Simple linear regression spline
Quadratic and cubic regression splines
Smoothing splines (alias penalised splines)
Weighted linear regression on a window around the target value. Move target value.
Gradient is divided in segments using knots. Fit bivariate linear regression model on each segment.
Gradient is divided in segments using knots. Fit a quadratic or cubic polynomial on each segment, and ensure a smooth connection at the knots.
Gradient is divided in a large number of segments. Fit a cubic polynomial model on each segment, and ensure a smooth connection at the knots. Minimise the penalised sum of squares in Equation (3.9).
Size of the span
Number and location of knots
Number of knots, location of knots, and degree of polynomial
will probably also rain at 50 m. Hence, there is also a correlation issue here. On top of this, we noticed that there is violation of homogeneity along the depth gradient (more variation towards the surface). Then there is another issue if we analyse data of all 19 stations; these are nested data. Data from the same station may be more similar than data from different stations.
All these issues (heterogeneity, nested data, and correlation) are addressed in Chapters 4, 5, 6, and 7.
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