Evaluate a Dirichlet-multinomial log-likelihood

Computes the Dirichlet-multinomial log-likelihood following the parameterization of Thorson et al. (CCSRA). The concentration parameters are \(\alpha_k = \exp(\ln\theta) \times N \times \hat{p}_k\), so \(\exp(\ln\theta)\) is the per-observation overdispersion scalar: values near zero approach the multinomial and larger values increase variance. Non-integer observed counts are supported via lgamma.

Usage

ddirmult(obs, pred, Ntotal, ln_theta, give_log = TRUE)

Arguments

obs

Numeric vector of observed proportions of length \(K\) (need not sum exactly to 1 after addtotag offsets).

pred

Numeric vector of predicted proportions of length \(K\); must sum to 1.

Ntotal

Numeric. Total count (input sample size \(N\)).

ln_theta

Numeric. Log overdispersion parameter. The Dirichlet concentration is \(\exp(\ln\theta) \times N \times \hat{p}_k\).

give_log

Logical. If TRUE (default), returns the log-likelihood; otherwise returns the likelihood.

Value

Numeric. Log-likelihood (or likelihood if give_log = FALSE).