simulate_fosr: Simulate a function-on-scalar regression model

In drkowal/fosr: Function-on-Scalars Regression for High Dimensional Data

Description

Simulate data from a function-on-scalar regression model, allowing for subject-specific random effects. The predictors are multivariate normal with mean zero and covariance corr^abs(j1-j2) for correlation parameter corr between predictors j1 and j2. More predictors than observations (p > n) is allowed.

Usage

simulate_fosr(
  n = 100,
  m = 50,
  RSNR = 5,
  K_true = 4,
  p_0 = 1000,
  p_1 = 5,
  sparse_factors = TRUE,
  corr = 0,
  perc_missing = 0,
  X = NULL
)

Arguments

n	number of observed curves (i.e., number of subjects)
m	total number of observation points (i.e., points along the curve)
RSNR	root signal-to-noise ratio
K_true	rank of the model (i.e., number of basis functions used for the functional data simulations)
p_0	number of true zero regression coefficients
p_1	number of true nonzero regression coefficients
sparse_factors	logical; if TRUE, then for each nonzero predictor j, sample a subset of k=1:K_true factors to be nonzero#'
corr	correlation parameter for predictors
perc_missing	percentage of missing data (between 0 and 1); default is zero
X	the design matrix to use. By default, X is NULL. When X is NULL, a design matrix is created. If X is specified, then params p_0, n and

Value

a list containing the following:

• Y: the simulated n x m functional data matrix

• X: the simulated n x p design matrix

• tau: the m-dimensional vector of observation points

• Y_true: the true n x m functional data matrix (w/o noise)

• alpha_tilde_true the true m x p matrix of regression coefficient functions

• alpha_arr_true the true K_true x p matrix of regression coefficient factors

• Beta_true the true n x K_true matrix of factors

• F_true the true m x K_true matrix of basis (loading curve) functions

• sigma_true the true observation error standard deviation

Note

The basis functions (or loading curves) are orthonormalized polynomials, so large values of K_true are not recommended.

Examples

# Example: simulate FOSR
sim_data = simulate_fosr(n = 100, m = 20, p_0 = 100, p_1 = 5)
Y = sim_data$Y; X = sim_data$X; tau = sim_data$tau

drkowal/fosr documentation built on Oct. 2, 2020, 11:20 a.m.