Compare nested models using likelihoods, degrees, and alpha. Get test statistics, decisions, and fit summaries. Export results instantly with practical guidance and example tables.
| Restricted Model | Unrestricted Model | LL0 | LL1 | df | Alpha | LRT | Interpretation |
|---|---|---|---|---|---|---|---|
| Logistic with age only | Logistic with age and income | -145.23 | -138.11 | 2 | 0.05 | 14.24 | Reject restricted model |
| Poisson base model | Poisson with exposure term | -208.44 | -205.90 | 1 | 0.05 | 5.08 | Reject restricted model |
| Survival baseline model | Survival with treatment effect | -96.70 | -95.98 | 1 | 0.05 | 1.44 | Fail to reject restricted model |
The log likelihood ratio test compares two nested models. The restricted model is the smaller model. The unrestricted model is the larger model.
LRT statistic: G² = -2 × (LL0 - LL1) = 2 × (LL1 - LL0)
Likelihood ratio: λ = exp(LL0 - LL1)
Reference distribution: G² follows an approximate chi square distribution with df = parameter difference.
P value: p = P(Χ²df ≥ G²)
If the p value is less than or equal to alpha, reject the restricted model. That means the larger model provides a statistically better fit.
If you enter sample size and parameter counts, the file also reports AIC and BIC. Those measures help compare fit and complexity.
A log likelihood ratio test calculator helps compare two nested statistical models. It checks whether the larger model improves fit enough to justify added complexity. This matters in regression, generalized linear models, survival analysis, and many other areas. Analysts often need a quick way to confirm whether extra predictors or terms add real explanatory value.
The test uses the restricted model log likelihood and the unrestricted model log likelihood. It converts that gap into an LRT statistic. The statistic is then compared with a chi square reference distribution. The output includes the test statistic, p value, approximate critical value, and final decision. That makes interpretation faster and more consistent.
A small p value suggests the unrestricted model fits significantly better. In that case, the added parameters improve the model enough to reject the simpler version. A larger p value means the evidence is weaker. Then the restricted model may still be adequate. This helps you keep models parsimonious and easier to explain.
This page also supports optional AIC and BIC reporting. Those measures are helpful when you want fit statistics beyond the hypothesis test. They can guide model selection when complexity matters. The export tools also make reporting easier. You can save the result as a CSV file or a PDF summary.
Use this calculator only for nested models fitted on the same data. The unrestricted model should include all terms from the restricted model. Its log likelihood should usually be greater than or equal to the restricted value. If that condition fails, review the model setup. Careful inputs produce reliable statistical decisions.
It is a statistical test for comparing two nested models. It checks whether the larger model improves fit enough to reject the simpler model.
Nested models are models where the smaller one can be created by constraining parameters in the larger one. They must be fitted to the same dataset.
No. The likelihood ratio test is designed for nested comparisons. For non nested models, use other criteria such as AIC, BIC, cross validation, or specialized tests.
The larger model has at least the same flexibility. Under proper estimation, it should fit at least as well as the restricted model. A smaller value suggests a setup issue.
It is the difference in free parameters between the unrestricted and restricted models. That value determines the chi square reference distribution used for the p value.
Many analysts use 0.05. Stricter work may use 0.01. Your choice should match the study design, error tolerance, and reporting standard.
Not always. You should also consider model purpose, effect meaning, sample size, diagnostics, and whether the added terms improve interpretation or prediction.
When you enter parameter counts and sample size, AIC and BIC provide extra fit complexity information. They can support model selection beside the formal likelihood ratio test.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.