Event History Analysis

Statistical theory and Application in the Social Sciences

Hans-Peter Blossfeld, Alfred Hamerle, Karl Ulrich Mayer

• Publisher: Psychology Press
• Year: 2014
• ISBN:
  9781317785712
• Edition: 1
• Topic: Psychology
• Subtopic: History & Theory in Psychology
• Index: Psychology

Serving as both a student textbook and a professional reference/handbook, this volume explores the statistical methods of examining time intervals between successive state transitions or events. Examples include: survival rates of patients in medical studies, unemployment periods in economic studies, or the period of time it takes a criminal to break the law after his release in a criminological study. The authors illustrate the entire research path required in the application of event-history analysis, from the initial problems of recording event-oriented data to the specific questions of data organization, to the concrete application of available program packages and the interpretation of the obtained results. Event History Analysis: * makes didactically accessible the inclusion of covariates in semi-parametric and parametric regression models based upon concrete examples * presents the unabbreviated close relationship underlying statistical theory * details parameter-free methods of analysis of event-history data and the possibilities of their graphical presentation * discusses specific problems of multi-state and multi-episode models * introduces time-varying covariates and the question of unobserved population heterogeneity * demonstrates, through examples, how to implement hypotheses tests and how to choose the right model.

Chapter 1:

Aim and Structure of the Book

This book tries to give a comprehensive overview of the most important methods of event history analysis. By “event history analysis” we mean statistical methods used to analyze time intervals between successive state transitions or events. The number of states occupied by the analyzed units are finite, but the events may occur at any point in time. Consequently, in event history analyses statistical methods for analyzing stochastic processes with discrete states and continuous time are used.

A wide range of statistical tools are available today to analyze event history data as exemplified in a variety of models, approaches, and methods. These statistical methods have, however, not yet found their place in standard statistics textbooks. There are several reasons for this. First, event history analysis applies stochastic models that are not often found in normal applications. Second, incomplete or censored data frequently occur only in very specific research designs. And third, due to the development and application of these methods in various disciplines such as medicine, demography, technology, economics, and the social sciences, the terminology is not uniform and thus the methods are not easily accessible to the user.

Consequently, the aim of this book is to show how modern statistical methods can be used to analyze event history data as well as to give some examples of event history analysis in practical research. To complement a comprehensive presentation of the statistical background we will use examples taken from current sociological research to illustrate the applications of event history analysis.

Following this overview (Chapter 1), Chapter 2 first illustrates three different ways in which in event history analysis problems are conceptualized and solved. Section 2.1 discusses the wide palette of subject areas in which event history analysis may be applied. Section 2.2 reviews the design of the German Life History Study (GLHS) which forms the empirical base of the examples used in Chapters 4 to 6. Finally, the theoretical and methodological advantages of collecting and analyzing event history data as compared to cross-sectional and traditional panel data are discussed in Section 2.3.

The statistical foundations of event history analysis are presented in Chapter 3. In addition to the classification of event history analysis within the structure of stochastic processes, Section 3.1 presents the basic concepts of event history analysis such as the hazard rate, the survivor function, cumulative hazard rates, and so on, as well as nonparametric methods of estimation including the life table method and the Kaplan-Meier estimator (Section 3.2). Of special importance for the textbook is Section 3.3 in which the inclusion of explanatory variables in semiparametric Cox models and parametric models such as the exponential, Weibull, Gompertz-(Makeham), and the log-logistic model are presented. The general theory of multiple state and multiple event cases are then given in Sections 3.4 and 3.5. Section 3.6 follows with the maximum likelihood estimation of unknown model parameters and Section 3.7 discusses methods of constructing hypotheses tests and how to choose models. The inclusion of time-dependent covariates is dealt with in Section 3.8, and models with unobserved population heterogeneity are presented in Section 3.9. Finally, the theoretically oriented Chapter 3 closes with a brief presentation of hazard rate models with discrete time.

Chapters 4 to 6 are specifically designed for the potential users of event history analysis in research. One may, however, also use the material in these chapters as a type of workbook to introduce the empirical analysis of occupational and job trajectories within labor market research. Based on the GLHS, the strategies required for preparing and evaluating event history data are discussed in a stepwise fashion. Using concrete examples, it is then shown how the formulation of a research question may be realized at the methodological and statistical level, which available computer program packages are adequate (SPSS, BMDP, GLIM, RATE, SAS) for specific analytical aims, how the control cards must be structured, and how the results of the analyses are to be interpreted and evaluated.

Chapter 4 looks at aspects of the technical implementation of event history data structures (Section 4.1) and the various ways to present them graphically (Section 4.2). The application of the life table method and the Kaplan-Meier estimator are also discussed (Section 4.3).

Chapter 5 focuses on the application of Cox models and the partial likelihood estimation. After an examination of the proportionality assumption in Section 5.1, the interpretation of the Cox model is discussed in detail in Section 5.2. Model choice with the aid of stepwise regression is demonstrated in Section 5.3. Especially important for the application of event history analysis in economics and the social sciences are those instances in which time-dependent covariates are introduced into a Cox model (Section 5.4) and the practical application of the multiple state cases (Section 5.5).

Chapter 6 is devoted to the application of parametric models. After the graphical examination of the distribution assumptions in Section 6.1, Section 6.2 discusses in detail the exponential model, its interpretation and residual analysis. This is followed by examples of introducing time-dependent covariates with the aid of episode splitting (Section 6.3) and examples of models with periodical durations (Section 6.4). Special duration models are presented in Section 6.5, whereby extensive interpretative examples and residual tests of the Gompertz-(Makeham) (Section 6.5.1), the Weibull (Section 6.5.2), the log-logistic (Section 6.5.3), and the lognormal distributions (Section 6.5.4) are given. Section 6.6 concludes with applications and examples of unobserved population heterogeneity for parametric models.

