APPENDIX 3 The following analysis looks at the quality of living conditions among families living in 3 major cities in Thailand. In this analysis, quality of living conditions (qols_ord=0 if low standard of living, 1 if medium, 2 if high standard of living) was examined as the response with the following predictors: • • . Father's Education: feduc1 = 8 if <=8 years of education, 11 if 9-11 years, 12 if >=12 years Mother's Education: meduc1 = 8 if <=8 years of education, 11 if 9-11 years, 12 if >=12 years Country where mother was born: countryBorn-1 if Thailand; 2 if Burma Read_and_write in Thai: readwrite-1 if yes, 0 if no Income: in 10,000 Bhat. So, a value of 9 would indicate the family's income was 90,000 Bhat. SAS Output is given below. The LOGISTIC Procedure Model Information Data Set Response Variable WORK.QOLS qols_ord cumulative logit Number of Response Levels3 Model Optimization Technique Fisher's scoring Number of Observations Read320 Number of Observations Used275 Response Profile Valueqols_ord Frequency Ordered 12 21 30 Total 98 87 90 Probabilities modeled are cumulated over the lower Ordered Values. Note: 45 observations were deleted due to missing values for the response or explanatory variables Class feduc1 Class Level Information Value Design Variables 8 0 11 1 12 0 1 meduc1 8 0 11 12 12 1 0 0 1 country Born 1 0 2 1 readwrite 1 1 2 0 Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Score Test for the Proportional Odds Assumption Chi-Square DF Pr> ChiSq 8.6237 7 0.2808 Model Fit Statistics Criterion Intercept Only Intercept and Covariates AIC SC -2 Log L 607.537 614.770 603.537 579.436 611.987 561.436 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DFPr > ChiSq Likelihood Ratio 42.1006 7 <.0001 Score 36.8569 7 <.0001 Wald 37.1203 7 <.0001 Type 3 Analysis of Effects Effect feduc1 meduc1 Wald DF Chi-Square Pr> ChiSq 2 4.9680 0.0834 2 0.0485 0.9760 10.3629 0.0013 country Born 1 readwrite Income 1 7.6497 0.0057 1 17.6500 <.0001 Analysis of Maximum Likelihood Estimates Parameter Standard Wald DF Estimate Error Chi-Square Pr> ChiSq Intercept 2 1 -2.9119 0.4847 36.0875 <.0001 Intercept 1 1 -1.4323 0.4618 9.6213 0.0019 feduc1 11 1 0.0807 0.3316 0.0593 0.8077 feduc1 12 1 0.6796 0.3476 3.8229 0.0506 meduc1 11 1 -0.0734 0.3771 0.0379 0.8456 meduc1 12 1 -0.0227 0.3863 country Born2 readwrite 1 Income 1 1.6156 0.5019 1 1.3890 0.5022 1 0.6291 0.1497 0.0035 0.9531 10.3629 0.0013 7.6497 0.0057 17.6500 <.0001 Odds Ratio Estimates 95% Wald Effect feduc1 11 vs 8 Point Estimate Confidence Limits 1.084 0.566 2.077 feduc1 12 vs 8 1.973 0.998 3.899 meduc1 11 vs 8 0.929 0.444 1.946 meduc1 12 vs 8 0.978 0.458 2.084 country Born 2 vs 1 5.031 1.881 13.454 readwrite 1 vs 2 4.011 1.499 10.733 Income 1.876 1.399 2.516 Association of Predicted Probabilities and Observed Responses Percent Concordant 68.6Somers' D0.383 Percent Discordant 30.3Gamma 0.387 Percent Tied Pairs 1.1 Tau-a 0.256 25176c 0.692 12 13

APPENDIX 3 The following analysis looks at the quality of living conditions among families living in 3 major cities in Thailand. In this analysis, quality of living conditions (qols_ord=0 if low standard of living, 1 if medium, 2 if high standard of living) was examined as the response with the following predictors: • • . Father's Education: feduc1 = 8 if <=8 years of education, 11 if 9-11 years, 12 if >=12 years Mother's Education: meduc1 = 8 if <=8 years of education, 11 if 9-11 years, 12 if >=12 years Country where mother was born: countryBorn-1 if Thailand; 2 if Burma Read_and_write in Thai: readwrite-1 if yes, 0 if no Income: in 10,000 Bhat. So, a value of 9 would indicate the family's income was 90,000 Bhat. SAS Output is given below. The LOGISTIC Procedure Model Information Data Set Response Variable WORK.QOLS qols_ord cumulative logit Number of Response Levels3 Model Optimization Technique Fisher's scoring Number of Observations Read320 Number of Observations Used275 Response Profile Valueqols_ord Frequency Ordered 12 21 30 Total 98 87 90 Probabilities modeled are cumulated over the lower Ordered Values. Note: 45 observations were deleted due to missing values for the response or explanatory variables Class feduc1 Class Level Information Value Design Variables 8 0 11 1 12 0 1 meduc1 8 0 11 12 12 1 0 0 1 country Born 1 0 2 1 readwrite 1 1 2 0 Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Score Test for the Proportional Odds Assumption Chi-Square DF Pr> ChiSq 8.6237 7 0.2808 Model Fit Statistics Criterion Intercept Only Intercept and Covariates AIC SC -2 Log L 607.537 614.770 603.537 579.436 611.987 561.436 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DFPr > ChiSq Likelihood Ratio 42.1006 7 <.0001 Score 36.8569 7 <.0001 Wald 37.1203 7 <.0001 Type 3 Analysis of Effects Effect feduc1 meduc1 Wald DF Chi-Square Pr> ChiSq 2 4.9680 0.0834 2 0.0485 0.9760 10.3629 0.0013 country Born 1 readwrite Income 1 7.6497 0.0057 1 17.6500 <.0001 Analysis of Maximum Likelihood Estimates Parameter Standard Wald DF Estimate Error Chi-Square Pr> ChiSq Intercept 2 1 -2.9119 0.4847 36.0875 <.0001 Intercept 1 1 -1.4323 0.4618 9.6213 0.0019 feduc1 11 1 0.0807 0.3316 0.0593 0.8077 feduc1 12 1 0.6796 0.3476 3.8229 0.0506 meduc1 11 1 -0.0734 0.3771 0.0379 0.8456 meduc1 12 1 -0.0227 0.3863 country Born2 readwrite 1 Income 1 1.6156 0.5019 1 1.3890 0.5022 1 0.6291 0.1497 0.0035 0.9531 10.3629 0.0013 7.6497 0.0057 17.6500 <.0001 Odds Ratio Estimates 95% Wald Effect feduc1 11 vs 8 Point Estimate Confidence Limits 1.084 0.566 2.077 feduc1 12 vs 8 1.973 0.998 3.899 meduc1 11 vs 8 0.929 0.444 1.946 meduc1 12 vs 8 0.978 0.458 2.084 country Born 2 vs 1 5.031 1.881 13.454 readwrite 1 vs 2 4.011 1.499 10.733 Income 1.876 1.399 2.516 Association of Predicted Probabilities and Observed Responses Percent Concordant 68.6Somers' D0.383 Percent Discordant 30.3Gamma 0.387 Percent Tied Pairs 1.1 Tau-a 0.256 25176c 0.692 12 13

