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Simulate data from a negative-binomial distribution with linear mean function.
simulate_nb_lm(
n = 100,
p = 10,
r_nb = 1,
b_int = log(1.5),
b_sig = log(2),
sigma_true = sqrt(2 * log(1)),
ar1 = 0,
intercept = FALSE,
seed = NULL
)A named list with the simulated count response y, the simulated design matrix X
(possibly including the intercept), the true expected counts Ey,
and the true regression coefficients beta_true.
number of observations
number of predictors (including the intercept)
the dispersion parameter of the Negative Binomial dispersion; smaller values imply greater overdispersion, while larger values approximate the Poisson distribution.
intercept; default is log(1.5), which implies the expected count is 1.5 when all predictors are zero
regression coefficients for true signals; default is log(2.0), which implies a twofold increase in the expected counts for a one unit increase in x
standard deviation of the Gaussian innovation; default is zero.
the autoregressive coefficient among the columns of the X matrix; default is zero.
a Boolean indicating whether an intercept column should be included in the returned design matrix; default is FALSE
optional integer to set the seed for reproducible simulation; default is NULL which results in a different dataset after each run
The log-expected counts are modeled as a 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 standard normal distributions.
# Simulate and plot the count data:
sim_dat = simulate_nb_lm(n = 100, p = 10);
plot(sim_dat$y)
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