Parameterized as mu (the conditional mean) and shape (the same quantity
as size in rnbinom()). Thus Var(y) = mu + mu^2 / shape, which approaches
the Poisson variance as shape approaches infinity.
Read more.
Details
shape is required by the likelihood, so it includes an intercept in segment 1.
Later segments that do not include shape() are joined. For example, y ~ 1 + x + shape(1 + x)
models both the mean and shape. Regression coefficients for both dpars are
on their link scales, e.g., shape_Intercept_1 and shape_x_1.
Without shape(), shape_1 is the shape itself with a dinvgamma(0.4, 0.3) prior,
as in brms, much like the implicit sigma_1 in gaussian().
Examples
# Fit an overdispersed count model with the default log links
data = data.frame(time = 1:6, count = c(1, 2, 8, 3, 12, 5))
fit = mcp(list(count ~ 1), data, family = negbinomial(), par_x = "time", sample = FALSE)
mcp_pars(fit)$parameter # Show the mean and shape parameters
#> [1] "Intercept_1" "shape_1"