Log-likelihood is the logarithm of the likelihood function: the probability of observing the data given a statistical model and its parameter values. It measures how closely those parameters explain the observed data. section 5.2.3 section 7.3.10
Use log-likelihood to:
- Compare a fitted logistic regression with its intercept-only null model; a larger difference indicates greater predictive value from the independent variables. section 5.2.3
- Evaluate competing models fitted to the same data, while recognizing that the raw value is difficult to interpret in isolation. section 5.2.3 section 7.3.10
- Assess time-series model fit and combine fit information with AIC, BIC, or HQIC when model complexity matters. section 7.3.10
Logistic-regression fit
A fitted logistic regression stores the model and null-model log-likelihoods. McFadden’s pseudo R² uses their quotient to summarize the added value of predictors, producing a more readily interpretable fit measure between 0 and 1. section 5.2.3
