Description
Age-Period-Cohort analysis has a wide range of applications, from chronic disease incidence and mortality data in public health and epidemiology, to many social events (birth, death, marriage, etc) in social sciences and demography, and most recently investment, healthcare and pension contribution in economics and finance. Although APC analysis has been studied for the past 40 years and a lot of methods have been developed, the identification problem has been a major hurdle in analyzing APC data, where the regression model has multiple estimators, leading to indetermination of parameters and temporal trends. A Practical Guide to Age-Period Cohort Analysis: The Identification Problem and Beyond provides practitioners a guide to using APC models as well as offers graduate students and researchers an overview of the current methods for APC analysis while clarifying the confusion of the identification problem by explaining why some methods address the problem well while others do not.
Features
· Gives a comprehensive and in-depth review of models and methods in APC analysis.
· Provides an in-depth explanation of the identification problem and statistical approaches to addressing the problem and clarifying the confusion.
· Utilizes real data sets to illustrate different data issues that have not been addressed in the literature, including unequal intervals in age and period groups, etc.
Wenjiang Fu is a professor of statistics at the University of Houston. Professor Fu’s research interests include modeling big data, applied statistics research in health and human genome studies, and analysis of complex economic and social science data.
Table of Contents
1. Motivation of Age - Period - Cohort Analysis Examples and Applications
What Is Age-Period-Cohort Analysis?
Why Age - Period - Cohort Analysis?
Four Data Sets in APC Studies
Special Features of These Data Sets
Data Source
R Programming and Video Online Instruction
Suggested Readings
Exercises
2. Preliminary Analysis of Age - Period - Cohort Data - Graphic Methods
D Plots in Age, Period, and Cohort
D Plot in Age, Period, and Cohort
Suggested Readings
Exercises
3. Preliminary Analysis of Age - Period - Cohort Data - Basic Models
Linear Models for Continuous Response
Single Factor Models
Two Factor Models
R Programming for Linear Models
Loglinear Models for Discrete Response
Single Factor Models
Two Factor Models
R Programming for Loglinear Models
Suggested Readings
Exercises
4. Age-Period-Cohort Model - Complexity with Linearly Dependent Covariates
Lexis Diagram and Pattern in Age, Period, and Cohort
Lexis Diagram and Dependence among Age, Period, and Cohort
Explicit Pattern in APC Data with Identical Spans in Age and Period
Implicit Pattern in APC Data with Unequal Spans in Age and Period
Complexity in Full Age - Period - Cohort Model
Regression with Linearly Dependent Covariates
Age-Period-Cohort Models and the Complexity
R Programming for Generating the Design Matrix for APC Models
Suggested Readings
Exercises
5. Age-Period-Cohort Model - The Identification Problem and Various Approaches
The Identification Problem and Confusion
Two Popular Approaches to the Identification Problem
Constraint Approach
Estimable Function Approach
Other Approaches to the Identification Problem
Suggested Readings
Exercises
6. The Intrinsic Estimator, the Rationale and Properties
Structure of Multiple Estimators of Age-Period-Cohort Models
Intrinsic Estimator - Unbiased Estimation and Other Properties
Robust Estimation via Sensitivity Analysis
Summary of Asymptotic Properties of the Multiple Estimators
Computation of the Intrinsic Estimator and Standard Errors
Computation of the Intrinsic Estimator
Computation of the Standard Errors
Suggested Readings
Exercises
7. Data Analysis with Intrinsic Estimator and Comparison with Others
Illustration of Data Analysis with the Intrinsic Estimator
Modeling Lung Cancer Mortality Data among US Males
Intrinsic Estimator of Linear Models
Intrinsic Estimator of Loglinear Models
Modeling the HIV Mortality Data
Intrinsic Estimator of Linear Models
Intrinsic Estimator of Loglinear Models
Illustration of Data Analysis with Constrained Estimators
Illustration of Equality Constraints
Illustration of Non-contrast Constraints
Suggested Readings
Exercises
8. Asymptotic Behavior of the Multiple Estimators - Theoretical Results
Settings and Strategies to Study the Asymptotics of Multiple Estimators
Assumptions and Regularity Conditions for the Asymptotics
Asymptotics of Multiple Estimators
Asymptotics of Multiple Estimators with Fixed t
Asymptotics of Linearly Constrained Estimators
Linear constraint on age effects
Linear constraint on period or cohort effects
Suggested Readings
Exercises
9. Variance Estimation and Selection of Side-condition
Variance Estimation of the Intrinsic Estimator
The Delta Method for the Variance of Period and Cohort Effect Estimates
Comparison of Standard Errors between the PCA and Delta Methods
Selection of Side Condition
Side-conditions for One-way ANOVA Models
Side-conditions for Two-way ANOVA Models
Side-conditions for Age - Period - Cohort Models
Conclusion on Side-condition Selection
10. Unequal Spans in Age Groups and Periods with Applications to Survey Data
APC Data with Unequal Spans
The Intend-to-Collapse (ITC) Method
APC Models for Unequal Spans
Identification Problem and Intrinsic Estimator for Unequal Span Data
Multiple Estimators and Identification Problem
The Intrinsic Estimator for Unequal Span Data
Analyzing APC Data with Unequal Spans by the Intrinsic Estimator
Fitting Unequal Span Data with R Function apclinkfit
Exercises
Bibliography
