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## Proceedings of the Conference on Multidimensional Mathematical Demography Held at the University of Maryland, College Park, Maryland, March 23-25, 1981, Sponsored by the National Science Foundation

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Contributors

Preface

Acknowledgments

1 Multidimensional Mathematical Demography: An Overview

1. Introduction

2. Recent Developments in Multistate Demographic Models

3. The Conference on Multidimensional Mathematical Demography

4. Organization of the Volume

5. Conclusions and Next Steps

2 Multidimensional Population Analysis with Incomplete Data

1. Introduction

2. Data Requirements and Data Availability

3. Modeling the Data in the Account

4. Parameter Estimation from Available Data

5. Numerical Applications

6. Conclusion

3 Model Schedules in Multistate Demographic Analysis: The Case of Migration

1. Synthetic Model Migration Schedules: I. The Correlational Perspective

2. Synthetic Model Migration Schedules: II. The Relational Perspective

3. Concluding Remarks

4 Multistate Life Table Methodology: A Probabilist Critique

1. Introduction

2. The Markov Chain Model

3. Integration Hypotheses

4. Occurrence/Exposure Rates

5. Other Observational Plans

6. Sampling and Heterogeneity

5 Statistical Methods for Markov-Generated Increment-Decrement Life Tables with Polynomial Gross Flow Functions

1. Introduction

2. Model Specification

3. Age-Specific Methods for Occurrence/Exposure Rates

4. Marital Dissolution and Remarriage in Sweden: Application and Comparison of Methods

5. Application of the Methods to Survivorship Proportions

6. Concluding Comments

6 Transition Probability Estimation in Increment-Decrement Life Tables: Using Mobility Data from a Census or a Survey

1. Introduction

2. Approach A: Estimation from Mobility Rates

3. Approach B: Estimation from Transition Proportions

4. A Brief Comparison of the Two Alternative Approaches

5. Conclusion

7 Generalizing the Life Table Model to Incorporate Interactions between the Sexes

1. Introduction

2. Life Table Models

3. A TWOFIDS Model for the United States/California 1970

4. Conclusion

Appendix: The TWONUP First Marriage Matrix

Appendix: Input Data for the TWOFIDS Model

8 Multiregional Population Projections by Place of Previous Residence

1. Introduction

2. Stationary and Stable Population Distributions

3. Multiregional Population Projections by Place of Birth

4. Multiregional Population Projections by Place of Previous Residence

5. Native-Dependent Multiregional Population Projections

6. Conclusion

Appendix A: Native-Independent Multistate Projection: Biregional Model

Appendix B: Separation Factors

9 Multiregional Age-Structured Populations with Changing Rates: Weak and Stochastic Ergodic Theorems

1. Introduction

2. The Formalism of Multiregional Population Models

3. Weak Ergodic Theorems for Multiregional Populations Models

4. Stochastic Ergodic Theorems

5. Relative Rates of Convergence

6. Extensions and Applications

10 High- and Low-Intensity Model of Mobility

1. Introduction

2. The High- and Low-Intensity Model of Mobility

3. Solution of the Model

4. Verification of the Model

5. Implementation of the Model

6. A Possible Extension

Appendix

11 Increment-Decrement Life Tables and Semi-Markovian Processes from a Sample Path Perspective

1. Introduction

2. Defining Basic Probabilities on Sample Paths

3. Semi-Markovian Processes

4. Parametric Forms of One-Step Transition Matrices, Competing Risks, and Likelihood Functions

5. One-Step Transition Matrices and Multiple Decrement Life Tables

6. The Kolmogorov Differential Equations

7. Integral Equations for Age-Dependent Semi-Markov Processes

8. Numerical Algorithms for Solving Renewal-Type Equations

12 Population Heterogeneity in Demographic Models

1. Introduction

2. Duration Models and Unobservables

3. Sensitivity of Parameter Estimates

4. Qualitative Properties of Mixtures

5. Estimation in Mixture Models

6. Performance of the EM Algorithm and Revised Estimates for the Kiefer-Neumann Data

7. Discussion and Conclusions

Index

Participants

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1st Edition - September 28, 1982

Editors: Kenneth C Land, Andrei Rogers

Language: EnglisheBook ISBN:

9 7 8 - 1 - 4 8 3 2 - 6 9 8 4 - 9

Multidimensional Mathematical Demography is a collection of papers dealing with the problems of inaccurate or unavailable demographic data, transformation of data into… Read more

