/* 5. Outliers and influential observations */

proc logistic data=hw5.mus14data plots(only)=(dfbetas); model ins(event='1') = retire age hstatusg hhincome educyear married hisp / link=logit; run; ods graphics off; /*a. Continuing with the same model as in question 4, examine whether there are any outliers.*/

/*b. Examine whether there are influential observations by plotting the DFBETAS*/

/*c. What do you conclude with regard to outliers or influential observations.*/

The SAS System The LOGISTIC Procedure Model Information Data Set HW5.MUS14DATA Response Variable ins Number of Response Levels 2 Model binary logit Optimization Technique Fisher's scoring Number of Observations Read 3206 Number of Observations Used 3206 Response Profile Ordered Value ins Total Frequency 1 0 1965 2 1 1241 Probability modeled is ins='1'. Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Criterion Intercept Only Intercept and Covariates AIC 4281.542 4005.757 SC 4287.615 4054.339 -2 Log L 4279.542 3989.757 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 289.7856 7 <.0001 Score 264.8691 7 <.0001 Wald 238.0011 7 <.0001 Analysis of Maximum Likelihood Estimates Parameter DF Estimate Standard Error Wald Chi-Square Pr > ChiSq Intercept 1 -1.7155 0.7486 5.2516 0.0219 retire 1 0.1969 0.0842 5.4691 0.0194 age 1 -0.0146 0.0113 1.6720 0.1960 hstatusg 1 0.3123 0.0917 11.6022 0.0007 hhincome 1 0.00230 0.000762 9.1386 0.0025 educyear 1 0.1143 0.0142 64.7335 <.0001 married 1 0.5786 0.0933 38.4466 <.0001 hisp 1 -0.8096 0.1957 17.1137 <.0001 Odds Ratio Estimates Effect Point Estimate 95% Wald Confidence Limits retire 1.218 1.032 1.436 age 0.986 0.964 1.008 hstatusg 1.367 1.142 1.635 hhincome 1.002 1.001 1.004 educyear 1.121 1.090 1.153 married 1.784 1.485 2.142 hisp 0.445 0.303 0.653 Association of Predicted Probabilities and Observed Responses Percent Concordant 66.7 Somers' D 0.335 Percent Discordant 33.3 Gamma 0.335 Percent Tied 0.0 Tau-a 0.159 Pairs 2438565 c 0.667