Model settings for a negative binomial
distribution with an independent mean for each dose.
This function is to be used within a call
to beaver_mcmc().
model_negbin_indep(mu_b1, sigma_b1, mu_b2, sigma_b2, w_prior = 1)A list with the model's prior weight and hyperparameter values.
hyperparameters. See the model description below for context.
the prior weight for the model.
Let \(y_{ij}\) be the \(j\)th subject on the \(k\)th dose. The model is $$y_{ij} ~ NB(p_i, r_i)$$ $$p_i ~ Uniform(0, 1)$$ $$r_{ij} = (\mu_{ij} * p_i) / (1 - p_i)$$ $$log(\mu_{ij}) = x_{ij} * b1 + b2_k$$ $$b1 ~ N(`mu_b1`, `sigma_b1`^2)$$ $$b2_k ~ N(`mu_b2`, `sigma_b2`^2)$$ The model is parameterized in terms of the mean of the negative binomial distribution and the usual probability parameter p. The prior on the mean is an exponential model, and the prior on p at each dose is Uniform(0, 1). The model can adjust for baseline covariates, ($$x_{ij}$$).
Other models:
beaver_mcmc(),
model_negbin_emax(),
model_negbin_exp(),
model_negbin_linear(),
model_negbin_loglinear(),
model_negbin_logquad(),
model_negbin_quad(),
model_negbin_sigmoid_emax()