Model settings for a negative binomial distribution assuming
an linear model on the mean. This function is to be used within a call
to beaver_mcmc().
model_negbin_linear(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 dose \(d_i\). The model is $$y_{ij} ~ NB(p_i, r_i)$$ $$p_i ~ Uniform(0, 1)$$ $$r_{ij} = (\mu_{ij} * p_i) / (1 - p_i)$$ $$log(\mu_{ij}) = x_{ij} * b1 + b2 * d_i$$ $$b1 ~ N(`mu_b1`, `sigma_b1`^2)$$ $$b2 ~ N(`mu_b2`, `sigma_b2`^2)$$ 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 a linear 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_indep(),
model_negbin_loglinear(),
model_negbin_logquad(),
model_negbin_quad(),
model_negbin_sigmoid_emax()