Likelihood Ratio Testing in Model Comparison
The likelihood ratio test is used when two statistical models are nested. The reduced model is simpler. The full model includes every reduced model term, plus extra parameters. The test asks whether those extra parameters improve fit enough to justify added complexity.
Why This Calculator Helps
Manual likelihood comparison can be error prone. You must track log likelihoods, parameter counts, degrees of freedom, and the chosen significance level. This calculator puts those pieces in one place. It returns the likelihood ratio statistic, p value, critical value, decision, AIC, BIC, and basic evidence notes.
Good Input Practice
Use maximized log likelihoods from models fitted to the same dataset. The response variable, sample, weights, offsets, and estimation method should match. A likelihood ratio result is weak when the models use different records or different likelihood definitions. The full model should not have a smaller maximized log likelihood. If it does, check convergence, constraints, or whether the models are truly nested.
Interpreting Results
A small p value suggests that the extra full model parameters add meaningful explanatory power. In that case, you reject the reduced model at the selected alpha. A large p value means the simpler model is not clearly worse. It may be preferred for clarity, stability, or prediction under limited data.
Advanced Notes
The chi square approximation is asymptotic. It works best with adequate sample size and regular parameter conditions. Boundary parameters, mixture models, penalized estimates, and small samples may need special treatment. The optional half chi square adjustment can help for one boundary parameter, but it is not universal. Use domain knowledge and diagnostics before reporting final conclusions.
Reporting Guidance
A useful report names both models. It gives log likelihoods, degrees of freedom, the test statistic, p value, and alpha. It also explains the decision in plain language. AIC and BIC are not the same as a hypothesis test. They are model selection criteria. Include them as supporting context, not as replacements for the test.
Common Uses
Common uses include logistic regression, survival models, generalized linear models, and hierarchical models. The method is helpful when a theory predicts specific added terms. It also supports careful variable screening when exploratory choices are clearly documented.