Johan H. L. Oud

CONTINUOUS TIME STATE SPACE MODELING OF PANEL DATA BY MEANS OF SEM

Maximum likelihood parameter estimation of the continuous time linear stochastic state space model is considered on the basis of largeN discrete time data using a structural equation modeling (SEM) program. Random subject effects are allowed to be part of the model. The exact discrete model (EDM) is employed which links the discrete time model parameters to the underlying continuous time model parameters by means of nonlinear restrictions. The EDM is generalized to cover not only time-invariant parameters but also the cases of stepwise time-varying (piecewise time-invariant) parameters and parameters varying continuously over time according to a general polynomial scheme. The identification of the continuous time parameters is discussed and an educational example is presented.

An SEM Approach to Continuous Time Modeling of Panel Data: Relating Authoritarianism and Anomia

Panel studies, in which the same subjects are repeatedly observed at multiple time points, are among the most popular longitudinal designs in psychology. Meanwhile, there exists a wide range of different methods to analyze such data, with autoregressive and cross-lagged models being 2 of the most well known representatives. Unfortunately, in these models time is only considered implicitly, making it difficult to account for unequally spaced measurement occasions or to compare parameter estimates across studies that are based on different time intervals. Stochastic differential equations offer a solution to this problem by relating the discrete time model to its underlying model in continuous time. It is the goal of the present article to introduce this approach to a broader psychological audience. A step-by-step review of the relationship between discrete and continuous time modeling is provided, and we demonstrate how continuous time parameters can be obtained via structural equation modeling. An empirical example on the relationship between authoritarianism and anomia is used to illustrate the approach.

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.

Information and other criteria in structural equation model selection

This article presents the results of a simulation study evaluating information criteria in conjunction with other well-known criteria for model selection in structural equation modeling (SEM). Two sets of simulation experiments were performed. In both sets, sample sizes of n = 100,400,1000,6000 were used and the performance of 18 criteria was assessed by the frequency with which each of five analytic models was selected as best by each criterion in 500 replications. In the first set of experiments correctly specified analytic models (noncentrality parameter 0) were entertained in combination with misspecified ones, while in the second set all five models were misspecified. In both sets of experiments, we found that the information criteria perform better than the other criteria overall, but that Cudeck and Brownes cross-validation index ( CVI) remains an attractive option. Within the class of information criteria, Akaikes information criterion (AIC) is found to show some overfitting tendency. We demonst...

The relationship between mutual family relations and child psychopathology.

The associations of the mutual mother-child, father-child, and mother-father relationship and various patterns of family relations with child psychopathology were investigated in a sample of 137 families referred to outpatient mental health services. Assessment of the relative association of the different family dyads showed that both the mother-child and the mother-father relationship were related to child problem behaviour. However, whereas the mother-child relationship was consistently more related to externalising behaviour, the mother-father relationship was particularly related to internalising behaviour. Our findings gave clear support for the cumulative risk model: having more negatively qualified relationships was associated with more problem behaviour. Furthermore, our results suggested a protective influence of the parent-child relationship: having one or two positive parent-child relationships was associated with less problem behaviour. No support was found for the cross-generational coalition hypothesis. Implications for future research are discussed.

How to get rid of W: a latent variables approach to modelling spatially lagged variables

In this paper we propose a structural equation model (SEM) with latent variables to model spatial dependence. Rather than using the spatial weights matrix W, we propose to use latent variables to represent spatial dependence and spillover effects, of which the observed spatially lagged variables are indicators. This approach allows us to incorporate and test more information on spatial dependence and offers more flexibility than the representation in terms of Wy or Wx. Furthermore, we adapt the ML estimator included in the software package Mx to estimate SEMs with spatial dependence. We present illustrations based on Anselins Columbus, Ohio, crime dataset.

Assessment of bidirectional influences between family relationships and adolescent problem behavior: Discrete versus continuous time analysis

In family research, bidirectional influences between the family and the individual are usually analyzed in discrete time. Results from discrete time analysis, however, have been shown to be highly dependent on the length of the observation interval. Continuous time analysis using stochastic differential equations has been proposed to circumvent this problem. The present study examined the bidirectional influences between family relationships and adolescent problem behavior by means of both discrete- and continuous-time cross-lagged panel analysis. The effect of the length of the observation interval on the results from both procedures was investigated. Data were collected from a community sample of 288 Dutch families consisting of a father, a mother, and two of their adolescent children. Whereas results from discrete time analyses differed considerably when a 2-year instead of a 1-year interval between measurements was used, results from continuous time analysis appeared to be less affected by the length of the observation interval. Continuous time analysis revealed family relationship characteristics and levels of adolescent problem behavior to be highly stable over time. Relatively small cross-lagged effects were found between family relationships and adolescent problem behaviors.

Current and Recollected Perceptions of Family Relationships: The Social Relations Model Approach Applied to Members of Three Generations

Data from 81 three-generation families (comprising 567 participants) were analyzed to assess perceptions of current-family and family-of-origin relationships. The dimensions studied (Restrictiveness, Justice, Affection, and Trust) were derived from the family systems theories as developed by Boszormenyi-Nagy (I. Boszormenyi-Nagy & B. R. Krasner, 1986; I. Boszormenyi-Nagy & G. Spark, 1984; I. Boszormenyi-Nagy & D. N. Ulrich, 1981) and Stierlin (H. Stierlin, 1974, 1978; H. Stierlin, I. Rucker-Embden, N. Wetzel, & M. Wirsching, 1980). The social relations model (SRM) was used to disentangle the perception scores into characteristics of the perceiver (actor component), the target (partner component), and the family as a whole. For both current-family and family-of-origin relationships, significant variances of actor as well as family components were found. Empirical evidence for an association between current-family and (mothers) family-of-origin components was only found on the dimension of Restrictiveness. Clear differences were found between the means of current-family and family-of-origin perceptions, which could be explained by differences between current and past SRM components.

Longitudinal research with latent variables

The book combines longitudinal research and latent variable research, i.e. it explains how longitudinal studies with objectives formulated in terms of latent variables should be performed. The emphasis is on exposing how the methods are applied. Because currently longitudinal research with latent variables follows different approaches with different histories, different types of research questions, and different computer programs to perform the analysis, the book is divided in nine chapters. Starting from (a) some background information about the specific approach (short history and main publications), the chapter (b) describes the type of research questions the approach is able to answer, (c) gives the statistical and mathematical explanation of the model(s) used in the data analysis, (d) discusses the input and output of the program(s) used, and (e) provides one or more examples with typical data sets enabling the readers to apply the programs themselves.

Longitudinal Factor Score Estimation Using the Kalman Filter

The advantages of the Kalman filter as a factor score estimator in the presence of longitudinal data are described. Because the Kalman filter presup poses the availability of a dynamic state space model, the state space model is reviewed first, and it is shown to be translatable into the LISREL model. Several extensions of the LISREL model specification are discussed in order to enhance the applicability of the Kalman filter for behavioral research data. The Kalman filter and its main properties are summarized. Relationships are shown between the Kalman filter and two well- known cross-sectional factor score estimators: the regression estimator, and the Bartlett estimator. The indeterminacy problem of factor scores is also discussed in the context of Kalman filtering, and the differences are described between Kalman filtering on the basis of a zero-means and a structured-means LISREL model. By using a structured-means LISREL model, the Kalman filter is capable of estimating absolute latent develop mental curves. An educational research example is presented.