Fit Statistics

The likelihood function estimates the probability of an observed sample given all possible parameter values. The log likelihood is simply the logarithm of the likelihood function. The likelihood function value is -2 times the log likelihood. Smaller values are preferred.

Akaike’s Information Criterion. Smaller values indicate better models, and AIC values can become negative. AIC is based on the Kullback-Leibler information measure of discrepancy between the true distribution of the response variable and the distribution specified by the model.

Corrected Akaike’s Information Criterion. This version of AIC adjusts the value to account for sample size. The result is that extra effects penalize AICC more than AIC. As the sample size increases, AICC and AIC converge.

The Bayesian Information Criterion (BIC), also known as Schwarz’s Bayesian Criterion (SBC), is an increasing function of the model's residual sum of squares and the number of effects. Unexplained variations in the response variable and the number of effects increase the value of the BIC. As a result, a lower BIC implies either fewer explanatory variables, better fit, or both. BIC penalizes free parameters more strongly than AIC.

The R-squared value is an indicator of how well the model fits the data. R-squared values can range from 0 to 1. Values closer to 1 are preferred.

The observed R-squared value divided by the maximum attainable R-squared value. This value is useful when there are multiple independent category variables. Values can range from 0 to 1. Values closer to 1 are preferred.