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Über dieses Buch

Since Charles Spearman published his seminal paper on factor analysis in 1904 and Karl Joresk ¨ og replaced the observed variables in an econometric structural equation model by latent factors in 1970, causal modelling by means of latent variables has become the standard in the social and behavioural sciences. Indeed, the central va- ables that social and behavioural theories deal with, can hardly ever be identi?ed as observed variables. Statistical modelling has to take account of measurement - rors and invalidities in the observed variables and so address the underlying latent variables. Moreover, during the past decades it has been widely agreed on that serious causal modelling should be based on longitudinal data. It is especially in the ?eld of longitudinal research and analysis, including panel research, that progress has been made in recent years. Many comprehensive panel data sets as, for example, on human development and voting behaviour have become available for analysis. The number of publications based on longitudinal data has increased immensely. Papers with causal claims based on cross-sectional data only experience rejection just for that reason.



Chapter 1. Loglinear Latent Variable Models for Longitudinal Categorical Data

Errors and unreliability in categorical data in the form of independent or systematic misclassifications may have serious consequences for the substantive conclusions. This is especially true in the analysis of longitudinal data where very misleading conclusions about the underlying processes of change may be drawn that are completely the result of even very small amounts of misclassifications. Latent class models offer unique possibilities to correct for all kinds of misclassifications. In this chapter, latent class analysis will be used to show the possible distorting influences of misclassifications in longitudinal research and how to correct for them. Both simple and more complicated analyses will be dealt with, discussing both systematic and independent misclassifications.
Jacques A. Hagenaars

Chapter 2. Random Effects Models for Longitudinal Data

Mixed models have become very popular for the analysis of longitudinal data, partly because they are flexible and widely applicable, partly also because many commercially available software packages offer procedures to fit them. They assume that measurements from a single subject share a set of latent, unobserved, random effects which are used to generate an association structure between the repeated measurements. In this chapter, we give an overview of frequently used mixed models for continuous as well as discrete longitudinal data, with emphasis on model formulation and parameter interpretation. The fact that the latent structures generate associations implies that mixed models are also extremely convenient for the joint analysis of longitudinal data with other outcomes such as dropout time or some time-to-event outcome, or for the analysis of multiple longitudinally measured outcomes. All models will be extensively illustrated with the analysis of real data.
Geert Verbeke, Geert Molenberghs, Dimitris Rizopoulos

Chapter 3. Multivariate and Multilevel Longitudinal Analysis

This chapter presents a review of perspectives and methods for analysis of longitudinal data on several related variables. A connection is made with multilevel analysis in which the longitudinal and multivariate dimensions of the data can naturally be subsumed. With the focus on large-scale longitudinal studies of human subjects who are in general disinterested in and not highly motivated by the agenda of the study, methods for dealing with nonresponse are an essential addendum to the analytical equipment.
Nicholas T. Longford

Chapter 4. Longitudinal Research Using Mixture Models

This chapter provides a state-of-the-art overview of the use of mixture and latent class models for the analysis of longitudinal data. It first describes the three basic types mixture models for longitudinal data: the mixture growth, mixture Markov, and latent Markov model. Subsequently, it presents an integrating framework merging various recent developments in software and algorithms, yielding mixture models for longitudinal data that can (1) not only be used with categorical, but also with continuous response variables (as well as combinations of these), (2) be used with very long time series, (3) include covariates (which can be numeric or categorical, as well as time-constant or time-varying), (4) include parameter restrictions yielding interesting measurement models, and (5) deal with missing values (which is very important in longitudinal research). Moreover, it discusses other advanced models, such as latent Markov models with dependent classification errors across time points, mixture growth and latent Markov models with random effects, and latent Markov models for multilevel data and multiple processes. The appendix shows how the presented models can be defined using the Latent GOLD syntax system (Vermunt and Magidson, 2005, 2008).
Jeroen K. Vermunt

Chapter 5. An Overview of the Autoregressive Latent Trajectory (ALT) Model

Autoregressive cross-lagged models and latent growth curve models are frequently applied to longitudinal or panel data. Though often presented as distinct and sometimes competing methods, the Autoregressive Latent Trajectory (ALT) model (Bollen and Curran, 2004) combines the primary features of each into a single model. This chapter: (1) presents the ALT model, (2) describes the situations when this model is appropriate, (3) provides an empirical example of the ALT model, and (4) gives the reader the input and output from an ALT model run on the empirical example. It concludes with a discussion of the limitations and extensions of the ALT model. Our focus is on repeated measures of continuous variables.
Kenneth A. Bollen, Catherine Zimmer

Chapter 6. State Space Methods for Latent Trajectory and Parameter Estimation by Maximum Likelihood

We review Kalman filter and related smoothing methods for the latent trajectory in multivariate time series. The latent effects in the model are modelled as vector unobserved components for which we assume particular dynamic stochastic processes. The parameters in the resulting multivariate unobserved components time series models will be estimated by maximum likelihood methods. Some essential details of the state space methodology are discussed in this chapter. An application in the modelling of traffic safety data is presented to illustrate the methodology in practice.
Jacques J. F. Commandeur, Siem Jan Koopman, Kees van Montfort

Chapter 7. Continuous Time Modeling of Panel Data by means of SEM

After a brief history of continuous time modeling and its implementation in panel analysis by means of structural equation modeling (SEM), the problems of discrete time modeling are discussed in detail. This is done by means of the popular cross-lagged panel design. Next, the exact discrete model (EDM) is introduced, which accounts for the exact nonlinear relationship between the underlying continuous time model and the resulting discrete time model for data analysis. In addition, a linear approximation of the EDM is discussed: the approximate discrete model (ADM). It is recommended to apply the ADM-SEM procedure by means of a SEM program such as LISREL in the model building phase and the EDM-SEM procedure by means of Mx in the final model estimation phase. Both procedures are illustrated in detail by two empirical examples: Externalizing and Internalizing Problem Behavior in children; Individualism, Nationalism and Ethnocentrism in the Flemish electorate.
Johan H. L. Oud, Marc J. M. H. Delsing

Chapter 8. Five Steps in Latent Curve and Latent Change Score Modeling with Longitudinal Data

This paper describes a set of applications of one class of longitudinal growth analysis - latent curve (LCM) and latent change score (LCS) analysis using structural equation modeling (SEM) techniques. These techniques are organized in five sections based on Baltes & Nesselroade (1979). (1) Describing the observed and unobserved longitudinal data. (2) Characterizing the developmental shape of both individuals and groups. (3) Examining the predictors of individual and group differences in developmental shapes. (4) Studying dynamic determinants among variables over time. (5) Studying group differences in dynamic determinants among variables over time. To illustrate all steps, we present SEM analyses of a relatively large set of data from the National Longitudinal Survey of Youth (NLSY). The inclusion of all five aspects of latent curve modeling is not often used in longitudinal analyses, so we discuss why more efforts to include all five are needed in developmental research.
John J. McArdle, Kevin J. Grimm

Chapter 9. Structural Interdependence and Unobserved Heterogeneity in Event History Analysis

This chapter introduces how latent variables are handled in event history analysis, a popular method used to examine both the occurrence and the timing of events. We first emphasize why event history models are popular and what kinds of research questions the model can be used to answer. We also review the major estimation issues, briefly trace the development of event history models, and highlight the differences and similarities across various types of event history models. We then consider how latent variables are handled in event history analysis and demonstrate this with an example of latent variable analysis. In the conclusion we consider possible areas for future research.
Daniel J. Blake, Janet M. Box-Steffensmeier, Byungwon Woo
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