The LOGISTIC Procedure
- Overview
- Getting Started
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Syntax
PROC LOGISTIC Statement BY Statement CLASS Statement CONTRAST Statement EFFECT Statement EFFECTPLOT Statement ESTIMATE Statement EXACT Statement EXACTOPTIONS Statement FREQ Statement LSMEANS Statement LSMESTIMATE Statement MODEL Statement ODDSRATIO Statement OUTPUT Statement ROC Statement ROCCONTRAST Statement SCORE Statement SLICE Statement STORE Statement STRATA Statement TEST Statement UNITS Statement WEIGHT Statement -
Details
Missing Values Response Level Ordering Link Functions and the Corresponding Distributions Determining Observations for Likelihood Contributions Iterative Algorithms for Model Fitting Convergence Criteria Existence of Maximum Likelihood Estimates Effect-Selection Methods Model Fitting Information Generalized Coefficient of Determination Score Statistics and Tests Confidence Intervals for Parameters Odds Ratio Estimation Rank Correlation of Observed Responses and Predicted Probabilities Linear Predictor, Predicted Probability, and Confidence Limits Classification Table Overdispersion The Hosmer-Lemeshow Goodness-of-Fit Test Receiver Operating Characteristic Curves Testing Linear Hypotheses about the Regression Coefficients Regression Diagnostics Scoring Data Sets Conditional Logistic Regression Exact Conditional Logistic Regression Input and Output Data Sets Computational Resources Displayed Output ODS Table Names ODS Graphics
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Examples
Stepwise Logistic Regression and Predicted Values Logistic Modeling with Categorical Predictors Ordinal Logistic Regression Nominal Response Data: Generalized Logits Model Stratified Sampling Logistic Regression Diagnostics ROC Curve, Customized Odds Ratios, Goodness-of-Fit Statistics, R-Square, and Confidence Limits Comparing Receiver Operating Characteristic Curves Goodness-of-Fit Tests and Subpopulations Overdispersion Conditional Logistic Regression for Matched Pairs Data Firth’s Penalized Likelihood Compared with Other Approaches Complementary Log-Log Model for Infection Rates Complementary Log-Log Model for Interval-Censored Survival Times Scoring Data Sets Using the LSMEANS Statement
- References
| Model Fitting Information |
For the 
th observation, let 
be the estimated probability of the observed response. The three criteria displayed by the LOGISTIC procedure are calculated as follows:
-
–2 log likelihood:
where
and 
are the weight and frequency values of the th observation, and 
is the dispersion parameter, which equals 
unless the SCALE= option is specified. For binary response models that use events/trials MODEL statement syntax, this is 
where
is the number of events, 
is the number of trials, is the estimated event probability, and the statistic is reported both with and without the constant term. -
Akaike’s information criterion:
where
is the number of parameters in the model. For cumulative response models, 
, where 
is the total number of response levels minus one and 
is the number of explanatory effects. For the generalized logit model, 
. -
Schwarz (Bayesian information) criterion:
where
is the number of parameters in the model, is the number of trials when events/trials syntax is specified, and 
with single-trial syntax.
The AIC and SC statistics give two different ways of adjusting the –2 Log L statistic for the number of terms in the model and the number of observations used. These statistics can be used when comparing different models for the same data (for example, when you use the SELECTION=STEPWISE option in the MODEL statement). The models being compared do not have to be nested; lower values of the statistics indicate a more desirable model.
The difference in the –2 Log L statistics between the intercepts-only model and the specified model has a 
degree-of-freedom chi-square distribution under the null hypothesis that all the explanatory effects in the model are zero, where is the number of parameters in the specified model and is the number of intercepts. The likelihood ratio test in the "Testing Global Null Hypothesis: BETA=0" table displays this difference and the associated p-value for this statistic. The score and Wald tests in that table test the same hypothesis and are asymptotically equivalent; see the sections Residual Chi-Square and Testing Linear Hypotheses about the Regression Coefficients for details.