Stagewise cognitive development: an application of catastrophe theory.

In this article an overview is given of traditional methodological approaches to stagewise cognitive developmental research. These approaches are evaluated and integrated on the basis of catastrophe theory. In particular, catastrophe theory specifies a set of common criteria for testing the discontinuity hypothesis proposed by Piaget. Separate criteria correspond to distinct methods used in cognitive developmental research. Such criteria are, for instance, the detection of spurts in development, bimodality of test scores, and increased variability of responses during transitional periods. When a genuine stage transition is present, these criteria are expected to be satisfied. A revised catastrophe model accommodating these criteria is proposed for the stage transition in cognitive development from the preoperational to the concrete operational stage.     

Comment on fitting MA time series by structural equation models

In a recent paper by van Buuren (1997) it is concluded that parameter estimates in pure moving-average (MA) models, obtained by software for fitting structural equation models (SEMs), are biased and inefficient. In this comment it is shown that this negative finding may be due to a particular feature of van Buuren's simulation experiment. A modified procedure for fitting MA models by means of SEM software is proposed, and some of its implications are discussed.     

A framework for ML estimation of parameters of (mixtures of) common reaction time distributions given optional truncation or censoring

We present a framework for distributional reaction time (RT) analysis, based on maximum likelihood (ML) estimation. Given certain information relating to chosen distribution functions, one can estimate the parameters of these distributions and of finite mixtures of these distributions. In addition, left and/or right censoring or truncation may be imposed. Censoring and truncation are useful methods by which to accommodate outlying observations, which are a pervasive problem in RT research. We consider five RT distributions: the Weibull, the ex-Gaussian, the gamma, the log-normal, and the Wald. We employ quasi-Newton optimization to obtain ML estimates. Multicase distributional analyses can be carried out, which enable one to conduct detailed (across or within subjects) comparisons of RT data by means of loglikelihood difference tests. Parameters may be freely estimated, estimated subject to boundary constraints, constrained to be equal (within or over cases), or fixed. To demonstrate the feasibility of ML estimation and to illustrate some of the possibilities offered by the present approach, we present three small simulation studies. In addition, we present three illustrative analyses of real data.     

The power to detect sex differences in IQ test scores using Multi-Group Covariance and Means Structure Analyses

Research into sex differences in general intelligence, g, has resulted in two opposite views. In the first view, a g-difference is nonexistent, while in the second view, g is associated with a male advantage. Past research using Multi-Group Covariance and Mean Structure Analysis (MG-CMSA) found no sex difference in g. This failure raised the question whether the g-difference is truly absent or whether MG-CMSA lacked statistical power to detect it. The present study used the likelihood ratio test to investigate the power to detect a g-difference in the WAIS-III factor structure with MG-CMSA. Various situations were examined including those reported in the literature. Results showed that power varies greatly among different scenarios. The scenarios based on previous results were associated with power coefficients of about 0.5–0.6. Implications of these findings are discussed in the light of research into sex differences in IQ.     

The integrated trait–state model

It has been acknowledged that both trait and state contribute to psychological measurements. However, existing structural equation models for disentangling these sources of variability are based on assumptions that are not tenable in the light of empirical results. A new model is presented, termed the integrated trait–state (ITS) model, which both decomposes state and trait variance and allows one to test the assumptions that underly existing approaches. This is illustrated with an empirical example. The relationship between the ITS model and other analytic approaches as well as conceptual models of traits and states are discussed.     

Finite mixture distribution models of simple discrimination learning

Through the application of finite mixture distribution models, we investigated the existence of distinct modes of behavior in learning a simple discrimination. The data were obtained in a repeated measures study in which subjects aged 6 to 10 years carried out a simple discrimination learning task. In contrast to distribution models of exclusively rational learners or exclusively incremental learners, a mixture distribution model of rational learners and slow learners was found to fit the data of all measurement occasions and all age groups. Hence, the finite mixture distribution analysis provides strong support for the existence of distinct modes of learning behavior. The results of a second experiment support this conclusion by crossvalidation of the models that fit the data of the first experiment. The effect of verbally labeling the values on the relevant stimulus dimension and the consistency of behavior over measurement occasions are related to the mixture model estimates.     

A generalized linear factor model approach to the hierarchical framework for responses and response times

We show how the hierarchical model for responses and response times as developed by van der Linden (2007), Fox, Klein Entink, and van der Linden (2007), Klein Entink, Fox, and van der Linden (2009), and Glas and van der Linden (2010) can be simplified to a generalized linear factor model with only the mild restriction that there is no hierarchical model at the item side. This result is valuable as it enables all well‐developed modelling tools and extensions that come with these methods. We show that the restriction we impose on the hierarchical model does not influence parameter recovery under realistic circumstances. In addition, we present two illustrative real data analyses to demonstrate the practical benefits of our approach.