Generate cross-validation folds

Description

Randomly split the data indexes into nfolds folds.

Usage

cvfolds(nfolds, datasize)

Arguments

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.

Usage

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

Arguments

Value

A list of

Examples

# Generate simulated data
simdata = data_gen(R = 0.7, K = 1, n = 50, ntest = 10, M0 = 4, typ = 1, design = 1)
train_dat = simdata[[1]]
scalars.train = train_dat[,1:4]
fd.train = train_dat[,5:104]
Y.train = train_dat[,106]


test_dat = simdata[[2]]
scalars.test = test_dat[,1:4]
fd.test = test_dat[,5:104]
Y.test = test_dat[,106]

tps = seq(0, 1, length.out = 100)

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

Output the prediction risks of the cross-validation model averaging (CVMA) 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.

Usage

cvpredRisk(
  M,
  nump,
  numq,
  a2,
  a3,
  nfolds,
  X.train,
  ZZ.train,
  Y.train,
  X.pred,
  ZZ.pred,
  Y.pred,
  nbasis,
  tt
)

Arguments

Value

A list of

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, ntest, M0, typ, design)

Arguments

Value

A list of K simulated training data sets and K simulated test 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.

Examples

library(MASS)
# Example: Design 1 in simulation study
set.seed(22)
data1 <- data_gen(R = 0.6, K = 2, n = 10, ntest = 5, M0 = 4, typ = 1, design = 1)
str(data1)
# List of 4
#$ : num [1:10, 1:106] -0.501 -1.266 -0.564 -0.563 -0.395 ...
#$ : num [1:10, 1:106] -1.207 -0.089 -0.782 0.123 0.66 ...
#$ : num [1:5, 1:106] 0.816 0.679 0.816 -0.563 -1.367 ...
#$ : num [1:5, 1:106] -0.089 -0.785 0.899 -0.785 -0.445 ...


# Example: Design 2 in simulation study
data_gen(R = 0.3, K = 3, n = 10, ntest = 5, M0 = 20, typ = 1, design = 2)

# Example: Design 3 in simulation study
data_gen(R = 0.9, K = 5, n = 20, ntest = 10, M0 = 4, typ = 2, 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

Value

A list of

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 candidate models

Description

Specify non-nested or 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.

Usage

modelspec(nump, numq, method = NULL)

Arguments

Value

A list of

Examples

# Example 1: non-nested models
# 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

# Example 2: nested models
# Given nump = 2 and numq = 3, resulting in 6 candidate models
modelspec(2, 3, method = "nested")
#$a1
# [1] 2 2 2 1 1 1
#$a2
# [1] 3 2 1 3 2 1
#$a3
#      [,1] [,2] [,3] [,4] [,5]
# [1,]    1    2    3    4    5
# [2,]    1    2    3    4    0
# [3,]    1    2    3    0    0
# [4,]    1    0    3    4    5
# [5,]    1    0    3    4    0
# [6,]    1    0    3    0    0

Fitting partial linear functional additive model

Description

Calculate the prediction values and prediction errors across all candidate models.

Usage

plam.fit(
  M,
  nump,
  numq,
  a3,
  X.train,
  ZZ.train,
  y.train,
  X.pred,
  ZZ.pred,
  y.pred,
  nbasis,
  tt
)

Arguments

Value

A list of