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Multidimensional Mathematical Demography is a collection of papers dealing with the problems of inaccurate or unavailable demographic data, transformation of data into probabilities, multidimensional population dynamic models, and the problems of heterogeneity. The papers suggest a unified perspective with emphasis on data structure to work out multidimensional analysis with incomplete data. To solve inaccuracies in data, one paper notes that designs and use of model multistate schedules, for example, methods of inferring data, should be a major part in multistate modeling. Other papers discuss the state-of-the-art in abridged increment-decrement life table methodology. They also describe the estimation of transition probabilities in increment-decrement life tables where mobility data available is from the count of movers from a population survey. One paper reviews the possible extension of a multiregional stochastic theorem associated in a single-regional case; and then analyzes what the stochastic model needs when it is used with real data. Another paper explains strategies concerning population heterogeneity when it pertains to the mixtures of Markov and semi-Markov processes; Markov processes subject to measurement error; and the Heckman and Borjas model. This collection can be read profitably by statisticians, mathematicians, mathematical demographers, mathematical sociologists, economists, professionals in census bureaus, and students of sociology or geography.

Contributors

Preface

Acknowledgments

1 Multidimensional Mathematical Demography: An Overview

1. Introduction

2. Recent Developments in Multistate Demographic Models

3. The Conference on Multidimensional Mathematical Demography

4. Organization of the Volume

5. Conclusions and Next Steps

2 Multidimensional Population Analysis with Incomplete Data

1. Introduction

2. Data Requirements and Data Availability

3. Modeling the Data in the Account

4. Parameter Estimation from Available Data

5. Numerical Applications

6. Conclusion

3 Model Schedules in Multistate Demographic Analysis: The Case of Migration

1. Synthetic Model Migration Schedules: I. The Correlational Perspective

2. Synthetic Model Migration Schedules: II. The Relational Perspective

3. Concluding Remarks

4 Multistate Life Table Methodology: A Probabilist Critique

1. Introduction

2. The Markov Chain Model

3. Integration Hypotheses

4. Occurrence/Exposure Rates

5. Other Observational Plans

6. Sampling and Heterogeneity

5 Statistical Methods for Markov-Generated Increment-Decrement Life Tables with Polynomial Gross Flow Functions

1. Introduction

2. Model Specification

3. Age-Specific Methods for Occurrence/Exposure Rates

4. Marital Dissolution and Remarriage in Sweden: Application and Comparison of Methods

5. Application of the Methods to Survivorship Proportions

6. Concluding Comments

6 Transition Probability Estimation in Increment-Decrement Life Tables: Using Mobility Data from a Census or a Survey

1. Introduction

2. Approach A: Estimation from Mobility Rates

3. Approach B: Estimation from Transition Proportions

4. A Brief Comparison of the Two Alternative Approaches

5. Conclusion

7 Generalizing the Life Table Model to Incorporate Interactions between the Sexes

1. Introduction

2. Life Table Models

3. A TWOFIDS Model for the United States/California 1970

4. Conclusion

Appendix: The TWONUP First Marriage Matrix

Appendix: Input Data for the TWOFIDS Model

8 Multiregional Population Projections by Place of Previous Residence

1. Introduction

2. Stationary and Stable Population Distributions

3. Multiregional Population Projections by Place of Birth

4. Multiregional Population Projections by Place of Previous Residence

5. Native-Dependent Multiregional Population Projections

6. Conclusion

Appendix A: Native-Independent Multistate Projection: Biregional Model

Appendix B: Separation Factors

9 Multiregional Age-Structured Populations with Changing Rates: Weak and Stochastic Ergodic Theorems

1. Introduction

2. The Formalism of Multiregional Population Models

3. Weak Ergodic Theorems for Multiregional Populations Models

4. Stochastic Ergodic Theorems

5. Relative Rates of Convergence

6. Extensions and Applications

10 High- and Low-Intensity Model of Mobility

1. Introduction

2. The High- and Low-Intensity Model of Mobility

3. Solution of the Model

4. Verification of the Model

5. Implementation of the Model

6. A Possible Extension

Appendix

11 Increment-Decrement Life Tables and Semi-Markovian Processes from a Sample Path Perspective

1. Introduction

2. Defining Basic Probabilities on Sample Paths

3. Semi-Markovian Processes

4. Parametric Forms of One-Step Transition Matrices, Competing Risks, and Likelihood Functions

5. One-Step Transition Matrices and Multiple Decrement Life Tables

6. The Kolmogorov Differential Equations

7. Integral Equations for Age-Dependent Semi-Markov Processes

8. Numerical Algorithms for Solving Renewal-Type Equations

12 Population Heterogeneity in Demographic Models

1. Introduction

2. Duration Models and Unobservables

3. Sensitivity of Parameter Estimates

4. Qualitative Properties of Mixtures

5. Estimation in Mixture Models

6. Performance of the EM Algorithm and Revised Estimates for the Kiefer-Neumann Data

7. Discussion and Conclusions

Index

Participants

- No. of pages: 620
- Language: English
- Edition: 1
- Published: September 28, 1982
- Imprint: Academic Press
- eBook ISBN: 9781483269849

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