Model Summary table for Fit Cox Model in a Counting Process Form

Find definitions and interpretation guidance for every statistic in the Model Summary table.

In This Topic

Log-likelihood
R-sq
AIC, AICc and BIC

The Model Summary table includes two rows. One row is for a row for a model without any terms. The other row is for a model with the terms in the analysis. Compare the two rows to assess the improvement of the model with terms over the model without terms. Use the row for the model with terms to describe the performance of the model. Use the AIC, AICc, and BIC to compare models with different terms from one analysis to another.

Log-likelihood

Use the log-likelihood to compare two models that use the same data to estimate the coefficients. Because the values are negative, the closer to 0 the value is, the better the model fits the data.

The log-likelihood cannot decrease when you add terms to a model. For example, a model with terms has a higher log-likelihood than a model without terms. A larger difference in the log-likelihood values between the two models indicates a greater contribution of the model to the fit of the data.

When you compare two models with terms, the difference in performance is clearest if the models have the same number of terms. Use the p-values for the terms in the Coefficients table to decide which terms to include in the model.

R-sq

R² is the percentage of variation in the response that is explained by the model.

Interpretation

Use R² to determine how well the model fits your data. The higher the R² value, the better the model fits your data. R² is always between 0% and 100%.

Consider the following issues when interpreting the R² value:

R² always increases when you add additional predictors to a model. For example, the best five-predictor model will always have an R² that is at least as high as the best four-predictor model. Therefore, R² is most useful when you compare models of the same size.
Small samples do not provide a precise estimate of the strength of the relationship between the response and predictors. For example, if you need R² to be more precise, you should use a larger sample.
Goodness-of-fit statistics are just one measure of how well the model fits the data. Even when a model has a desirable value, you should verify that the model meets the model assumptions.

AIC, AICc and BIC

The Akaike's Information Criterion (AIC), corrected Akaike’s Information Criterion (AICc), and the Bayesian Information Criterion (BIC) are measures of the relative quality of a model that account for fit and the number of terms in the model.

Interpretation

Use AIC, AICc and BIC to compare different models. Smaller values are desirable. However, the model with the least value for a set of predictors does not necessarily fit the data well. Also use tests and plots to assess how well the model fits the data.

AICc and AIC: When the sample size is small relative to the parameters in the model, AICc performs better than AIC. AICc performs better because with relatively small sample sizes, AIC tends to be small for models with too many parameters. Usually, the two statistics give similar results when the sample size is large enough relative to the parameters in the model.
AICc and BIC: Both AICc and BIC assess the likelihood of the model and then apply a penalty for adding terms to the model. The penalty reduces the tendency to overfit the model to the sample data. This reduction can yield a model that performs better in general.; As a general guideline, when the number of parameters is small relative to the sample size, BIC has a larger penalty for the addition of each parameter than AICc. In these cases, the model that minimizes BIC tends to be smaller than the model that minimizes AICc.; In some common cases, such as screening designs, the number of parameters is usually large relative to the sample size. In these cases, the model that minimizes AICc tends to be smaller than the model that minimizes BIC. For example, for a 13-run definitive screening design, the model that minimizes AICc will tend to be smaller than the model that minimizes BIC among the set of models with 6 or more parameters.; For more information on AICc and BIC, see Burnham and Anderson.¹

¹ Burnham, K. P., & Anderson, D. R. (2004). Multimodel inference: Understanding AIC and BIC in model selection. Sociological Methods & Research, 33(2), 261-304. doi:10.1177/0049124104268644