simulate_nb_friedman: Simulate count data a Friedman's nonlinear regression

In drkowal/rSTAR: MCMC and EM algorithms for Simultaneous Transformation and Rounding (STAR) Models

Simulate count data a Friedman's nonlinear regression

Description

Simulate data from a negative-binomial distribution with nonlinear mean function.

Usage

simulate_nb_friedman(
  n = 100,
  p = 10,
  r_nb = 1,
  b_int = log(1.5),
  b_sig = log(5),
  sigma_true = sqrt(2 * log(1))
)

Arguments

n	number of observations
p	number of predictors (including the intercept)
r_nb	the dispersion parameter of the Negative Binomial dispersion; smaller values imply greater overdispersion, while larger values approximate the Poisson distribution.
b_int	intercept; default is log(1.5).
b_sig	regression coefficients for true signals; default is log(5.0).
sigma_true	standard deviation of the Gaussian innovation; default is zero.

Details

The log-expected counts are modeled using the Friedman (1991) nonlinear function with interactions, which linear function of covariates, possibly with additional Gaussian noise (on the log-scale). We assume that half of the predictors are associated with the response, i.e., true signals. For sufficiently large dispersion parameter r_nb, the distribution will approximate a Poisson distribution. Here, the predictor variables are simulated from independent uniform distributions.

Value

A named list with the simulated count response y, the simulated design matrix X (including an intercept), and the true expected counts Ey.

Note

Specifying sigma_true = sqrt(2*log(1 + a)) implies that the expected counts are inflated by 100*a% (relative to exp(X*beta)), in addition to providing additional overdispersion.

Examples

# Simulate and plot the count data:
sim_dat = simulate_nb_friedman(n = 100, p = 10);
plot(sim_dat$y)

drkowal/rSTAR documentation built on July 5, 2023, 2:18 p.m.