Philippe Rast
Modelling individual differences in nonlinear change using structured growth models
Authors
Philippe Rast (University of Zurich)
The aim of this talk is to show ways to model inherently nonlinear trajectories
by means of structured growth curve models using two different functions,
namely the hyperbolic function, as proposed by Mazur and Hastie (1978)
and the exponential function as advocated by Heathcote, Brown, and Mewhort
(2000), which both result in three learning parameters: Initial performance (beta),
learning rate (gamma), and potential maximum performance (alpha). Note that basically
all functions that are part of the Richards family can be used in non-linear
modelling. One approach to model non-linear change is to use non-linear mixed
effects procedures as provided in statistics packages as R (nlme) or SAS (PROC
NLMIXED) which, however, are cumbersome and computationally intense. As
a viable alternative, Browne (1993; Browne & Du Toit, 1991) suggested to apply
structured latent curve models, which impose specific nonlinear constraints on
the pattern matrix of otherwise standard latent growth curve models. Combining
the non-linear mixed models approach with structural equation techniques
leads to estimable latent curve models who offer one the possibility to
model interindividual differences in intraindividual change and the inclusion of
explanatory variables that may account for the diversity in longitudinal trajectories.
This more manageable and tractable approach is demonstrated in a
sample using verbal learning data from six trials.
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Daniel Zimprich
Analyzing Longitudinal Data Using Adaptive Splines with Random Effects
Authors
Daniel Zimprich (University of Zurich)
During the last years, the linear mixed model has become the standard for analyzing longitudinal data. If, however, the longitudinal trajectory of the repeated measurements is inherently non-linear, an alternative to parametric non-linear models as, e.g., implemented in SAS NLMIXED or the nlme module of R, is given by adaptive spline models with random effects. They combine nonparametric techniques (B-splines, kernel smoothing, piecewise polynomials) with random effects. The present talk aims at detailing the application and interpretation of adaptive splines by analysing a example data coming from the Bonn Longitudinal Study of Aging. In a sample of 191 older adults, the WAIS subtest Block Design was measured across six measurement occa-sions across a time interval of up to 18 years. An adaptive splines analyses of these data pro-vided new insights into the cognitive ageing process, because results showed that, depending on the period of change, there are different influences on interindividual differences in intraindi-vidual change.
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Susanne Eschmann
Mixed Effects Models for Binary Outcome Data from a Longitudinal Study in Adolescents and Young Adults
Authors
Susanne Eschmann (University of Zurich)
Daniel Zimprich (University of Zurich)
Christa Winkler Metzke (University of Zurich)
Hans-Christoph Steinhausen (University of Zurich)
Objective: Psychological outcome variables are binary quite frequently. Typical examples include the presence or absence of a syndrome.
Method: In the present study, longitudinal change in a binary variable (0 = substance use not at risk versus 1 = substance use at risk) was modelled. Data of 593 adolescents (Mean age at first measurement occasion: 13.6 years, SD = 1.6; 284 males, 309 females) come from the Zurich Psychology and Psychopathology Study (ZAPPS), covering three measurement occasions across seven years. A probit linear effects model of longitudinal change was imposed in order to capture the probability of becoming an at-risk-substance-user.
Results: Results show that, across age, the risky substance use trajectory was non-linear and declined in early adulthood. Moreover, females showed consistently lower increases of substance use at risk. Finally, adolescents with externalising problems at first assessment showed a stronger increase in substance use at risk. Conclusions: It’s possible to model substance use at risk in youth to obtain a pattern with associated and predictive factors.
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Thomas Ledermann
Analyzing mediation processes in dyadic research on the individual and dyadic level
Authors
Thomas Ledermann (University of Fribourg)
Siegfried Macho (University of Fribourg)
Guy Bodenmann (University of Fribourg)
Models of mediated effects are common and of great importance in social sciences as they provide information about causal processes that are mediated by one or more set of intervening variables. In this paper a framework is presented for analyzing mediation in dyadic research using Structural Equation Modeling. First two conceptually different types of methodological models are introduced that are called the Common Fate Mediator Model, and Actor-Partner Mediator Model. Second, a procedure for testing mediation on the dyad-level is specified using the Common Fate Mediator Model that ought to be used if variables measured on the individual level are indicators of dyad-common factors (e.g., marital stress) and if the relations between the variables should be analyzed on the dyad-level. Third, the method and the application of the Common Fate Mediator Model are illustrated using data on dyadic coping, stress and marital quarreling in heterosexual couples. Fourth, the procedure for evaluating mediation on the individual level is explicated using the Actor-Partner Mediator Model that may be suitable, if the relations between the variables ought to be analyzed on the individual level. Fifth, the function of this test procedure along with the Actor Partner Mediator Model is demonstrated using data on relationship external and internal daily stress and marital quarreling. Finally, the possibility of statistically equivalent models and the problem of omitted variables are discussed.
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Siegfried Macho
Estimation and Causal Interpretation of Mediator Effects
Authors
Siegfried Macho (University of Fribourg)
The problem of inconsistent estimation of the mediator effect resulting from model misspecification due to omitted variables is considered in the context of the three variable mediator model. Two causal configurations of measured and omitted variables prevent, in general, the consistent estimation of the mediator effect: (a) omitted common causes affecting the mediator variable as well as at least one other measured variable, and (b) reciprocal causation mediated by omitted variables between any pair of variables included in the model. An instrumental variable procedure is delineated that permits the testing for relevant omitted variables and enables the consistent estimation of the mediator effect in case of relevant variables being left out. Implications for the causal interpretation of mediator effects are discussed.
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