Simulate count data from Friedman's nonlinear regression

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)),
  seed = NULL
)

Arguments

n

number of observations

p

number of predictors

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.

seed

optional integer to set the seed for reproducible simulation; default is NULL which results in a different dataset after each run

Value

A named list with the simulated count response y, the simulated design matrix X, and the true expected counts Ey.

Details

The log-expected counts are modeled using the Friedman (1991) nonlinear function with interactions, 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.

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)