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Give a p-value for the proportional odds assumption. Give your answer to four numbers after the decimal place.

Transcribed Image Text:APPENDIX 3 The following analysis looks at the quality of living conditions among families living in 3 major cities in Thailand. In this analysis, quality of living conditions (qols_ord=0 if low standard of living, 1 if medium, 2 if high standard of living) was examined as the response with the following predictors: • • . Father's Education: feduc1 = 8 if <=8 years of education, 11 if 9-11 years, 12 if >=12 years Mother's Education: meduc1 = 8 if <=8 years of education, 11 if 9-11 years, 12 if >=12 years Country where mother was born: countryBorn-1 if Thailand; 2 if Burma Read_and_write in Thai: readwrite-1 if yes, 0 if no Income: in 10,000 Bhat. So, a value of 9 would indicate the family's income was 90,000 Bhat. SAS Output is given below. The LOGISTIC Procedure Model Information Data Set Response Variable WORK.QOLS qols_ord cumulative logit Number of Response Levels3 Model Optimization Technique Fisher's scoring Number of Observations Read320 Number of Observations Used275 Response Profile Valueqols_ord Frequency Ordered 12 21 30 Total 98 87 90 Probabilities modeled are cumulated over the lower Ordered Values. Note: 45 observations were deleted due to missing values for the response or explanatory variables Class feduc1 Class Level Information Value Design Variables 8 0 11 1 12 0 1 meduc1 8 0 11 12 12 1 0 0 1 country Born 1 0 2 1 readwrite 1 1 2 0 Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Score Test for the Proportional Odds Assumption Chi-Square DF Pr> ChiSq 8.6237 7 0.2808 Model Fit Statistics Criterion Intercept Only Intercept and Covariates AIC SC -2 Log L 607.537 614.770 603.537 579.436 611.987 561.436 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DFPr > ChiSq Likelihood Ratio 42.1006 7 <.0001 Score 36.8569 7 <.0001 Wald 37.1203 7 <.0001 Type 3 Analysis of Effects Effect feduc1 meduc1 Wald DF Chi-Square Pr> ChiSq 2 4.9680 0.0834 2 0.0485 0.9760 10.3629 0.0013 country Born 1 readwrite Income 1 7.6497 0.0057 1 17.6500 <.0001 Analysis of Maximum Likelihood Estimates Parameter Standard Wald DF Estimate Error Chi-Square Pr> ChiSq Intercept 2 1 -2.9119 0.4847 36.0875 <.0001 Intercept 1 1 -1.4323 0.4618 9.6213 0.0019 feduc1 11 1 0.0807 0.3316 0.0593 0.8077 feduc1 12 1 0.6796 0.3476 3.8229 0.0506 meduc1 11 1 -0.0734 0.3771 0.0379 0.8456 meduc1 12 1 -0.0227 0.3863 country Born2 readwrite 1 Income 1 1.6156 0.5019 1 1.3890 0.5022 1 0.6291 0.1497 0.0035 0.9531 10.3629 0.0013 7.6497 0.0057 17.6500 <.0001 Odds Ratio Estimates 95% Wald Effect feduc1 11 vs 8 Point Estimate Confidence Limits 1.084 0.566 2.077 feduc1 12 vs 8 1.973 0.998 3.899 meduc1 11 vs 8 0.929 0.444 1.946 meduc1 12 vs 8 0.978 0.458 2.084 country Born 2 vs 1 5.031 1.881 13.454 readwrite 1 vs 2 4.011 1.499 10.733 Income 1.876 1.399 2.516 Association of Predicted Probabilities and Observed Responses Percent Concordant 68.6Somers' D0.383 Percent Discordant 30.3Gamma 0.387 Percent Tied Pairs 1.1 Tau-a 0.256 25176c 0.692 12 13

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