Suppose that the model contains p parameters and that n observations are used in model fitting. The fit criteria displayed by the LIFEREG procedure are calculated as follows:
–2 log likelihood:
where L is the maximized likelihood for the model.
Akaike’s information criterion:
corrected Akaike’s information criterion:
Bayesian information criterion:
If you specify the Weibull, exponential, lognormal, log-logistic, or gamma distribution, then maximum likelihood estimates of model parameters are computed by maximizing the log likelihood of the distribution of the logarithm of the response. This is equivalent to computing maximum likelihood parameter estimates based on the response on the original, rather than log, scale. If you specify the Weibull, exponential, lognormal, log-logistic, or gamma distribution, then fit statistics based on the maximized log likelihood of the log of the response are reported in the “Fit Statistics” table. Fit criteria computed in this way cannot be meaningfully compared with fit criteria that are based on the log likelihood of the unlogged response. If you specify the normal or logistic distribution, or if you specify the NOLOG option in the MODEL statement, then the fit criteria reported in the “Fit Statistics” table are based on the response on the original, rather than log, scale.
In addition to the “Fit Statistics” table described previously, if you specify the Weibull, exponential, lognormal, log-logistic, or gamma distribution, fit criteria that are based on the distribution of the response on the original scale, rather than the log of the response, are reported in the “Fit Statistics (Unlogged Response)” table.
When comparing models, you should compare fit criteria based on the log likelihood that is computed by using the response on the same scale, either always based on the log of the response or always based on the response on the original scale.
See Akaike (1981, 1979) for details of AIC and BIC. See Simonoff (2003) for a discussion of using AIC, AICC, and BIC in statistical modeling.