What statistic is the natural logarithm of the likelihood and serves as a measure of model fit?

• A. Log-likelihood
• B. Likelihood
• C. Posterior probability
• D. Prior probability

Answer: (A)

The log-likelihood is the natural logarithm of the likelihood and serves as a measure of how well a model fits the data. The likelihood multiplies the probabilities of all observed data under the model, which can be unwieldy to work with. Taking the natural log turns that product into a sum, making the function easier to differentiate and optimize. Because the natural log is a monotone transformation, maximizing the likelihood and maximizing the log-likelihood yield the same parameter estimates. In practice, higher log-likelihood values indicate better fit, and it forms the basis for model comparison tools like AIC and BIC. The other terms mentioned are Bayesian concepts (posterior and prior) and do not directly measure model fit to the observed data in the same way.