penReg: Function to fit penalised regression

Description Usage Arguments Value Author(s) References Examples

Description

The function penReg() can be used to fit a P-spline. It can be used as demonstration of how the penalised B-splines can be fitted to one explanatory variable. For more that one explanatory variables use the function pb() in gamlss. The function penRegQ() is similar to the function penReg() but it estimates the "random effect" sigmas using the Q-function (marginal likelihood). The Q-function estimation takes longer but it has the advantage that standard errors are provided for \log σ_e and \log σ_b, where the sigmas are the standard errors for the response and the random effects respectively. The function pbq() is a smoother within GAMLSS and should give identical results to the additive function pb(). The function gamlss.pbq is not for use.

Usage

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penReg(y, x, weights = rep(1, length(y)), df = NULL, lambda = NULL, start = 10, 
      inter = 20, order = 2, degree = 3,  plot = FALSE,
      method = c("ML", "ML-1", "GAIC", "GCV", "EM"), k = 2, ...)
penRegQ(y, x, weights = rep(1, length(y)), order = 2, start = 10, 
       plot = FALSE, lambda = NULL, inter = 20, degree = 3, 
       optim.proc = c("nlminb", "optim"), 
       optim.control = NULL)        
pbq(x, control = pbq.control(...), ...)
gamlss.pbq(x, y, w, xeval = NULL, ...)

Arguments

y

the response variable

x

the unique explanatory variable

weights

prior weights

w

weights in the iretation withing GAMLSS

df

effective degrees of freedom

lambda

the smoothing parameter

start

the lambda starting value if the local methods are used

inter

the no of break points (knots) in the x-axis

order

the required difference in the vector of coefficients

degree

the degree of the piecewise polynomial

plot

whether to plot the data and the fitted function

method

The method used in the (local) performance iterations. Available methods are "ML", "ML-1", "EM", "GAIC" and "GCV"

k

the penalty used in "GAIC" and "GCV"

optim.proc

which function to be use to optimise the Q-function, options are c("nlminb", "optim")

optim.control

options for the optimisation procedures

control

arguments for the fitting function. It takes one two: i) order the order of the B-spline and plot whether to plot the data and fit.

xeval

this is use for prediction

...

for extra arguments

Value

Returns a fitted object of class penReg. The object contains 1) the fitted coefficients 2) the fitted.values 3) the response variable y, 4) the label of the response variable ylabel 5) the explanatory variable x, 6) the lebel of the explanatory variable 7) the smoothing parameter lambda, 8) the effective degrees of freedom df, 9) the estimete for sigma sigma, 10) the residual sum of squares rss, 11) the Akaike information criterion aic, 12) the Bayesian information criterion sbc and 13) the deviance

Author(s)

Mikis Stasinopoulos [email protected], Bob Rigby [email protected] and Paul Eilers

References

Eilers, P. H. C. and Marx, B. D. (1996). Flexible smoothing with B-splines and penalties (with comments and rejoinder). Statist. Sci, 11, 89-121.

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), Appl. Statist., 54, part 3, pp 507-554.

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.

Examples

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set.seed(1234)
x <- seq(0,10,length=200); y<-(yt<-1+2*x+.6*x^2-.1*x^3)+rnorm(200, 4)
library(gamlss)
#------------------ 
# df fixed
g1<-gamlss(y~pb(x, df=4))
m1<-penReg(y,x, df=4) 
cbind(g1$mu.coefSmo[[1]]$lambda, m1$lambda)
cbind(g1$mu.df, m1$edf)
cbind(g1$aic, m1$aic)
cbind(fitted(g1), fitted(m1))[1:10,]
# identical
#------------------
# estimate lambda using ML
g2<-gamlss(y~pb(x))
m2<-penReg(y,x) 
cbind(g2$mu.df, m2$edf)
cbind(g2$mu.lambda, m2$lambda) 
cbind(g2$aic, m2$aic) # different lambda
cbind(fitted(g2), fitted(m2))[1:10,]
# identical
#------------------
#  estimate lambda using GCV
g3 <- gamlss(y~pb(x, method="GCV"))
m3 <- penReg(y,x, method="GCV") 
cbind(g3$mu.df, m3$edf)
cbind(g3$mu.lambda, m3$lambda)
cbind(g3$aic, m3$aic)
cbind(fitted(g3), fitted(m3))[1:10,]
# almost identical
#------------------
#  estimate lambda using  GAIC(#=3)
g4<-gamlss(y~pb(x, method="GAIC", k=3))
m4<-penReg(y,x, method="GAIC", k=3) 
cbind(g4$mu.df, m4$edf )
cbind(g4$mu.lambda, m4$lambda)
cbind(g4$aic, m4$aic)
cbind(g4$mu.df, m4$df)
cbind(g4$mu.lambda, m4$lambda)
cbind(fitted(g4), fitted(m4))[1:10,]

#-------------------
plot(y~x)
lines(fitted(m1)~x, col="green")
lines(fitted(m2)~x, col="red")
lines(fitted(m3)~x, col="blue")
lines(fitted(m4)~x, col="yellow")
lines(fitted(m4)~x, col="grey")
# using the Q function

# the Q-function takes longer
system.time(g6<-gamlss(y~pbq(x)))
system.time(g61<-gamlss(y~pb(x)))
AIC(g6, g61)
#
system.time(m6<-penRegQ(y,x))
system.time(m61<-penReg(y,x)) 
AIC(m6, m61)

cbind(g6$mu.df, g61$mu.df,m6$edf, m61$edf)
cbind(g6$mu.lambda,g61$mu.lambda, m6$lambda, m61$lambda) 
cbind(g6$aic, AIC(g6), m6$aic, AIC(m6), m61$aic, AIC(m61)) 
cbind(fitted(g6), fitted(m6))[1:10,]

Example output

Loading required package: gamlss.dist
Loading required package: MASS
Loading required package: gamlss
Loading required package: splines
Loading required package: gamlss.data
Loading required package: nlme
Loading required package: parallel
 **********   GAMLSS Version 5.0-2  ********** 
For more on GAMLSS look at http://www.gamlss.org/
Type gamlssNews() to see new features/changes/bug fixes.

