A comparison of spline methods in R for building explanatory models
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1 A comparison of spline methods in R for building explanatory models Aris Perperoglou on behalf of TG2 STRATOS Initiative, University of Essex ISCB2017 Aris Perperoglou Spline Methods in R ISCB / 36
2 Introduction Aris Perperoglou Spline Methods in R ISCB / 36
3 The Splines project: Identify R packages that provide the ability to use splines as a functional transformation in univariable and/or multivariable analysis. Collect information on packages. Compile documentation for practical use. Evaluate quality of available packages. Compare approaches, further guidance for use in practice. Aris Perperoglou Spline Methods in R ISCB / 36
4 Splines Aris Perperoglou Spline Methods in R ISCB / 36
5 Splines Splines are piecewise polynomial functions. Given the range of a continuous variables, define points on this interval (knots). Fit a simple polynomial between these knots. Depending on the selection of knots and the type of polynomial the type of spline is named as: polynomial, natural, restricted regression spline, truncated power basis, b-spline (de Boor 1978) smoothing splines (see Generalized Additive Models (Hastie and Tibshirani 1990), p-spline (Marx and Eilers 1996), penalized regression spline, thin plate regression splines (Wood 2006) Aris Perperoglou Spline Methods in R ISCB / 36
6 Challenges ISCB2015: More than 6200 packages available on CRAN. Banff2016: CRAN package repository features 8670 available packages. ISCB2017: More than packages available on CRAN. Aris Perperoglou Spline Methods in R ISCB / 36
7 Aris Perperoglou Spline Methods in R ISCB / 36
8 Types of splines in R Aris Perperoglou Spline Methods in R ISCB / 36
9 The splines Package bs: B-Spline Basis for Polynomial Splines bs(x,df=null,knots=null,degree=3,boundary.knots=range(x)) ns: Generate a Basis Matrix for Natural Cubic Splines ns(x,df=null,knots=null,boundary.knots=range(x)) Aris Perperoglou Spline Methods in R ISCB / 36
10 B-splines basis bs(x, knots = knts(1), degree = 1) Deg=1, k=3 Deg=1, k= bs(x, knots = knts(1)) Deg=3, k=3 Deg=3, k= Aris Perperoglou Spline Methods in R ISCB / 36
11 Natural splines ns(x, knots = knts(1)) k=3 k= ns(x, knots = knts(5)) k=7 k= Aris Perperoglou Spline Methods in R ISCB / 36
12 Scatterplot smoothing: Tricepts skinfold thikness by age 892 females under 50 years in three villages in West Africa (Cole and Green 1992, (Royston and Sauerbrei 2008). Figure 1 shows the relationship between age and triceps skinfold thickness measured in log scale. plot(x,y,ylab="lntriceps",xlab="age") fit.bs = lm(y ~ bs(x)) fit.ns = lm(y~ns(x)) lines(x, predict(fit.bs, data.frame(x=x)), col=2,lwd=2) lines(x, predict(fit.ns, data.frame(x=x)), col=3,lwd=2) Aris Perperoglou Spline Methods in R ISCB / 36
13 Scatterplot smoothing (default values) lntriceps B Splines Natural age Aris Perperoglou Spline Methods in R ISCB / 36
14 Scatterplot smoothing (k=4) lntriceps B Splines Natural age Aris Perperoglou Spline Methods in R ISCB / 36
15 Scatterplot smoothing (k=12) lntriceps B Splines Natural age Aris Perperoglou Spline Methods in R ISCB / 36
16 Simulation Mean Square Error depending on the number of knots Three different scenarios: Scenario (a) Scenario (b) Scenario (c) Aris Perperoglou Spline Methods in R ISCB / 36
17 Sim (a): n=100 Aris Perperoglou Spline Methods in R ISCB / 36
18 Sim (a): n=200 Aris Perperoglou Spline Methods in R ISCB / 36
19 Sim (a): n=500 Aris Perperoglou Spline Methods in R ISCB / 36
