splmm (version 1.1.2)

splmmTuning: Tuning funtion of 'splmm' object

Description

This function fits 'splmm' function over grids of lambda1 and/or lambda2 and determine the best fit model based on model selection information criterion. The function takes a scalar or a grid of lambda1 and/or lambda2 and determine the optimal tuning parameter value for the best model fit. If both lambda1 and lambda2 are inputted as scalars, an 'splmm' object is returned; if either or both lambda1 and lambda2 are inputted as grids, an 'splmm.tuning' object is returned. Currently the model selection criterion include AIC and BIC, and BIC is used to determine the optimal model.

Usage

splmmTuning(x, y, z, grp, lam1.seq, lam2.seq, nonpen.b=1,nonpen.L=1,
                          penalty.b=c("lasso","scad"),
                          penalty.L=c("lasso","scad"),
                          CovOpt=c("nlminb","optimize"),
                          standardize=TRUE,control=splmmControl())

Arguments

x

matrix of dimension N x p including the fixed-effects covariables. An intercept has to be included in the first column as (1,...,1).

y

response variable of length N.

z

random effects matrix of dimension N x q. It has to be a matrix, even if q=1.

grp

grouping variable of length N

lam1.seq

a grid of regularization parameter for fixed effects penalization, could be a scalar if no need to tune.

lam2.seq

a grid of regularization parameter for random effects penalization, could be a scalar if no need to tune.

nonpen.b

Index of indices of fixed effects not penalized. The default value is 1, which means the fixed intercept is not penalized.

nonpen.L

Index of indices of random effects not penalized. The default value is 1, which means the random intercept is not penalized.

penalty.b

The penalty method for fixed effects penalization. Currently available options include LASSO penalty and SCAD penalty.

penalty.L

The penalty method for fixed effects penalization. Currently available options include LASSO penalty and SCAD penalty.

CovOpt

which optimization routine should be used for updating the variance parameter. The available options include optimize and nlminb. nlminb uses the estimate of the last iteration as a starting value. nlminb is faster if there are many Gauss-Seidel iterations.

standardize

A logical parameter specifying whether the fixed effects matrix x and random effects matrix z should be standardized such that each column has mean 0 and standard deviation 1. The default value is TRUE.

control

control parameters for the algorithm and the Armijo Rule, see 'splmmControl' for the details.

Value

A 'splmm.tuning' object is returned, for which plot method exist.

lam1.seq

lambda1 grid used for tuning. Only available when lambda1 is inputted as a vector.

lam2.seq

lambda2 grid used for tuning. Only available when lambda2 is inputted as a vector.

BIC.lam1

A vector of BIC values of splmm models fitting over a lambda1 grid.

BIC.lam2

A vector of BIC values of splmm models fitting over a lambda2 grid.

fit.BIC

An array of BIC values of splmm models fitting over lambda 1 grid x lambda2 grid.

AIC.lam1

A vector of AIC values of splmm models fitting over a lambda1 grid.

AIC.lam2

A vector of AIC values of splmm models fitting over a lambda2 grid.

fit.AIC

An array of AIC values of splmm models fitting over lambda 1 grid x lambda2 grid.

BBIC.lam1

A vector of BBIC values of splmm models fitting over a lambda1 grid.

BBIC.lam2

A vector of BBIC values of splmm models fitting over a lambda2 grid.

fit.BBIC

An array of BBIC values of splmm models fitting over lambda 1 grid x lambda2 grid.

EBIC.lam1

A vector of EBIC values of splmm models fitting over a lambda1 grid.

EBIC.lam2

A vector of EBIC values of splmm models fitting over a lambda2 grid.

fit.EBIC

An array of EBIC values of splmm models fitting over lambda 1 grid x lambda2 grid.

min.BIC

The minimum BIC value from tuning over a grid. This is only available when either lambda1 or lambda2 is a scalar.

min.AIC

The minimum AIC value from tuning over a grid. This is only available when either lambda1 or lambda2 is a scalar.

min.BBIC

The minimum BBIC value from tuning over a grid. This is only available when either lambda1 or lambda2 is a scalar.

min.EBIC

The minimum EBIC value from tuning over a grid. This is only available when either lambda1 or lambda2 is a scalar.

best.model

The index of the optimal model. This is only available when either lambda1 or lambda2 is a scalar.

best.fit

The optimal model chosen by the minimum BIC as an splmm object.

min.lam1

lambda1 value that results in the optimal model. This is only available when input lambda1 is a vector.

min.lam2

lambda2 value that results in the optimal model. This is only available when input lambda2 is a vector.

lam1.tuning

A logical parameter specifying if tuning is performed over lamdbda1 grid. lam1.tuning=TRUE if input lambda1 is a vector.

lam2.tuning

A logical parameter specifying if tuning is performed over lamdbda2 grid. lam1.tuning=TRUE if input lambda2 is a vector.

Examples

# NOT RUN {
# }
# NOT RUN {
data(cognitive)

x <- model.matrix(ravens ~schoolid+treatment+year+sex+age_at_time0
                  +height+weight+head_circ+ses+mom_read+mom_write
                  +mom_edu, cognitive)
z <- x

## Tuning over lambda1 grid
lam1 = seq(0.1,0.5,0.1)
lam2 = 0.1
fit1 <-splmmTuning(x=x,y=cognitive$ravens,z=z,grp=cognitive$id,lam1.seq=lam1,
lam2.seq=lam2,penalty.b="scad", penalty.L="scad")
plot.splmm(fit1)

## Tuning over lambda2 grid
lam1 = 0.1
lam2 = seq(0.1,0.5,0.1)
fit2 <-splmmTuning(x=x,y=cognitive$ravens,z=z,grp=cognitive$id,lam1.seq=lam1,
lam2.seq=lam2,penalty.b="scad", penalty.L="scad")
plot.splmm(fit2)

## Tuning over both lambda1 and lambda2 grid
lam1 = seq(0.1,0.5,0.2)
lam2 = seq(0.1,0.5,0.2)
fit3 <-splmmTuning(x=x,y=cognitive$ravens,z=z,grp=cognitive$id,lam1.seq=lam1,
lam2.seq=lam2,penalty.b="scad", penalty.L="scad")
plot.splmm(fit3)
# }
# NOT RUN {
# }