Likelihood Ratio Test

Computes the likelihood ratio test (LRT) for comparing nested models. Works with femtofit objects or raw log-likelihood values.

Usage

lrt(null_model, alt_model, df = NULL)

Arguments

null_model

Either a femtofit object (simpler model) or a numeric log-likelihood value.

alt_model

Either a femtofit object (more complex model) or a numeric log-likelihood value.

df

Degrees of freedom. If NULL and both arguments are femtofit objects, computed as the difference in number of parameters.

Value

A likelihood_ratio_test object (also inherits from hypothesis_test) containing:

stat

The LRT statistic: -2 * (loglik_null - loglik_alt)

p.value

P-value from chi-squared distribution

dof

Degrees of freedom

null_loglik

Log-likelihood of null model

alt_loglik

Log-likelihood of alternative model

Details

The likelihood ratio test statistic is: $$\Lambda = -2 (\ell_0 - \ell_1)$$ where \(\ell_0\) is the log-likelihood under the null (simpler) model and \(\ell_1\) is the log-likelihood under the alternative (complex) model.

Under the null hypothesis and regularity conditions, \(\Lambda\) asymptotically follows a chi-squared distribution with degrees of freedom equal to the difference in number of free parameters.

Examples

if (FALSE) { # \dontrun{
# Generate data
set.seed(42)
x <- rnorm(100, mean = 5, sd = 2)

# Fit full model (estimate both mu and sigma)
full <- fit(
  function(mu, log_sigma) {
    sigma <- exp(log_sigma)
    loglik_normal(mu, sigma, x)
  },
  params = c(mu = 0, log_sigma = 0)
)

# Fit null model (mu fixed at 0)
null <- fit(
  function(log_sigma) {
    sigma <- exp(log_sigma)
    loglik_normal(0, sigma, x)  # mu = 0
  },
  params = c(log_sigma = 0)
)

# Likelihood ratio test
test <- lrt(null, full)
test
pval(test)
is_significant_at(test, 0.05)

# Can also use raw log-likelihoods
lrt(null_loglik = -150, alt_loglik = -140, df = 1)
} # }