20 Sim (b): n=200 Aris Perperoglou Spline Methods in R ISCB / 36
21 Sim (c): n=100 Aris Perperoglou Spline Methods in R ISCB / 36
22 Some ideas There is no such thing as an optimal number of knots. MSE varies with number of knots, sample size, type of spline and type of data. B-splines tend to behave better with a smaller number of parameters. They should outperform natural splines when the fit needed is quite flexible. The choice of basis becomes less relevant as number of knots increases. Aris Perperoglou Spline Methods in R ISCB / 36
23 Other packages Package Description Authors gss General Smoothing Splines C Gu polspline Polynomial spline routines C Kooperberg pspline Penalized Smoothing Splines B Ripley cobs Constrained B-Splines PT Ng and M Maechler crs Categorical Regression Splines JS Racine, Z Nie, BD R bigsplines Smoothing Splines for Large Samples NE Helwig bezier Bezier Curve and Spline Toolkit A Olsen freeknotsplines Free-Knot Splines S Spiriti, P Smith, P Lec Orthogonal splinebasis Orthogonal B-Spline Functions A Redd pbs Periodic B Splines S Wang logspline Logspline density estimation routines C Kooperberg episplinedensity Density Estimation Exponential S Buttrey, J Royset, R W Hmisc, rms restricted cubic splines, plots F Harrell Aris Perperoglou Spline Methods in R ISCB / 36
24 Regression Packages Aris Perperoglou Spline Methods in R ISCB / 36
25 A brief overview of packages Package Downloads Vignette Book Website Datasets quantreg X X 7 mgcv X X 2 survival X X 33 VGAM X X X 50 gbm X 3 gam X X 1 gamlss X X X 29 Aris Perperoglou Spline Methods in R ISCB / 36
26 Splines in packages package bs ns s p-splines gam x x x mgcv x x x x gamlss x x cs x Aris Perperoglou Spline Methods in R ISCB / 36
27 Common bases in mgcv tp: Thin plate regression spline, ts as tp but with a modification to the smoothing penalty ds: Duchon splines (generalisation of thin plate splines) ps: p-splines cr: Cubic regression splines, cs specifies a shrinkage version of cr, cc specifies a cyclic cubic regression splines i.e. a penalized cubic regression splines whose ends match, up to second derivative. re: parametric terms penalized by a ridge penalty Aris Perperoglou Spline Methods in R ISCB / 36
28 Common basis in Gamlss Aris Perperoglou Spline Methods in R ISCB / 36
29 Comparison at default values Thin plate regression splines (Wood 06) vs p-splines (Eilers & Marx 96) Aris Perperoglou Spline Methods in R ISCB / 36
30 P-splines vs Thin Plate Regression Splines Sample size n=50 Aris Perperoglou Spline Methods in R ISCB / 36
31 P-splines vs Thin Plate Regression Splines Sample size n=1000 Aris Perperoglou Spline Methods in R ISCB / 36
32 P-splines vs Thin Plate Regression Splines Sample size n=50 Aris Perperoglou Spline Methods in R ISCB / 36
33 P-splines vs Thin Plate Regression Splines Sample size n=1000 Aris Perperoglou Spline Methods in R ISCB / 36
34 MSE p-splines vs thin plate splines vs smoothing splines scenario (a) n mgcv tp gamlss pb gam s scenario (b) mgcv tp gamlss pb gam s scenario (c) n mgcv tp gamlss pb gam s Aris Perperoglou Spline Methods in R ISCB / 36
35 Discussion Aris Perperoglou Spline Methods in R ISCB / 36
36 Some points Anything is possible for the experts, not so straight forward for applied analysts. Not an easy task to suggest an overall strategy. Paper on review of spline methods in R almost completed. Paper on evaluation of spline methods in R in progress. Aris Perperoglou Spline Methods in R ISCB / 36
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