Package 'cvmaPLFAM'

Title: Cross-Validation Model Averaging for Partial Linear Functional Additive Models
Description: Produce an averaging estimate/prediction by combining all candidate models for partial linear functional additive models, using multi-fold cross-validation criterion. More details can be referred to Shishi Liu and Jingxiao Zhang. (2021) <arXiv:2105.00966>.
Authors: Shishi Liu [aut, cre], Jingxiao Zhang [aut]
Maintainer: Shishi Liu <[email protected]>
License: GPL (>= 3)
Version: 0.1.0
Built: 2024-12-09 06:51:44 UTC
Source: CRAN

Help Index

Generate cross-validation folds

Description

Randomly split the data indexes into nfolds folds.

Usage

cvfolds(nfolds, datasize)

Arguments

nfolds

The number of folds used in cross-validation.
datasize

The sample size.

Value

A list. Each element contains the index vector of sample data included in this fold.

Examples

# Given sample size 20, generate 5 folds
set.seed(1212)
cvfolds(5, 20)
#[[1]]
# [1]  6 11 14 16
#[[2]]
# [1]  3  5 10 18
#[[3]]
# [1]  4  7  8 19
#[[4]]
# [1]  2  9 12 15
#[[5]]
# [1]  1 13 17 20

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

Simulated data

Description

Simulate sample data for illustration, including a M0-column design matrix of scalar predictors, a 100-column matrix of the functional predictor, a one-column vector of mu, a one-column vector of Y, and a one-column vector of testY.

Usage

data_gen(R, K, n, M0 = 50, typ, design)

Arguments

R

A scalar of value ranging from 0.1 to 0.9. The ratio of var(mu)/var(Y).
K

A scalar. The number of replications.
n

A scalar. The sample size of simulated data.
M0

A scalar. True dimension of scalar predictors.
typ

A scalar of value 1 or 2. Type of the additive function for the functional predictor.
design

A scalar of value 1, 2, or 3. Designs 1, 2, 3 corresponding to simulation studies.

Value

A list of K simulated data sets. Each data set is of matrix type, whose first M0 columns corresponds to the design matrix of scalar predictors, followed by the recording/measurement matrix of the functional predictor, and vectors mu, Y, testY.

Examples

library(MASS)
# Example: Design 1 in simulation study
data_gen(R = 0.6, K = 2, n = 10, typ = 1, design = 1)

# Example: Design 2 in simulation study
data_gen(R = 0.3, K = 3, n = 10, typ = 2, design = 2)

# Example: Design 3 in simulation study
data_gen(R = 0.9, K = 5, n = 20, typ = 1, design = 3)

Calculate functional principal component (fpc) scores

Description

Conduct functional principal component analysis (FPCA) on the observation matrix of the functional predictor.

Usage

fpcscore(Z, nbasis, tt)

Arguments

Z

An n by nT matrix. The recording/measurement matrix of the functional predictor.
nbasis

The number of basis functions used for spline approximation.
tt

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

Value

A list of

score

An n by nbasis matrix. The estimated functional principal component scores.
eigv

A vector of estimated eigen-values related to FPCA.
varp

A vector of percents of variance explained related to FPCA.

Examples

# Generate a recording/measurement matrix of the functional predictor
fddata = matrix(rnorm(1000), nrow = 10, ncol = 100)
tpoints = seq(0, 1, length.out = 100)

library(fda)
# Using 20 basis functions for spline approximation
fpcscore(fddata, nbasis = 20, tt = tpoints)

# Generate simulated data
simdata = data_gen(R = 0.7, K = 1, n = 20, M0 = 20, typ = 1, design = 1)
# Extract functional data from 'simdata', columns (M0+1):(M0+100)
simfd = simdata[[1]][,21:120]
# Calculate fpc scores
fpcres = fpcscore(simfd, nbasis = 50, tt = seq(0, 1, length.out = 100))
fpcres$score
fpcres$eigv
cumsum(fpcres$varp)

Generate non-nested candidate models

Description

Specify non-nested candidate models, according to the prescribed number of scalar predictors and the number of functional principal components (FPCs). Each candidate model comprises at least one scalar predictor and one FPC, leading to a total number of candidate models (2^nump-1)*(2^numq-1).

Usage

modelspec(nump, numq)

Arguments

nump

The number of scalar predictors used in candidate models.
numq

The number of functional principal components (FPCs) used in candidate models.

Value

A list of

a1

The number of scalar predictors in each candidate model.
a2

The number of FPCs in each candidate model.
a3

The index for each component in each candidate model.

Examples

# Given nump = 2 and numq = 2, resulting in 9 candidate models
modelspec(2, 2)
#$a1
#[1] 2 2 2 1 1 1 1 1 1
#$a2
#[1] 2 1 1 2 1 1 2 1 1
#$a3
#      [,1] [,2] [,3] [,4]
# [1,]    1    2    3    4
# [2,]    1    2    3    0
# [3,]    1    2    0    4
# [4,]    1    0    3    4
# [5,]    1    0    3    0
# [6,]    1    0    0    4
# [7,]    0    2    3    4
# [8,]    0    2    3    0
# [9,]    0    2    0    4

Output the prediction risks of each method for partial linear functional additive models (PLFAMs)

Description

Calculate the estimated weights for averaging across all candidate models and the corresponding mean squared prediction error risk. The methods include AIC, BIC, SAIC, SBIC, and CVMA for PLFAMs.

Usage

predRisk(M, nump, numq, a2, a3, nfolds, XX.train, Y.train, XX.pred, Y.pred)

Arguments

M

The number of candidate models.
nump

The number of scalar predictors in candidate models.
numq

The number of funtional principal components (FPCs) in candidate models.
a2

The number of FPCs in each candidate model. See modelspec.
a3

The index for each component in each candidate model. See modelspec.
nfolds

The number of folds used in cross-validation.
XX.train

The training data of predictors processed.
Y.train

The training data of response variable.
XX.pred

The test data of predictors processed.
Y.pred

The test data of response variable.

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.
ws

A list of weights estimator for five methods.
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.