Chapter 2:

Domains and Rationale for the Application of Event History Analysis

In the fields of economics and the social sciences there are many good reasons for studying the processes and course of development. First of all, an adequate description of reality necessitates the systematic characterization of processes, change, and transitions. Naturally, this proposal is not new. However, interest in characterizing change has increased in a time that is seen as the turning point for many middle and long-term economic and social developments. Recently, it has been recognized that explanations based upon cross-sectional data are appropriate only in the relatively rare cases where there is no change in causal variables (Tuma and Hannan, 1984; Petersen, 1988). In other situations processes of change are best comprehended with the aid of longitudinal data. Furthermore, only those models of processes that capture the right causal mechanisms, and so do more than just account for certain outcomes, should be used as the basis of rational political intervention.

In the past, in the field of economics and the social sciences, the possibility to measure and formalize processes using mathematical models was rather limited. This was due, not only to the lack of available data, but also to the lack of mathematical and statistical methods. The application of differential equations requires continuously measured metric variables over time (Hannan, Blossfeld, and Schömann, 1988). These variables are sometimes available in economics as monetary units, but rarely in other social sciences. Two- and multiple-wave panel studies collect—as we show in Section 2.3—processes over time incompletely, and as a rule are distorted by externally set time points of data collection. On the other hand, time series analysis and the numerous types of econometric models require a large number of points of measurement with constant intervals.

Nowadays event histories are increasingly being collected or made available in which the exact time of transition between states of the unit analyzed are registered. Such data offers information about the exact duration until events and their sequence occur. In addition to these durations or waiting times, variables that individually or in combination influence the timing of an event are of interest. These may be time stable characteristics or attributes that vary over time.

2.1 Application Examples

In the following, some examples are presented that illustrate the specific way in which in event history analysis problems are conceptualized. It should then become quite clear, that event history analysis is amenable to a wide range of questions.

Example 1: Unemployment Studies

In labor market research, event history analysis has been applied to the study of unemployment (Heckman and Borjas, 1980; Flinn and Heckman, 1983; Heckman and Singer, 1982, 1984a; Hamerle, 1988; Sørensen, 1988; Hujer and Schneider, 1988). These studies start from the idea that in analyzing unemployment, cross sections of unemployed or the number of entrants into unemployment in a given period are only partially informative and may even be misleading. Such indicators do not permit differentiation between short and long-term unemployment, and time-dependent covariates may not be included in the analysis.

In unemployment studies, the successive phases of unemployment a worker experiences represent the “duration” variable that is included in event history analyses. Periods of unemployment might be terminated due to various reasons, for example, by beginning a new occupation, through governmental job programs, re-education or re-training, retirement or the recognition of an employment disability. Such different end states may be formulated and examined as “competing risks” or multiple state models.

Example 2: Consumer Behavior Studies

A wide range of applications for event history analysis are to be found in the area of consumer research. Various product brands are offered for sale in a market. Consumers choose and purchase one of the brand names and, at a later point in time, they may either purchase the same brand again or switch to another brand. In this example, an episode or duration is equivalent to the time a consumer sticks to a given product. The states are initiated by the various brand names.

According to the methods presented in this book, the durations of brand loyalty may be related to exogeneous influences, some of which may change over time. Such influence factors include demographic variables (e.g., age, sex, family status, household size), socio-economic characteristics (e.g., income, education, occupation, social status), geographical aspects (metropolitan area, countryside location), or psychological conditions (e.g., personal attitudes, preferences, price awareness, quality awareness, buying habits). Furthermore, the duration a product is purchased, may also depend upon previous experiences with the commodity. Data from the prior history of the consumer process can be included in models and analyses of consumer behavior with the aid of the methods presented in this book.

Example 3: Medical Studies on the Course of Illness

In recent years the methods discussed in this book have been used in analyses of the healing process and survival time in medical and epidemiological studies (see, e.g., Kalbfleisch and Prentice, 1980 and the examples discussed there). Most of these studies deal with one or more absorbing end states. Here, “absorbing” means that once a respective end state has been obtained it is no longer possible to leave it, as, for example, is the case in the death of a patient.

There are few medical multiepisode models in the empirical literature although they are often appropriate. For example, the course of an illness is usually a succession of various stages characterized by events such as remission or death. Hamerle (1985b), for example, studied in female patients, the periods of nonillness following a breast cancer operation. One of the interesting points with regard to this example is the finding that the time period of nonillness appeared to be an especially good predictor of the final survival rate. In this example, separate examinations of the respective phases with single episode models were not adequate descriptors of the problem because they did not take into consideration the inherent dependence of the events and their temporal occurrence. In this book, we suggest methods to deal with special cases like these.

Example 4: Learning Experiments in Psychology and Instruction Research

In the psychology of learning, event history analysis may be used to obtain information regarding the temporal process of learning. The durations being modeled and analyzed here are simply the time spells required for learning some specific fact or task. Here it is possible to observe the speed of learning in relationship to personal and environmental factors.

In practical research on instruction, for example, event history analysis based upon video recordings has been applied to evaluate the concentration spells of pupils. One would ask, for example, whether instructional groups within classes or level of achievement influenced the concentration levels of pupils (Felml...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Foreword
• 1. Aim and Structure of the Book
• 2. Domains and Rationale for the Application of Event History Analysis
• 3. The Statistical Theory of Event History Analysis
• 4. Data Organization and Descriptive Methods
• 5. Semi-Parametric Regression Models: The Cox Proportional Hazards Model
• 6. Parametric Regression Models
• Appendices
• References
• Index