Objectives:

If your response variable is binary and you want to analyze the relation between the binary variable and other variables, logistic regression can deal with that.

Assume the binary variable, y, only contains two value 0 and 1.

Here is the logistic regression’s expression:

So, the outcome of logistic regression is the probability of getting the response variable equals to 1.

The is the odds ratio.

The general code can be expressed as following:

PROC LOGISTIC DATA=SAS-data-set ;

CLASS variables ;

MODEL response=predictors ;

UNITS independent1=list;

ODDSRATIO <‘label’> variable ;

OUTPUT OUT=SAS-data-set keyword=name ;

RUN;

CLASS names the classification variables to be used in the analysis. The CLASS statement must precede the MODEL statement. By default, these variables will be analyzed using effects coding parameterization. This can be changed with the PARAM= option.

MODEL specifies the response variable and the predictor variables.

OUTPUT creates an output data set containing all the variables from the input data set and any requested statistics.

UNITS enables you to obtain an odds ratio estimate for a specified change in a predictor variable. The unit of change can be a number, standard deviation (SD), or a number times the standard deviation (for example, 2*SD).

ODDSRATIO produces odds ratios for variables even when the variables are involved in interactions with other covariates, and for classification variables that use any parameterization. You can specify several ODDSRATIO statements.

Here is an example:

proc logistic data=sasuser.Titanic alpha=.05 plots(only)=(effect oddsratio);

model Survived(event='1')=Age / clodds=pl:

Survived=Age;

run;

SAS output:

The Model Information table describes the data set, the response variable, the number of response levels, the type of model, the algorithm used to obtain the parameter estimates, and the

number of observations read and used.

The Number of Observations Used is the count of all observations that are nonmissing for all variables specified in the MODEL statement. The ages of 263 of these 1309 passengers cannot be determined and cannot be used to estimate the model.

The Response Profile table shows the response variable values listed according to their ordered values. By default, PROC LOGISTIC orders the response variable alphanumerically so that it bases the logistic regression model on the probability of the smallest value. Because you used the EVENT=option in this example, the model is based on the probability of surviving (Survived=1). The Response Profile table also shows frequencies of response values.

The Model Fit Statistics provides three tests: • AIC is Akaike’s ‘A’ information criterion. • SC is the Schwarz criterion. • -2 Log L is -2 times the natural log of the likelihood. -2 Log L, AIC, and SC are goodness-of-fit measures that you can use to compare one model to another. These statistics measure relative fit among models, but they do not measure absolute fit of any single model. Smaller values for all of these measures indicate better fit.

The Testing Global Null Hypothesis: BETA=0 table provides three statistics to test the null hypothesis that all regression coefficients of the model are 0.

The Analysis of Maximum Likelihood Estimates table lists the estimated model parameters, their standard errors, Wald Chi-Square values, and p-values.

It can be expressed in the below.

The Wald chi-square and its associated p-value tests whether the parameter estimate is significantly different from 0. For this example, the p-values for the variable Age is not significant at the 0.05 significance level (p=0.0696). It cannot be concluded that Age is not important in a multivariate model.

The odds ratio and confidence interval can be found in the following table.