Log-likelihood is the logarithm of the likelihood of observed data under a statistical model. It serves as an overall indicator of model fit, but its value has no useful standalone interpretation; compare it across model iterations instead. section 9.1.2
Use log-likelihood as one part of model evaluation:
- Compare the relative fit of multiple versions of a model after changing predictors or transformations. section 9.1.2 section 9.4
- Read it alongside R-squared, adjusted R-squared, the F-statistic, AIC, BIC, and residual diagnostics rather than treating it as a standalone score. section 9.4
- Account for model complexity through AIC or BIC when deciding whether an apparent fit improvement justifies additional predictors. section 9.1.2
Comparing housing-price models
Fit an OLS model predicting housing prices from square footage and number of bedrooms, then inspect its statsmodels summary. Add the number of floors, fit the expanded model, and compare the resulting log-likelihood values; use AIC or BIC to judge the added complexity. section 9.1.2
