The LOGISTIC Procedure
- Overview
- Getting Started
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Syntax
PROC LOGISTIC StatementBY StatementCLASS StatementCODE StatementCONTRAST StatementEFFECT StatementEFFECTPLOT StatementESTIMATE StatementEXACT StatementEXACTOPTIONS StatementFREQ StatementID StatementLSMEANS StatementLSMESTIMATE StatementMODEL StatementNLOPTIONS StatementODDSRATIO StatementOUTPUT StatementROC StatementROCCONTRAST StatementSCORE StatementSLICE StatementSTORE StatementSTRATA StatementTEST StatementUNITS StatementWEIGHT Statement -
DetailsMissing ValuesResponse Level OrderingLink Functions and the Corresponding DistributionsDetermining Observations for Likelihood ContributionsIterative Algorithms for Model FittingConvergence CriteriaExistence of Maximum Likelihood EstimatesEffect-Selection MethodsModel Fitting InformationGeneralized Coefficient of DeterminationScore Statistics and TestsConfidence Intervals for ParametersOdds Ratio EstimationRank Correlation of Observed Responses and Predicted ProbabilitiesLinear Predictor, Predicted Probability, and Confidence LimitsClassification TableOverdispersionThe Hosmer-Lemeshow Goodness-of-Fit TestReceiver Operating Characteristic CurvesTesting Linear Hypotheses about the Regression CoefficientsRegression DiagnosticsScoring Data SetsConditional Logistic RegressionExact Conditional Logistic RegressionInput and Output Data SetsComputational ResourcesDisplayed OutputODS Table NamesODS Graphics
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ExamplesStepwise Logistic Regression and Predicted ValuesLogistic Modeling with Categorical PredictorsOrdinal Logistic RegressionNominal Response Data: Generalized Logits ModelStratified SamplingLogistic Regression DiagnosticsROC Curve, Customized Odds Ratios, Goodness-of-Fit Statistics, R-Square, and Confidence LimitsComparing Receiver Operating Characteristic CurvesGoodness-of-Fit Tests and SubpopulationsOverdispersionConditional Logistic Regression for Matched Pairs DataFirth’s Penalized Likelihood Compared with Other ApproachesComplementary Log-Log Model for Infection RatesComplementary Log-Log Model for Interval-Censored Survival TimesScoring Data SetsUsing the LSMEANS StatementPartial Proportional Odds Model
- References
Linear hypotheses for 
are expressed in matrix form as
![\[ H_0\colon \bL \bbeta = \mb {c} \]](images/statug_logistic0476.png){kind=small}
where 
is a matrix of coefficients for the linear hypotheses, and 
is a vector of constants. The vector of regression coefficients includes slope parameters as well as intercept parameters. The Wald chi-square statistic for testing 
is computed as
![\[ \chi ^2_{W} = (\bL {\widehat{\bbeta }} - \mb {c})’ [{\bL \widehat{\bV }({\widehat{\bbeta }})\bL ’}]^{-1} (\bL {\widehat{\bbeta }} - \mb {c}) \]](images/statug_logistic0477.png){kind=small}
where 
is the estimated covariance matrix. Under , 
has an asymptotic chi-square distribution with r degrees of freedom, where r is the rank of .
For models that use the less-than-full-rank parameterization (as specified by the PARAM=GLM option in the CLASS statement), a Type 3 test of an effect of interest is a test of the Type III estimable functions that are defined for that effect. When there are no missing cells, the Type 3 test of a main effect corresponds to testing the hypotheses of equal marginal means. For more information about Type III estimable functions, see Chapter 44: The GLM Procedure, and Chapter 15: The Four Types of Estimable Functions. Also see Littell, Freund, and Spector (1991).
For models that use a full-rank parameterization, all parameters are estimable when there are no missing cells; so it is unnecessary to define estimable functions. The Type 3 test of an effect of interest is the joint test that the parameters associated with that effect are zero. For a model that uses effects parameterization (as specified by the PARAM=EFFECT option in the CLASS statement), testing a main effect is equivalent to testing the equality of marginal means. For a model that uses reference parameterization (as specified by the PARAM=REF option in the CLASS statement), the Type 3 test is a test of the equality of cell means at the reference level of the other model effects. For more information about the coding scheme and the associated interpretation of results, see Muller and Fetterman (2002, Chapter 14).
For a model without an interaction term, the Type 3 tests of main effects are the same regardless of the type of parameterization that is used. For a model that contains an interaction term and no missing cells, the Type 3 test of a component main effect is the same under GLM parameterization and effect parameterization, because both test the equality of cell means. But this differs from reference parameterization, which tests the equality of cell means at the reference level of the other component main effect. If some cells are missing, you can obtain meaningful Type 3 tests only by testing a Type III estimable function, so in this case you should use GLM parameterization.
The results of a Type 3 analysis do not depend on the order in which the terms are specified in the MODEL statement.