nll_poisson_gamma {aeddo}

Negative Log-Likelihood for Poisson Gamma Model

Description

Calculate the negative log-likelihood for the Poisson Gamma modeling framework.

Usage

nll_poisson_gamma(theta, data, formula)

Arguments

theta

A numeric vector containing model parameters. The first part of the vector represents fixed effects, and the remaining part represents model parameters.

data

A tibble containing the time series data, including columns 'y' for observed values,'n' for population size, and other covariates of interest.

formula

A formula specifying the model structure.

Value

The negative log-likelihood value.

Examples

# Initial parameters
theta <- c(0.5, 0.1)

# Sample data
data <- data.frame(
  y = c(10, 15, 20, 30, 50, 100, 200, 40, 20, 10),
  n = c(100, 150, 200, 300, 500, 1000, 2000, 400, 200, 100)
)

# Fixed effects model formula
fixed_effects_formula <- y ~ 1

# Calculate negative log likelihood
nll_poisson_gamma(
  theta = theta,
  data = data,
  formula = fixed_effects_formula
)