Ordered Logit Models Vartanian: SW 541

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1 Ordered Logit Models Vartanian: SW 541 You are examining an ordered logit model the age at first marriage. You have a 3 level dependent variable for age at first marriage. Level 1 indicates the person was first married as a teenager, level 2 indicates the person was married in their 20s, and level 3 indicates that they were married in their 30s. You examine the effects of living in poverty as a child and the type of city they lived in as a child (with very rural areas being the excluded group). You get the results presented below. A. What do the odds ratios indicate for the independent variables? B. What do the probability estimates indicate? C. Are the effects of the independent variables proportional? C:\WP60_1\Lect2.phd\FINALrev\ordlogitfinal.doc 1

2 The LOGISTIC Procedure Model Information Data Set WORK.Z Response Variable firstm Number of Response Levels 3 Number of Observations 2809 Weight Variable WEIGHT Sum of Weights 2809 Model cumulative logit Optimization Technique Fisher's scoring Response Profile Ordered Total Total Value firstm Frequency Weight Probabilities modeled are cumulated over the lower Ordered Values. Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Score Test for the Proportional Odds Assumption Chi-Square DF Pr > ChiSq Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC SC Log L C:\WP60_1\Lect2.phd\FINALrev\ordlogitfinal.doc 2

3 The SAS System 07:46 Monday, April 28, The LOGISTIC Procedure Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio <.0001 Score <.0001 Wald <.0001 Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept <.0001 Intercept <.0001 INPOV BIGCITY <.0001 URBANY CITY3Y SUBY RURY Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits INPOV BIGCITY URBANY CITY3Y SUBY RURY Association of Predicted Probabilities and Observed Responses Percent Concordant 50.8 Somers' D Percent Discordant 35.5 Gamma Percent Tied 13.8 Tau-a Pairs c C:\WP60_1\Lect2.phd\FINALrev\ordlogitfinal.doc 3

4 The SAS System 07:46 Monday, April 28, Response Value= The MEANS Procedure ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ PROB Estimated Probability _LEVEL_ Response Value pr_pov pr_npov pr_vrur pr_rur pr_suby pr_city3y pr_urbany pr_big ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Response Value= ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ PROB Estimated Probability _LEVEL_ Response Value pr_pov pr_npov pr_vrur pr_rur pr_suby pr_city3y pr_urbany pr_big ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ C:\WP60_1\Lect2.phd\FINALrev\ordlogitfinal.doc 4

5 You are examining an ordered model for number of marriages (I m searching for an ordered variable here). You examining city of residence and poverty level as independent variables. You come up with the following results. A. What do the odds ratios indicate for the independent variables? B. What do the probability estimates indicate? C. Are the effects of the independent variables proportional? The SAS System 07:46 Monday, April 28, The LOGISTIC Procedure Model Information Data Set WORK.Z Response Variable NUMMARR Number of Response Levels 5 Number of Observations 2746 Weight Variable WEIGHT Sum of Weights 2746 Model cumulative logit Optimization Technique Fisher's scoring Response Profile Ordered Total Total Value NUMMARR Frequency Weight Probabilities modeled are cumulated over the lower Ordered Values. Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Score Test for the Proportional Odds Assumption Chi-Square DF Pr > ChiSq Model Fit Statistics Intercept Intercept and C:\WP60_1\Lect2.phd\FINALrev\ordlogitfinal.doc 5

6 Criterion Only Covariates AIC SC Log L C:\WP60_1\Lect2.phd\FINALrev\ordlogitfinal.doc 6

7 The SAS System 07:46 Monday, April 28, The LOGISTIC Procedure Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio <.0001 Score <.0001 Wald <.0001 Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept <.0001 Intercept <.0001 Intercept <.0001 Intercept <.0001 INPOV BIGCITY URBANY CITY3Y SUBY RURY Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits INPOV BIGCITY URBANY CITY3Y SUBY RURY Association of Predicted Probabilities and Observed Responses Percent Concordant 27.1 Somers' D Percent Discordant 21.7 Gamma Percent Tied 51.2 Tau-a Pairs c C:\WP60_1\Lect2.phd\FINALrev\ordlogitfinal.doc 7

8 The SAS System 07:46 Monday, April 28, Response Value= The MEANS Procedure PROB Estimated Probability _LEVEL_ Response Value pr_pov pr_npov pr_vrur pr_rur pr_suby pr_city3y pr_urbany pr_big Response Value= PROB Estimated Probability _LEVEL_ Response Value pr_pov pr_npov pr_vrur pr_rur pr_suby pr_city3y pr_urbany pr_big Response Value= PROB Estimated Probability _LEVEL_ Response Value pr_pov pr_npov pr_vrur pr_rur pr_suby pr_city3y pr_urbany pr_big C:\WP60_1\Lect2.phd\FINALrev\ordlogitfinal.doc 8

9 The SAS System 07:46 Monday, April 28, Response Value= The MEANS Procedure PROB Estimated Probability _LEVEL_ Response Value pr_pov pr_npov pr_vrur pr_rur pr_suby pr_city3y pr_urbany pr_big C:\WP60_1\Lect2.phd\FINALrev\ordlogitfinal.doc 9

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