Loading required package: zoo

Attaching package: 'zoo'

The following objects are masked from 'package:base':

    as.Date, as.Date.numeric

GAMLSS-RS iteration 1: Global Deviance = 588.0129 
GAMLSS-RS iteration 2: Global Deviance = 588.0127 
         [,1]     [,2]
[1,] 29.00139 32.12168
     [,1] [,2]
[1,]    6    6
         [,1]     [,2]
[1,] 602.0127 602.0127
          [,1]     [,2]
 [1,] 4.410963 4.410963
 [2,] 4.550483 4.550483
 [3,] 4.690062 4.690062
 [4,] 4.829716 4.829716
 [5,] 4.969463 4.969463
 [6,] 5.109318 5.109318
 [7,] 5.249299 5.249299
 [8,] 5.389422 5.389422
 [9,] 5.529704 5.529704
[10,] 5.670163 5.670163
GAMLSS-RS iteration 1: Global Deviance = 554.7323 
GAMLSS-RS iteration 2: Global Deviance = 554.7323 
        [,1]    [,2]
[1,] 11.8014 11.8014
          [,1]      [,2]
[1,] 0.9241998 0.8667171
         [,1]     [,2]
[1,] 580.3351 580.3351
          [,1]     [,2]
 [1,] 4.522962 4.522961
 [2,] 4.656743 4.656743
 [3,] 4.791038 4.791038
 [4,] 4.925999 4.925999
 [5,] 5.061780 5.061780
 [6,] 5.198533 5.198533
 [7,] 5.336412 5.336412
 [8,] 5.475569 5.475569
 [9,] 5.616157 5.616157
[10,] 5.758269 5.758269
GAMLSS-RS iteration 1: Global Deviance = 564.2135 
GAMLSS-RS iteration 2: Global Deviance = 564.2135 
         [,1]     [,2]
[1,] 8.316444 10.74549
         [,1]     [,2]
[1,] 5.973202 1.473257
         [,1]     [,2]
[1,] 582.8464 580.4273
          [,1]     [,2]
 [1,] 4.548077 4.526789
 [2,] 4.680495 4.662723
 [3,] 4.812954 4.798888
 [4,] 4.945465 4.935355
 [5,] 5.078042 5.072192
 [6,] 5.210699 5.209470
 [7,] 5.343449 5.347257
 [8,] 5.476305 5.485623
 [9,] 5.609281 5.624638
[10,] 5.742384 5.764334
GAMLSS-RS iteration 1: Global Deviance = 670.3158 
GAMLSS-RS iteration 2: Global Deviance = 565.6209 
GAMLSS-RS iteration 3: Global Deviance = 560.7827 
GAMLSS-RS iteration 4: Global Deviance = 560.5387 
GAMLSS-RS iteration 5: Global Deviance = 560.5263 
GAMLSS-RS iteration 6: Global Deviance = 560.5259 
         [,1]     [,2]
[1,] 9.345836 9.345927
        [,1]     [,2]
[1,] 3.27168 3.158211
         [,1]     [,2]
[1,] 581.2175 581.2175
         [,1]
[1,] 9.345836
        [,1]     [,2]
[1,] 3.27168 3.158211
          [,1]     [,2]
 [1,] 4.544514 4.544513
 [2,] 4.678921 4.678920
 [3,] 4.813387 4.813386
 [4,] 4.947932 4.947932
 [5,] 5.082576 5.082576
 [6,] 5.217339 5.217339
 [7,] 5.352240 5.352241
 [8,] 5.487299 5.487300
 [9,] 5.622536 5.622537
[10,] 5.757956 5.757957
GAMLSS-RS iteration 1: Global Deviance = 554.7323 
GAMLSS-RS iteration 2: Global Deviance = 554.7323 
   user  system elapsed 
  0.243   0.000   0.244 
GAMLSS-RS iteration 1: Global Deviance = 554.7323 
GAMLSS-RS iteration 2: Global Deviance = 554.7323 
   user  system elapsed 
  0.032   0.000   0.033 
         df      AIC
g6  12.8014 580.3351
g61 12.8014 580.3351
   user  system elapsed 
  0.008   0.000   0.008 
   user  system elapsed 
  0.004   0.000   0.004 
         df      AIC
m61 12.8014 580.3351
m6  12.8014 580.6976
        [,1]    [,2]    [,3]    [,4]
[1,] 11.8014 11.8014 11.8014 11.8014
          [,1]      [,2]      [,3]      [,4]
[1,] 0.9241996 0.9241998 0.8667171 0.8667171
         [,1]     [,2]     [,3]     [,4]     [,5]     [,6]
[1,] 580.3351 580.3351 580.6976 580.6976 580.3351 580.3351
          [,1]     [,2]
 [1,] 4.522962 4.522961
 [2,] 4.656743 4.656743
 [3,] 4.791038 4.791038
 [4,] 4.925999 4.925999
 [5,] 5.061780 5.061780
 [6,] 5.198533 5.198533
 [7,] 5.336412 5.336412
 [8,] 5.475569 5.475569
 [9,] 5.616157 5.616157
[10,] 5.758269 5.758269

gamlss.util documentation built on May 2, 2019, 7:10 a.m.