalized Additive models One way to overcome this difficulty is to divide the range of the x variable to a few segment and perform regression on each of the segments
- Slide 16
- Generalized Additive models One way to overcome this difficulty is to divide the range of the x variable to a few segment and perform regression on each of the segments
- Slide 17
- Generalized Additive models One way to overcome this difficulty is to divide the range of the x variable to a few segment and perform regression on each of the segments The cubic spline ensures the line looks smooth
- Slide 18
- Generalized Additive models Cubic spline bases (assuming 0