ri {gamlss}

Specify ridge or lasso Regression within a GAMLSS Formula

Description

The function ri() allow the user to fit a ridge regression within GAMLSS. It allows the coefficients of a set of explanatory variables to be shrunk towards zero. The amount of shrinking depends either on lambda, or on the equivalent degrees of freedom (df). The type of shrinking depends on the argument Lp see example.

Usage

ri(X = NULL, x.vars = NULL, df = NULL, lambda = NULL, 
   method = c("ML", "GAIC"), order = 0, start = 10, Lp = 2, 
   kappa = 1e-05, iter = 100, c.crit = 1e-06, k = 2)

Arguments

X

A matrix of explanatory variables X which is standardised (mean=0, sd=1) automatically. Note that in order to get predictions you should use the option x.vars

x.vars

which variables from the data.frame declared in data needs to be included. This is a way to fit the model if predictions are required.

df

the effective degrees of freedom df

lambda

the smoothing parameter lambda

method

which method is used for the estimation of the smoothing parameter, ‘ML’ or ‘GAIC’ are allowed.

order

the order of the difference applied to the coefficients with default zero. (Do not change this unless there is some ordering in the explanatory variables).)

start

starting value for lambda if it estimated using ‘ML’ or ‘GAIC’

Lp

The type of penalty required, Lp=2 a proper ridge regression is the default. Use Lp=1 for lasso and different values for different penalties.

kappa

a regulation parameters used for the weights in the penalties.

iter

the number of internal iteration allowed see details.

c.crit

c.crit is the convergent criterion

k

k is the penalty if ‘GAIC’ method is used.

Details

This implementation of ridge and related regressions is based on an idea of Paul Eilers which used weights in the penalty matrix. The type of weights are defined by the argument Lp. Lp=2 is the standard ridge regression, Lp=1 fits a lasso regression while Lp=0 allows a "best subset"" regression see Hastie et al (2009) page 71.

Value

x is returned with class "smooth", with an attribute named "call" which is to be evaluated in the backfitting additive.fit() called by gamlss()

Author(s)

Mikis Stasinopoulos, Bob Rigby and Paul Eilers

References

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.

Rigby, R. and Stasinopoulos, D. M (2013) Automatic smoothing parameter selection in GAMLSS with an application to centile estimation, Statistical methods in medical research.

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC. An older version can be found in https://www.gamlss.com/.

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, https://www.jstatsoft.org/v23/i07/.

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

(see also https://www.gamlss.com/).

See Also

gamlss

Examples

# USAIR DATA
# standarise data 1-------------------------------------------------------------
# ridge
m1<- gamlss(y~ri(x.vars=c("x1","x2","x3","x4","x5","x6")), 
            data=usair)
# lasso
m2<- gamlss(y~ri(x.vars=c("x1","x2","x3","x4","x5","x6"), Lp=1), 
     data=usair)
# best subset
m3<- gamlss(y~ri(x.vars=c("x1","x2","x3","x4","x5","x6"), Lp=0), 
     data=usair)
#--------  plotting the coefficients
op <- par(mfrow=c(3,1))
plot(getSmo(m1)) #
plot(getSmo(m2))
plot(getSmo(m3))
par(op)