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
| Determining Observations for Likelihood Contributions |
If you use events/trials MODEL statement syntax, each observation is split into two observations. One has response value 1 with a frequency equal to the frequency of the original observation (which is 1 if the FREQ statement is not used) times the value of the events variable. The other observation has response value 2 and a frequency equal to the frequency of the original observation times the value of (trials–events). These two observations will have the same explanatory variable values and the same FREQ and WEIGHT values as the original observation.
For either single-trial or events/trials syntax, let 
index all observations. In other words, for single-trial syntax, indexes the actual observations. And, for events/trials syntax, indexes the observations after splitting (as described in the preceding paragraph). If your data set has 30 observations and you use single-trial syntax, has values from 1 to 30; if you use events/trials syntax, has values from 1 to 60.
Suppose the response variable in a cumulative response model can take on the ordered values 
, where 
is an integer 
. The likelihood for the th observation with ordered response value 
and explanatory variables vector 
is given by
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 |
where 
is the logistic, normal, or extreme-value distribution function, 
are ordered intercept parameters, and 
is the common slope parameter vector.
For the generalized logit model, letting the 
st level be the reference level, the intercepts are unordered and the slope vector 
varies with each logit. The likelihood for the th observation with response value and explanatory variables vector is given by
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