PROC LOGISTIC

The LOGISTIC procedure fits linear logistic regression models for binary (for example, success or failure) or ordinal (e.g., none, mild, severe) response variables. The PROC LOGISTIC provides:

model-selection methods: forward, backward, and stepwise selection of explanatory variables. As in other stepwise methods, you can specify the significance levels to for a variable to enter or be removed from the model.
regression diagnostics: measures of leverage, influence, and residuals for each observation, with optional index plots (plots against case number).
choice of link function: logit, normit (probit analysis), and complementary log-log function linking the proportion of observations in each response class to the linear model in the explanatory variables.
parallel-lines tests: for an ordinal response variable, the procedure fits a model with equal slopes for the explanatory variables. This may be an alternative to using PROC REG with dummy variables.

Specifications

These statements are used with PROC LOGISTIC:

PROC LOGISTIC DATA=SAS-data-set < options > ;
   MODEL response = independents < / options >;
   BY variables;
   OUTPUT <OUT=SAS-data-set>
          <keyword=name ... keyword=name>
          / <ALPHA=value>;
   WEIGHT variable;

The following example illustrates the use of PROC LOGISTIC. The data consist of the number, R, of ingots not ready for rolling, out of N tested, in relation to combinations of two independent variables, heating time, HEAT, and soaking time, SOAK. Note that the response on the model statement can be specified as "R/N", which means R events out of N trials.

data ingots;
   input heat soak r n @@;
datalines;
 7 1.0 0 10   7 1.7 0 17   7 2.2 0  7   7 2.8 0 12   7 4.0 0  9
14 1.0 0 31  14 1.7 0 43  14 2.2 2 33  14 2.8 0 31  14 4.0 0 19
27 1.0 1 56  27 1.7 4 44  27 2.2 0 21  27 2.8 1 22  27 4.0 1 16
51 1.0 3 13  51 1.7 0  1  51 2.2 0  1  51 2.8 0  1
;
proc logistic data=ingots;
   model r/n = heat soak;
   output out=results p=predict;

proc plot hpercent=50;
   plot predict * heat
        predict * soak ;

The output from the LOGISTIC procedure is shown in Figure 1. The Score statistic and - 2 % log % L in the section "Criteria for Assessing Model Fit" test the joint significance of the independent variables (also called covariates in logistic regression). The combined effect of HEAT and SOAK is highly significant. However, under "Analysis of Maximum Liklihood Estimates", we see that HEAT is significant, while SOAK is not.



                         The LOGISTIC Procedure

Data Set: WORK.INGOTS
Response Variable (Events): R
Response Variable (Trials): N
Number of Observations: 19
Link Function: Logit

                            Response Profile

                      Ordered  Binary
                        Value  Outcome      Count

                            1  EVENT           12
                            2  NO EVENT       375

                    Criteria for Assessing Model Fit

                           Intercept
              Intercept       and
 Criterion      Only      Covariates   Chi-Square for Covariates

 AIC            108.988      101.302        .
 SC             112.947      113.177        .
 -2 LOG L       106.988       95.302      11.686 with 2 DF (p=0.0029)
 Score             .            .         15.123 with 2 DF (p=0.0005)

                Analysis of Maximum Likelihood Estimates

           Parameter   Standard     Wald          Pr >     Standardized
 Variable   Estimate     Error   Chi-Square    Chi-Square    Estimate

 INTERCPT    -5.6600     1.1740     23.2426        0.0001             .
 HEAT         0.0832     0.0243     11.7351        0.0006      0.455521
 SOAK         0.0939     0.3450      0.0740        0.7856      0.048549

     Association of Predicted Probabilities and Observed Responses


               Concordant = 69.8%          Somers' D = 0.504
               Discordant = 19.3%          Gamma     = 0.566
               Tied       = 10.9%          Tau-a     = 0.030
               (4500 pairs)                c         = 0.752

Figure 1: Output from LOGISTIC procedure (edited)

Note: For logistic regression with a binary response, PROC LOGISTIC yields parameter estimates which are the negative of those produced by the former LOGIST procedure. In LOGIST, the EVENT or response variable must be coded 0/1, and the parameters produced are for estimating Pr(EVENT=1). In LOGISTIC, the response variable can be character or numeric, and, by default, LOGISTIC estimates the probability of the smallest response, Pr(EVENT=0) if 0/1 coding is used.

PROC LOGISTIC

Specifications

Example