simulate_fosr: Simulate a function-on-scalar regression model

In drkowal/dfosr: Dynamic Function-on-Scalars Regression

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)

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

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/dfosr documentation built on May 7, 2020, 3:09 p.m.