Age-Period-Cohort Models

Approaches and Analyses with Aggregate Data

By Robert O'Brien

© 2014 – Chapman and Hall/CRC

216 pages | 25 B/W Illus.

Purchasing Options:
Hardback: 9781466551534
pub: 2014-08-19
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About the Book

Develop a Deep Understanding of the Statistical Issues of APC Analysis

Age–Period–Cohort Models: Approaches and Analyses with Aggregate Data presents an introduction to the problems and strategies for modeling age, period, and cohort (APC) effects for aggregate-level data. These strategies include constrained estimation, the use of age and/or period and/or cohort characteristics, estimable functions, variance decomposition, and a new technique called the s-constraint approach.

See How Common Methods Are Related to Each Other

After a general and wide-ranging introductory chapter, the book explains the identification problem from algebraic and geometric perspectives and discusses constrained regression. It then covers important strategies that provide information that does not directly depend on the constraints used to identify the APC model. The final chapter presents a specific empirical example showing that a combination of the approaches can make a compelling case for particular APC effects.

Get Answers to Questions about the Relationships of Ages, Periods, and Cohorts to Important Substantive Variables

This book incorporates several APC approaches into one resource, emphasizing both their geometry and algebra. This integrated presentation helps researchers effectively judge the strengths and weaknesses of the methods, which should lead to better future research and better interpretation of existing research.


"This is an excellent book on age–period–cohort (APC) models for the analysis of data from demography and related fields. … an excellent work with wonderful resources on APC models. … It will be very useful to research scholars … looking for several advanced APC approaches. The book effectively presents the strengths and weaknesses of various statistical methods of APC analysis, which should lead to advanced future research and better interpretation of existing research."

International Statistical Review, 2015

Table of Contents

Introduction to the Age, Period, and Cohort Mix


Interest in Age, Period, and Cohort

Importance of Cohorts

Plan for the Book

Multiple Classification Models and Constrained Regression


Linearly Coded Age–Period–Cohort (APC) Model

Categorically Coded APC Model

Generalized Linear Models

Null Vector

Model Fit

Solution Is Orthogonal to the Constraint

Examining the Relationship between Solutions

Differences between Constrained Solutions as Rotations of Solutions

Solutions Ignoring One or More of the Age, Period, or Cohort Factors

Bias: Constrained Estimates and the Data Generating Parameters

Unbiased Estimation under a Constraint

A Plausible Constraint with Some Extra Empirical Support

Geometry of APC Models and Constrained Estimation


General Geometric View of Rank Deficient by One Models

Generalization to Systems with More Dimensions

APC Model with Linearly Coded Variables

Equivalence of the Geometric and Algebraic Solutions

Geometry of the Multiple Classification Model

Distance from Origin and Distance along the Line of Solutions

Empirical Example: Frost’s Tuberculosis Data

Summarizing Some Important Features from the Geometry of APC Models

Problem with Mechanical Constraints

Estimable Functions Approach


Estimable Functions

lsv Approach for Establishing Estimable Functions in APC Models

Some Examples of Estimable Functions Derived Using the lsv Approach

Comments on the lsv Approach

Estimable Functions with Empirical Data

More Substantive Examination of Differences of Male and Female Lung Cancer Mortality Rates

Partitioning the Variance in APC Models


Age–Period–Cohort Analysis of Variance (APC ANOVA) Approach to Attributing Variance

APC Mixed Model

Hierarchical APC Model

Empirical Example Using Homicide Offending Data

Factor-Characteristic Approach


Characteristics for One Factor

Characteristics for Two or More Factors

Variance Decomposition for Factors and for Factor Characteristics

Empirical Examples: Age–Period-Specific Suicide Rates and Frequencies

Age–Period–Cohort Characteristics (APCC) Analysis of Suicide Data with Two Cohort Characteristics

Age–Cohort–Period Characteristics (ACPC) Analysis of the Suicide Data with Two Period Characteristics

Age–Period–Characteristics–Cohort Characteristics Model

Approaches Based on Factor Characteristics and Mechanism

Additional Features and Analyses of Factor-Characteristic Models

Conclusions: An Empirical Example


Empirical Example: Homicide Offending


Conclusions and References appear at the end of each chapter.

About the Author

Robert M. O’Brien is a professor emeritus of sociology at the University of Oregon. He specializes in criminology and quantitative methods and has published extensively in both areas. In what is labeled semiretirement, he coedits Sociological Perspectives with James R. Elliott and Jean Stockard and works on research projects.

About the Series

Chapman & Hall/CRC Statistics in the Social and Behavioral Sciences

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General
MEDICAL / Epidemiology