SEM Based CARMA Time Series Modeling for Arbitrary N.

This article explains in detail the state space specification and estimation of first and higher-order autoregressive moving-average models in continuous time (CARMA) in an extended structural equation modeling (SEM) context for N = 1 as well as N > 1. To illustrate the approach, simulations will be presented in which a single panel model (T = 41 time points) is estimated for a sample of N = 1,000 individuals as well as for samples of N = 100 and N = 50 individuals, followed by estimating 100 separate models for each of the one-hundred N = 1 cases in the N = 100 sample. Furthermore, we will demonstrate how to test the difference between the full panel model and each N = 1 model by means of a subject-group-reproducibility test. Finally, the proposed analyses will be applied in an empirical example, in which the relationships between mood at work and mood at home are studied in a sample of N = 55 women. All analyses are carried out by ctsem, an R-package for continuous time modeling, interfacing to OpenMx.

Development and Validation of the Computerized Family Relations Test for Children.

The aim of the present study was to develop and investigate the psychometric properties of the Computerized Family Relations Test (CFRT) for children. This test assesses the quality of family relationships with the mother and father from a child's perspective. The CFRT consists of six scales relating to control (Restrictiveness and Justice), and support (Affection, Vulnerability, Acknowledgment, and Trust) within the family relationships. CFRT is an innovative approach to the Dutch Nijmegen Family Relations Test (NFRT) developed by Oud and Welzen (1989). The administration of the test has been computerized and graphical representations of female and male silhouettes were included to facilitate the child's parental identification. In total, 404 primary school children, aged 8 to 13 years (M = 11.0; SD = 1.17), took part in this study. The CFRT's reliability was assessed by McDonald's omega coefficients, and ranged from 0.71 to 0.86, except for Vulnerability which achieved the lowest reliability 0.57 for mothers' ratings and 0.56 for fathers' ratings. The test-retest procedure revealed higher stability for the ratings on father-child relationships of 0.71 compared to mother-child relationships of 0.67. Confirmatory factor analysis indicated that a six-factor model provided an adequate fit. Measurement invariance across the children's assessments of the quality of family relationships was achieved. The construct validity of CFRT was assessed by examining differences in the child's ratings of the relationships with the mother and father, the child's gender, and associations of CFRT scales with other variables such as depression, anxiety symptoms, and prosocial behavior.

The Relationships between Individualism, Nationalism, Ethnocentrism, and Authoritarianism in Flanders: A Continuous Time-Structural Equation Modeling Approach.

This article analyzes the relationships among nationalism (N), individualism (I), ethnocentrism (E), and authoritarianism (A) in continuous time (CT), estimated as a structural equation model. The analysis is based on the General Election Study for Flanders, Belgium, for 1991, 1995, and 1999. We find reciprocal effects between A and E and between E and I as well as a unidirectional effect from A on I. We furthermore find relatively small, but significant, effects from both I and E on N but no effect from A on N or from N on any of the other variables. Because of its central role in the N-I-E-A complex, mitigation of authoritarianism has the largest potential to reduce the spread of nationalism, ethnocentrism, and racism in Flanders.

Continuous time modelling with individually varying time intervals for oscillating and non-oscillating processes.

When designing longitudinal studies, researchers often aim at equal intervals. In practice, however, this goal is hardly ever met, with different time intervals between assessment waves and different time intervals between individuals being more the rule than the exception. One of the reasons for the introduction of continuous time models by means of structural equation modelling has been to deal with irregularly spaced assessment waves (e.g., Oud & Delsing, 2010). In the present paper we extend the approach to individually varying time intervals for oscillating and non-oscillating processes. In addition, we show not only that equal intervals are unnecessary but also that it can be advantageous to use unequal sampling intervals, in particular when the sampling rate is low. Two examples are provided to support our arguments. In the first example we compare a continuous time model of a bivariate coupled process with varying time intervals to a standard discrete time model to illustrate the importance of accounting for the exact time intervals. In the second example the effect of different sampling intervals on estimating a damped linear oscillator is investigated by means of a Monte Carlo simulation. We conclude that it is important to account for individually varying time intervals, and encourage researchers to conceive of longitudinal studies with different time intervals within and between individuals as an opportunity rather than a problem.

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.

Reply to Steele & Ferrer: Modeling Oscillation, Approximately or Exactly?

This article addresses modeling oscillation in continuous time. It criticizes Steele and Ferrer's article "Latent Differential Equation Modeling of Self-Regulatory and Coregulatory Affective Processes" (2011), particularly the approximate estimation procedure applied. This procedure is the latent version of the local linear approximation procedure based on Boker (2001) and Boker, Neale, and Rausch (2004). It furthermore presents two exact alternative estimation procedures, one using filter techniques and the other using structural equation modeling.

Perceptions of problem behavior in adolescents' families: perceiver, target, and family effects.

Considerable research has focused on the reliability and validity of informant reports of family behavior, especially maternal reports of adolescent problem behavior. None of these studies, however, has based their orientation on a theoretical model of interpersonal perception. In this study we used the social relations model (SRM) to examine family members' reports of each others' externalizing and internalizing problem behavior. Two parents and two adolescents in 69 families rated each others' behavior within a round-robin design. SRM analysis showed that within-family perceptions of externalizing and internalizing behaviors are consistently due to three sources of variance; perceiver, target, and family effects. A family/contextual effect on informant reports of problem behavior has not been previously reported.

Male and female development of delinquency during adolescence and early adulthood: a differential autoregressive model of delinquency using an overlapping cohort design.

Although it is well known that during adolescence the delinquent involvement of females is consistently less when compared to male involvement, it remains an important question whether the development of delinquency has a similar trajectory for both sexes. The main hypothesis tested is whether sex differences in delinquency, specifically growth, peak age, and decline, are constant. An autoregression model in continuous time, implemented as a structural equation model, is used for the description of the development of delinquency in males and females. The data are collected in an overlapping cohort design, and both within-person and between-persons data are integrated into a single model. The result shows that the involvement with delinquency over time is different for males and females. The main difference increases up to the age of 16, and decreases thereafter. The model indicates that both sexes reach the maximum in delinquency at the same age. It is concluded that males and females differ both in their start level at age 12 and in the amount of change with age.

Level validity of self-report whole-family measures.

This article introduces an approach to testing the level validity of family assessment instruments (i.e., whether a family instrument measures family functioning at the level of the system it purports to assess). Two parents and 2 adolescents in 69 families rated the warmth in each of their family relationships and in the family as a whole. Family members' ratings of whole-family warmth assessed family functioning not only at the family level (i.e., characteristics of the family as a whole) but also at the individual level of analysis (i.e., characteristics of family members as raters), indicating a lack of level validity. Evidence was provided for the level validity of a latent variable based on family members' ratings of whole-family warmth. The findings underscore the importance of assessing the level validity of individual ratings of whole-family functioning.

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 (mother's) 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.

Parents' reasons for enrolment of their motor-disabled child in a Dutch therapeutic toddler class.

This article describes and categorizes the reasons why parents enrol their motor-disabled children in the therapeutic toddler class, a special centre-based service in early intervention. The results among a representative Dutch sample of 84 mothers showed that child-related reasons were considered more important than family- and parent-related reasons. Family- and parent-related reasons were influenced by the presence and severity of the child's behaviour problems. The results of this study are discussed within the context of parental expectations in early intervention, and the concept of family centredness.