cvmaPLFAM {cvmaPLFAM}

Cross-Validation Model Averaging (CVMA) for Partial Linear Functional Additive Models (PLFAMs)

Description

Summarize the estimate of weights for averaging across all candidate models for PLFAMs, using multi-fold cross-validation criterion, and the corresponding mean squared prediction error risk. Additionally, the results of AIC, BIC, SAIC and SBIC are delivered simultaneously.

Usage

cvmaPLFAM(
  Y,
  scalars,
  functional,
  Y.test = NULL,
  scalars.test = NULL,
  functional.test = NULL,
  tt,
  nump,
  numfpcs,
  nbasis,
  nfolds,
  ratio.train = NULL
)

Arguments

Y

The vector of the scalar response variable.

scalars

The design matrix of scalar predictors.

functional

The matrix including records/measurements of the functional predictor.

Y.test

Test data: The vector of the scalar response variable.

scalars.test

Test data: The design matrix of scalar predictors.

functional.test

Test data: The matrix including records/measurements of the functional predictor.

tt

The vector of recording/measurement points for the functional predictor.

nump

The number of scalar predictors in candidate models.

numfpcs

The number of functional principal components (FPCs) for the functional predictor in candidate models.

nbasis

The number of basis functions used for spline approximation.

nfolds

The number of folds used in cross-validation.

ratio.train

The ratio of data for training, if test data are NULL.

Value

A list of

aic

Mean squared error risk in training data set, produced by AIC model selection method.

bic

Mean squared error risk in training data set, produced by BIC model selection method.

saic

Mean squared error risk in training data set, produced by SAIC model averaging method.

sbic

Mean squared error risk in training data set, produced by SBIC model averaging method.

cv

Mean squared error risk in training data set, produced by CVMA method.

waic

The selected candidate model by AIC model selection method.

wbic

The selected candidate model by BIC model selection method.

wsaic

The weights for each candidate model by SAIC model averaging method.

wsbic

The weights for each candidate model by SBIC model averaging method.

wcv

The weights for each candidate model by CVMA method.

predaic

Mean squared prediction error risk in test data set, produced by AIC model selection method.

predbic

Mean squared prediction error risk in test data set, produced by BIC model selection method.

predsaic

Mean squared prediction error risk in test data set, produced by SAIC model averaging method.

predsbic

Mean squared prediction error risk in test data set, produced by SBIC model averaging method.

predcv

Mean squared prediction error risk in test data set, produced by CVMA method.

Examples

# Generate simulated data
simdata = data_gen(R = 0.7, K = 1, n = 50, M0 = 20, typ = 1, design = 3)
dat1 = simdata[[1]]
scalars = dat1[,1:20]
fd = dat1[,21:120]
Y = dat1[,122]
tps = seq(0, 1, length.out = 100)

# Estimation
est_res = cvmaPLFAM(Y=Y, scalars = scalars, functional = fd, tt = tps,
       nump = 2, numfpcs = 3, nbasis = 50, nfolds = 5, ratio.train = 0.8)
# Weights estimated by CVMA method
est_res$wcv
# Prediction error risk on test data set
est_res$predcv