The SAS System 1 15:28 Monday, March 14, 2005 The CONTENTS Procedure Data Set Name WORK.MEPS Observations 9507 Member Type DATA Variables 7 Engine V9 Indexes 0 Created Monday, March 14, Observation Length 56 2005 03:28:27 PM Last Modified Monday, March 14, Deleted Observations 0 2005 03:28:27 PM Protection Compressed NO Data Set Type Sorted NO Label Data Representation LINUX_32, INTEL_ABI Encoding latin1 Western (ISO) Engine/Host Dependent Information Data Set Page Size 8192 Number of Data Set Pages 66 First Data Page 1 Max Obs per Page 145 Obs in First Data Page 115 Number of Data Set Repairs 0 File Name /usr/tmp/SAS_workF247000020E1_unix43. andrew.cmu.edu/meps.sas7bdat Release Created 9.0101M0 Host Created Linux Inode Number 243362 Access Permission rw-r--r-- Owner Name wilibear File Size (bytes) 548864 Alphabetic List of Variables and Attributes # Variable Type Len 1 age Num 8 4 employed Num 8 6 health Num 8 3 income Num 8 5 insured Num 8 2 sex Num 8 7 spending Num 8 The SAS System 2 15:28 Monday, March 14, 2005 The MEANS Procedure Variable N Mean Std Dev Minimum Maximum -------------------------------------------------------------------------------- age 9507 41.4276849 11.2859335 19.0000000 64.0000000 sex 9507 0.4638687 0.4987191 0 1.0000000 income 9507 25014.62 23163.32 0 173362.60 employed 9507 0.7642790 0.4244709 0 1.0000000 insured 9507 0.8361208 0.3701854 0 1.0000000 health 9507 2.2481330 1.0967146 1.0000000 5.0000000 spending 9507 1852.18 7850.16 0 427086.00 -------------------------------------------------------------------------------- The SAS System 3 15:28 Monday, March 14, 2005 The CORR Procedure 7 Variables: age sex income employed insured health spending Simple Statistics Variable N Mean Std Dev Sum Minimum Maximum age 9507 41.42768 11.28593 393853 19.00000 64.00000 sex 9507 0.46387 0.49872 4410 0 1.00000 income 9507 25015 23163 237813984 0 173363 employed 9507 0.76428 0.42447 7266 0 1.00000 insured 9507 0.83612 0.37019 7949 0 1.00000 health 9507 2.24813 1.09671 21373 1.00000 5.00000 spending 9507 1852 7850 17608708 0 427086 Pearson Correlation Coefficients, N = 9507 Prob > |r| under H0: Rho=0 age sex income employed insured health spending age 1.00000 0.00527 0.13404 -0.08860 0.10846 0.12547 0.06363 0.6075 <.0001 <.0001 <.0001 <.0001 <.0001 sex 0.00527 1.00000 0.18565 0.19606 -0.04233 -0.06391 -0.02567 0.6075 <.0001 <.0001 <.0001 <.0001 0.0123 income 0.13404 0.18565 1.00000 0.39822 0.20329 -0.22864 -0.02115 <.0001 <.0001 <.0001 <.0001 <.0001 0.0392 employed -0.08860 0.19606 0.39822 1.00000 0.07749 -0.27477 -0.10151 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 insured 0.10846 -0.04233 0.20329 0.07749 1.00000 -0.07732 0.06742 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 health 0.12547 -0.06391 -0.22864 -0.27477 -0.07732 1.00000 0.12305 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 spending 0.06363 -0.02567 -0.02115 -0.10151 0.06742 0.12305 1.00000 <.0001 0.0123 0.0392 <.0001 <.0001 <.0001 The SAS System 4 15:28 Monday, March 14, 2005 The FREQ Procedure Cumulative Cumulative insured Frequency Percent Frequency Percent ------------------------------------------------------------ 0 1558 16.39 1558 16.39 1 7949 83.61 9507 100.00 Table of insured by employed insured employed Frequency| Percent | Row Pct | Col Pct | 0| 1| Total ---------+--------+--------+ 0 | 483 | 1075 | 1558 | 5.08 | 11.31 | 16.39 | 31.00 | 69.00 | | 21.55 | 14.79 | ---------+--------+--------+ 1 | 