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SAS 8.2 release of MDC procedure analyzes conditional logit models.
Example 1: 1-1 Matching
This example is adapted from Chapter 7 of Applied Logistic Regression by Hosmer & Lemeshow (2000). You can download the SAS data file lbwt11.sas7bdat here.
The first 20 observations are listed below. Notice that variable pairid indicates that the observations are paired.
pairid lbwt age lastwt race smoke ptd ht ui race1 race2 race3 1 0 14 135 1 0 0 0 0 1 0 0 1 1 14 101 3 1 1 0 0 0 0 1 2 0 15 98 2 0 0 0 0 0 1 0 2 1 15 115 3 0 0 0 1 0 0 1 3 0 16 95 3 0 0 0 0 0 0 1 3 1 16 130 3 0 0 0 0 0 0 1 4 0 17 103 3 0 0 0 0 0 0 1 4 1 17 130 3 1 1 0 1 0 0 1 5 0 17 122 1 1 0 0 0 1 0 0 5 1 17 110 1 1 0 0 0 1 0 0 6 0 17 113 2 0 0 0 0 0 1 0 6 1 17 120 1 1 0 0 0 1 0 0 7 0 17 113 2 0 0 0 0 0 1 0 7 1 17 120 2 0 0 0 0 0 1 0 8 0 17 119 3 0 0 0 0 0 0 1 8 1 17 142 2 0 0 1 0 0 1 0 9 0 18 100 1 1 0 0 0 1 0 0 9 1 18 148 3 0 0 0 0 0 0 1 10 0 18 90 1 1 0 0 1 1 0 0 10 1 18 110 2 1 1 0 0 0 1 0proc mdc data = lbwt11; model lbwt = lastwt smoke race2 race3 ptd ht ui / type = clogit nchoice = 2; id pairid; run;The MDC Procedure Conditional Logit Estimates Model Fit SummaryDependent Variable lbwt Number of Observations 56 Number of Cases 112 Log Likelihood -25.79427 Maximum Absolute Gradient 2.30684E-6 Number of Iterations 5 Optimization Method Newton-Raphson AIC 65.58854 Schwarz Criterion 79.76600Discrete Response ProfileIndex CHOICE Frequency Percent 0 1 0 0.00 1 2 56 100.00Goodness-of-Fit Measures for Discrete Choice Models Measure Value Formula Likelihood Ratio (R) 26.044 2 * (LogL - LogL0) Upper Bound of R (U) 77.632 - 2 * LogL0 Aldrich-Nelson 0.3174 R / (R+N) Cragg-Uhler 1 0.3719 1 - exp(-R/N) Cragg-Uhler 2 0.4959 (1-exp(-R/N)) / (1-exp(-U/N)) Estrella 0.4325 1 - (1-R/U)^(U/N) Adjusted Estrella 0.2084 1 - ((LogL-K)/LogL0)^(-2/N*LogL0) McFadden's LRI 0.3355 R / UN = # of observations, K = # of regressors Goodness-of-Fit Measures for Discrete Choice Models Measure Value Formula Veall-Zimmermann 0.5464 (R * (U+N)) / (U * (R+N))N = # of observations, K = # of regressorsParameter EstimatesStandard Approx Parameter DF Estimate Error t Value Pr > |t| Gradient lastwt 1 -0.0184 0.0101 -1.82 0.0683 -2.31E-6 smoke 1 1.4007 0.6278 2.23 0.0257 3.741E-8 race2 1 0.5714 0.6896 0.83 0.4074 8.89E-10 race3 1 -0.0253 0.6992 -0.04 0.9711 -2.35E-9 ptd 1 1.8080 0.7887 2.29 0.0219 4.792E-8 ht 1 2.3612 1.0861 2.17 0.0297 1.5E-8 ui 1 1.4019 0.6962 2.01 0.0440 1.25E-8
Example 2: 1-M matching
This example is adapted from Chapter 7 of Applied Logistic Regression by Hosmer & Lemeshow (2000). You can download the SAS data file bbdm13.sas7bdat here.
The first 20 observations are listed below. Notice that variable str indicates that there are four choices for each subject.
str obs fndx chk agmn wt mod wid nvmr 1 1 1 1 13 118 55 0 0 1 2 0 2 11 175 1 0 0 1 3 0 2 12 135 1 0 0 1 4 0 1 11 125 55 0 0 2 1 1 1 14 118 55 0 0 2 2 0 2 15 183 55 0 0 2 3 0 2 11 218 55 0 0 2 4 0 1 13 192 55 0 0 3 1 1 1 15 125 55 0 0 3 2 0 2 14 123 55 0 0 3 3 0 1 13 140 55 0 0 3 4 0 1 13 160 55 0 0 4 1 1 1 14 150 55 0 1 4 2 0 1 13 130 1 0 0 4 3 0 2 14 140 55 0 0 4 4 0 1 16 130 55 0 0 5 1 1 1 17 150 1 0 0 5 2 0 2 12 148 55 0 0 5 3 0 1 13 134 55 0 0 5 4 0 1 14 138 55 1 0proc mdc data = in.bbdm13; model fndx = chk agmn wt mod wid nvmr / type = clogit nchoice = 4; id str; run;The MDC ProcedureConditional Logit Estimates Model Fit Summary Dependent Variable fndx Number of Observations 50 Number of Cases 200 Log Likelihood -45.21482 Maximum Absolute Gradient 2.36768E-6 Number of Iterations 5 Optimization Method Newton-Raphson AIC 102.42965 Schwarz Criterion 113.90179Discrete Response Profile Index CHOICE Frequency Percent 0 1 50 100.00 1 2 0 0.00 2 3 0 0.00 3 4 0 0.00Goodness-of-Fit Measures for Discrete Choice Models Measure Value Formula Likelihood Ratio (R) 48.200 2 * (LogL - LogL0) Upper Bound of R (U) 138.63 - 2 * LogL0 Aldrich-Nelson 0.4908 R / (R+N) Cragg-Uhler 1 0.6186 1 - exp(-R/N) Cragg-Uhler 2 0.6599 (1-exp(-R/N)) / (1-exp(-U/N)) Estrella 0.6941 1 - (1-R/U)^(U/N)N = # of observations, K = # of regressors The MDC ProcedureGoodness-of-Fit Measures for Discrete Choice Models Measure Value Formula Adjusted Estrella 0.5679 1 - ((LogL-K)/LogL0)^(-2/N*LogL0) McFadden's LRI 0.3477 R / U Veall-Zimmermann 0.6679 (R * (U+N)) / (U * (R+N))N = # of observations, K = # of regressorsParameter EstimatesStandard Approx Parameter DF Estimate Error t Value Pr > |t| Gradient chk 1 -1.1218 0.4474 -2.51 0.0122 -2.2E-8 agmn 1 0.3561 0.1292 2.76 0.0058 8.004E-8 wt 1 -0.0284 0.009978 -2.84 0.0045 -2.37E-6 mod 1 0.003760 0.0120 0.31 0.7538 1.802E-7 wid 1 -0.4916 0.8173 -0.60 0.5475 -1.21E-9 nvmr 1 1.4722 0.7582 1.94 0.0522 7.31E-9
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