Logistic regression for 2x2 table 1 The LOGISTIC Procedure Model Information Data Set WORK.SMOKE Response Variable (Events) y Response Variable (Trials) n Number of Observations 2 Model binary logit Optimization Technique Fisher's scoring Response Profile Ordered Binary Total Value Outcome Frequency 1 Event 1004 2 Nonevent 4371 Class Level Information Design Variables Class Value 1 s nosmoke 0 smoke 1 Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Deviance and Pearson Goodness-of-Fit Statistics Criterion DF Value Value/DF Pr > ChiSq Deviance 0 0.0000 . . Pearson 0 0.0000 . . Number of events/trials observations: 2 Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 5178.510 5151.390 SC 5185.100 5164.569 -2 Log L 5176.510 5147.390 Logistic regression for 2x2 table 2 The LOGISTIC Procedure Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 29.1207 1 <.0001 Score 27.6766 1 <.0001 Wald 27.3361 1 <.0001 Type III Analysis of Effects Wald Effect DF Chi-Square Pr > ChiSq s 1 27.3361 <.0001 Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 -1.8266 0.0786 540.2949 <.0001 s smoke 1 0.4592 0.0878 27.3361 <.0001 Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits s smoke vs nosmoke 1.583 1.332 1.880 Association of Predicted Probabilities and Observed Responses Percent Concordant 21.7 Somers' D 0.080 Percent Discordant 13.7 Gamma 0.226 Percent Tied 64.6 Tau-a 0.024 Pairs 4388484 c 0.540 Logistic regression for 2x2 table 3 Obs s y n prob 1 smoke 816 4019 0.20304 2 nosmoke 188 1356 0.13864 Logistic regression without intercept 4 The LOGISTIC Procedure Model Information Data Set WORK.SMOKE Response Variable (Events) y Response Variable (Trials) n Number of Observations 2 Model binary logit Optimization Technique Fisher's scoring Response Profile Ordered Binary Total Value Outcome Frequency 1 Event 1004 2 Nonevent 4371 Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. -2 Log L = 5176.51 Deviance and Pearson Goodness-of-Fit Statistics Criterion DF Value Value/DF Pr > ChiSq Deviance 1 29.1207 29.1207 <.0001 Pearson 1 27.6766 27.6766 <.0001 Number of events/trials observations: 2 Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 -1.4710 0.0350 1766.6938 <.0001 Logistic regression with PROC GENMOD 5 The GENMOD Procedure Model Information Data Set WORK.SMOKE Distribution Binomial Link Function Logit Response Variable (Events) y Response Variable (Trials) n Observations Used 2 Number Of Events 1004 Number Of Trials 5375 Class Level Information Class Levels Values s 2 nosmoke smoke Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance 1 29.1207 29.1207 Scaled Deviance 1 29.1207 29.1207 Pearson Chi-Square 1 27.6766 27.6766 Scaled Pearson X2 1 27.6766 27.6766 Log Likelihood -2588.2551 Algorithm converged. Analysis Of Parameter Estimates Standard Wald 95% Confidence Chi- Parameter DF Estimate Error Limits Square Pr > ChiSq Intercept 1 -1.4710 0.0350 -1.5396 -1.4024 1766.69 <.0001 Scale 0 1.0000 0.0000 1.0000 1.0000 NOTE: The scale parameter was held fixed. Loglinear model of indepedence 6 The GENMOD Procedure Model Information Data Set WORK.SMOKE Distribution Poisson Link Function Log Dependent Variable count Observations Used 4 Class Level Information Class Levels Values s 2 smoke nosmoke y 2 yes no Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance 1 29.1207 29.1207 Scaled Deviance 1 29.1207 29.1207 Pearson Chi-Square 1 27.6766 27.6766 Scaled Pearson X2 1 27.6766 27.6766 Log Likelihood 35169.4467 Algorithm converged. Analysis Of Parameter Estimates Likelihood Ratio Standard 95% Confidence Chi- Parameter DF Estimate Error Limits Square Pr > ChiSq Intercept 1 7.0055 0.0279 6.9503 7.0598 62903.9 <.0001 s smoke 1 1.0865 0.0314 1.0252 1.1484 1196.89 <.0001 s nosmoke 0 0.0000 0.0000 0.0000 0.0000 . . y yes 1 -1.4710 0.0350 -1.5401 -1.4029 1766.69 <.0001 y no 0 0.0000 0.0000 0.0000 0.0000 . . Scale 0 1.0000 0.0000 1.0000 1.0000 NOTE: The scale parameter was held fixed. LR Statistics For Type 3 Analysis Chi- Source DF Square Pr > ChiSq s 1 1379.46 <.0001 y 1 2274.82 <.0001 Loglinear model of indepedence 7 The GENMOD Procedure Observation Statistics Observation count s y Pred Xbeta Std HessWgt Lower Upper Resraw Reschi Resdev StResdev StReschi Reslik 1 816 smoke yes 750.71182 6.6210218 0.032539 750.71182 704.32968 800.14835 65.288184 2.3828569 2.3495125 5.1872357 5.2608532 5.2458344 2 3203 smoke no 3268.2882 8.0920216 0.0170749 3268.2882 