1758 | 6191 | 7949 | 18.49 | 65.12 | 83.61 | 22.12 | 77.88 | | 78.45 | 85.21 | ---------+--------+--------+ Total 2241 7266 9507 23.57 76.43 100.00 The SAS System 5 15:28 Monday, March 14, 2005 The MEANS Procedure Variable N Mean Std Dev Minimum Maximum -------------------------------------------------------------------------------- age 9507 41.4276849 11.2859335 19.0000000 64.0000000 sex 9507 0.4638687 0.4987191 0 1.0000000 employed 9507 0.7642790 0.4244709 0 1.0000000 insured 9507 0.8361208 0.3701854 0 1.0000000 health 9507 2.2481330 1.0967146 1.0000000 5.0000000 spending 9507 1852.18 7850.16 0 427086.00 incomeK 9507 25.0146191 23.1633176 0 173.3626000 -------------------------------------------------------------------------------- Linear probability model 6 15:28 Monday, March 14, 2005 The REG Procedure Model: MODEL1 Dependent Variable: insured Number of Observations Read 9507 Number of Observations Used 9507 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 4 71.41120 17.85280 137.77 <.0001 Error 9502 1231.26494 0.12958 Corrected Total 9506 1302.67613 Root MSE 0.35997 R-Square 0.0548 Dependent Mean 0.83612 Adj R-Sq 0.0544 Coeff Var 43.05259 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 0.65629 0.01627 40.33 <.0001 age 1 0.00276 0.00033422 8.27 <.0001 sex 1 -0.06238 0.00760 -8.20 <.0001 employed 1 0.01944 0.00969 2.01 0.0448 incomeK 1 0.00318 0.00017806 17.84 <.0001 Linear probability model 7 15:28 Monday, March 14, 2005 The REG Procedure Model: MODEL1 Dependent Variable: insured Consistent Covariance of Estimates Variable Intercept age sex employed incomeK Intercept 0.0003224904 -5.454458E-6 -4.877021E-6 -0.000100388 3.0484175E-7 age -5.454458E-6 1.2209078E-7 -1.918134E-7 8.2523245E-7 -1.250092E-8 sex -4.877021E-6 -1.918134E-7 0.0000581254 -6.877634E-6 -2.070643E-7 employed -0.000100388 8.2523245E-7 -6.877634E-6 0.0001154264 -8.213402E-7 incomeK 3.0484175E-7 -1.250092E-8 -2.070643E-7 -8.213402E-7 2.9450907E-8 LPM predicted probabilities 8 15:28 Monday, March 14, 2005 The MEANS Procedure Variable N Mean Std Dev Minimum Maximum -------------------------------------------------------------------------------- age 9507 41.4276849 11.2859335 19.0000000 64.0000000 sex 9507 0.4638687 0.4987191 0 1.0000000 employed 9507 0.7642790 0.4244709 0 1.0000000 insured 9507 0.8361208 0.3701854 0 1.0000000 health 9507 2.2481330 1.0967146 1.0000000 5.0000000 spending 9507 1852.18 7850.16 0 427086.00 incomeK 9507 25.0146191 23.1633176 0 173.3626000 Yhat 9507 0.8361208 0.0866731 0.6464055 1.3164528 Yhat01 9507 0.0430209 0.2029149 0 1.0000000 -------------------------------------------------------------------------------- Logit model 9 15:28 Monday, March 14, 2005 The LOGISTIC Procedure Model Information Data Set WORK.MEPS Response Variable insured Number of Response Levels 2 Model binary logit Optimization Technique Fisher's scoring Number of Observations Read 9507 Number of Observations Used 9507 Response Profile Ordered Total Value insured Frequency 1 1 7949 2 0 1558 Probability modeled is insured=1. Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 8483.136 7797.599 SC 8490.296 7833.398 -2 Log L 8481.136 7787.599 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 693.5372 4 <.0001 Score 521.1627 4 <.0001 Wald 497.7655 4 <.0001 Logit model 10 15:28 Monday, March 14, 2005 The LOGISTIC Procedure Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 0.3773 0.1178 10.2591 0.0014 age 1 0.0184 0.00256 51.6961 <.0001 sex 1 -0.5097 0.0594 73.7296 <.0001 employed 1 -0.1610 0.0737 4.7745 0.0289 incomeK 1 0.0451 0.00245 339.0575 <.0001 Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits age 1.019 1.013 1.024 sex 0.601 0.535 0.675 employed 0.851 0.737 0.984 incomeK 1.046 1.041 1.051 Association of Predicted Probabilities and Observed Responses Percent Concordant 71.3 Somers' D 0.431 Percent Discordant 28.2 Gamma 0.433 Percent Tied 0.5 Tau-a 0.118 Pairs 12384542 c 0.715 Probit model 11 15:28 Monday, March 14, 2005 The LOGISTIC Procedure Model Information Data Set WORK.MEPS Response Variable insured Number of Response Levels 2 Model binary probit Optimization Technique Fisher's scoring Number of Observations Read 9507 Number of Observations Used 9507 Response Profile Ordered Total Value insured Frequency 1 1 7949 2 0 1558 Probability modeled is insured=1. Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 8483.136 7848.534 SC 8490.296 7884.333 -2 Log L 8481.136 7838.534 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 642.6021 4 <.0001 Score 521.1627 4 <.0001 Wald 465.0409 4 <.0001 Probit model 12 15:28 Monday, March 14, 2005 The LOGISTIC Procedure Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 0.2709 0.0670 16.3396 <.0001 age 1 0.0107 0.00143 56.0431 <.0001 sex 1 -0.2740 0.0330 68.8884 <.0001 employed 1 -0.0191 0.0415 0.2127 0.6447 incomeK 1 0.0204 0.00120 289.6110 <.0001 Association of Predicted Probabilities and Observed Responses Percent Concordant 70.9 Somers' D 0.424 Percent Discordant 28.5 Gamma 0.427 Percent Tied 0.6 Tau-a 0.116 Pairs 12384542 c 0.712 Logit marginal effects 13 15:28 Monday, March 14, 2005 The MEANS Procedure Variable N Mean Std Dev Minimum Maximum -------------------------------------------------------------------------------- Phat 9507 0.8361191 0.0962910 0.5185547 0.9997849 me_incK 9507 0.0057617 0.0027987 9.6994885E-6 0.0112595 -------------------------------------------------------------------------------- Probit marginal effects 14 15:28 Monday, March 14, 2005 The MEANS Procedure Variable N Mean Std Dev Minimum Maximum -------------------------------------------------------------------------------- Phat 9507 0.8360325 0.0881405 0.5759475 0.9999747 me_incK 9507 0.0046994 0.0018464 2.2066708E-6 0.0079905 -------------------------------------------------------------------------------- Probit model --- testing joint hypothesis 15 15:28 Monday, March 14, 2005 The LOGISTIC Procedure Model Information Data Set WORK.MEPS Response Variable insured Number of Response Levels 2 Model binary probit Optimization Technique Fisher's scoring Number of Observations Read 9507 Number of Observations Used 9507 Response Profile Ordered Total Value insured Frequency 1 1 7949 2 0 1558 Probability modeled is insured=1. Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 8483.136 7971.647 SC 8490.296 7993.127 -2 Log L 8481.136 7965.647 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 515.4889 2 <.0001 Score 393.0221 2 <.0001 Wald 351.1622 2 <.0001 Probit model --- testing joint hypothesis 16 15:28 Monday, March 14, 2005 The LOGISTIC Procedure Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 0.6391 0.0308 429.3940 <.0001 employed 1 -0.1130 0.0402 7.8846 0.0050 incomeK 1 0.0206 0.00117 309.8673 <.0001 Association of Predicted Probabilities and Observed Responses Percent Concordant 69.4 Somers' D 0.403 Percent Discordant 29.1 Gamma 0.410 Percent Tied 1.5 Tau-a 0.111 Pairs 12384542 c 0.702