Extracts the log-likelihood from a fitted uncounted model.
Usage
# S3 method for class 'uncounted'
logLik(object, ...)Value
An object of class "logLik" with attributes df
(number of estimated parameters) and nobs (number of observations).
Details
For Poisson and Negative Binomial models, the true log-likelihood is returned as computed during maximum-likelihood estimation. For OLS and NLS models, a Gaussian pseudo-log-likelihood is returned, computed on the log scale as
$$\ell = -\frac{n}{2}\bigl(\log(2\pi\hat\sigma^2) + 1\bigr)$$
where \(\hat\sigma^2 = n^{-1}\sum(\log m_i - \log\hat\mu_i)^2\). This pseudo-log-likelihood enables AIC/BIC comparison among OLS/NLS variants but is not comparable to the true likelihood of count models.
References
McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models, 2nd ed. Chapman & Hall.
Examples
# Simulate synthetic data
set.seed(123)
df <- data.frame(
N = rep(1000, 30),
n = rpois(30, lambda = 50)
)
df$m <- rpois(30, lambda = df$N^0.5 * (df$n / df$N)^0.8)
fit <- estimate_hidden_pop(data = df, observed = ~m, auxiliary = ~n,
reference_pop = ~N, method = "poisson")
#> Warning: Some alpha values > 1 (max = 3.271). Population size estimates may be unreliable. Consider using constrained = TRUE or simplifying cov_alpha.
logLik(fit)
#> 'log Lik.' -48.35565 (df=3)
AIC(fit)
#> [1] 102.7113
BIC(fit)
#> [1] 106.9149