3160.721 3379.5161 -65.28819 -1.142022 -1.145856 -5.278516 -5.260853 -5.261687 3 188 nosmoke yes 253.28819 5.5345279 0.0393374 253.28819 234.49353 273.58924 -65.28819 -4.102297 -4.300704 -5.515293 -5.260853 -5.416991 4 1168 nosmoke no 1102.7118 7.0055277 0.027932 1102.7118 1043.9658 1164.7636 65.288185 1.9660908 1.9471533 5.2101804 5.2608533 5.2538053 Logistic regression for 2x3 table 8 The LOGISTIC Procedure Model Information Data Set WORK.SMOKE Response Variable (Events) y Response Variable (Trials) n Number of Observations 3 Model binary logit Optimization Technique Fisher's scoring Response Profile Ordered Binary Total Value Outcome Frequency 1 Event 1004 2 Nonevent 4371 Class Level Information Design Variables Class Value 1 2 s both 1 0 one 0 1 neither 0 0 Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Deviance and Pearson Goodness-of-Fit Statistics Criterion DF Value Value/DF Pr > ChiSq Deviance 0 0.0000 . . Pearson 0 0.0000 . . Number of events/trials observations: 3 Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 5178.510 5144.144 SC 5185.100 5163.913 -2 Log L 5176.510 5138.144 Logistic regression for 2x3 table 9 The LOGISTIC Procedure Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 38.3658 2 <.0001 Score 37.5663 2 <.0001 Wald 37.0861 2 <.0001 Type III Analysis of Effects Wald Effect DF Chi-Square Pr > ChiSq s 2 37.0861 <.0001 Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 -1.8266 0.0786 540.2949 <.0001 s both 1 0.5882 0.0970 36.8105 <.0001 s one 1 0.3491 0.0955 13.3481 0.0003 Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits s both vs neither 1.801 1.489 2.178 s one vs neither 1.418 1.176 1.710 Association of Predicted Probabilities and Observed Responses Percent Concordant 38.3 Somers' D 0.115 Percent Discordant 26.8 Gamma 0.177 Percent Tied 34.9 Tau-a 0.035 Pairs 4388484 c 0.558 Partition for the Hosmer and Lemeshow Test Event Nonevent Group Total Observed Expected Observed Expected 1 1356 188 188.00 1168 1168.00 2 2239 416 416.00 1823 1823.00 3 1780 400 400.00 1380 1380.00 Logistic regression for 2x3 table 10 The LOGISTIC Procedure Hosmer and Lemeshow Goodness-of-Fit Test Chi-Square DF Pr > ChiSq 0.0000 1 1.0000 Logistic regression for 2x3 table 11 Obs s y n prob 1 both 400 1780 0.22472 2 one 416 2239 0.18580 3 neither 188 1356 0.13864 Logistic regression fro 2x3 tables with residuals 12 The LOGISTIC Procedure Model Information Data Set WORK.SMOKE Response Variable (Events) y Response Variable (Trials) n Number of Observations 3 Model binary logit Optimization Technique Fisher's scoring Response Profile Ordered Binary Total Value Outcome Frequency 1 Event 1004 2 Nonevent 4371 Class Level Information Design Variables Class Value 1 2 s 0 0 0 1 1 0 2 0 1 Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Deviance and Pearson Goodness-of-Fit Statistics Criterion DF Value Value/DF Pr > ChiSq Deviance 0 0.0000 . . Pearson 0 0.0000 . . Number of events/trials observations: 3 Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 5178.510 5144.144 SC 5185.100 5163.913 -2 Log L 5176.510 5138.144 Logistic regression fro 2x3 tables with residuals 13 The LOGISTIC Procedure Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 38.3658 2 <.0001 Score 37.5663 2 <.0001 Wald 37.0861 2 <.0001 Type III Analysis of Effects Wald Effect DF Chi-Square Pr > ChiSq s 2 37.0861 <.0001 Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 -1.8266 0.0786 540.2949 <.0001 s 1 1 0.3491 0.0955 13.3481 0.0003 s 2 1 0.5882 0.0970 36.8105 <.0001 Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits s 1 vs 0 1.418 1.176 1.710 s 2 vs 0 1.801 1.489 2.178 Association of Predicted Probabilities and Observed Responses Percent Concordant 38.3 Somers' D 0.115 Percent Discordant 26.8 Gamma 0.177 Percent Tied 34.9 Tau-a 0.035 Pairs 4388484 c 0.558 Partition for the Hosmer and Lemeshow Test Event Nonevent Group Total Observed Expected Observed Expected 1 1356 188 188.00 1168 1168.00 2 2239 416 416.00 1823 1823.00 3 1780 400 400.00 1380 1380.00 Logistic regression fro 2x3 tables with residuals 14 The LOGISTIC Procedure Hosmer and Lemeshow Goodness-of-Fit Test Chi-Square DF Pr > ChiSq 0.0000 1 1.0000 Logistic regression diagnostics for 2x3 table 15 Obs s y n prob shat fhat pearson deviance 1 2 400 1780 0.22472 400.000 1380.00 -.000000031 0 2 1 416 2239 0.18580 416.000 1823.00 -3.6617E-15 0 3 0 188 1356 0.13864 188.000 1168.00 -.000001291 -.000001307