Han L. J. van der Maas

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.

A dynamical model of general intelligence: The positive manifold of intelligence by mutualism

Scores on cognitive tasks used in intelligence tests correlate positively with each other, that is, they display a positive manifold of correlations. The positive manifold is often explained by positing a dominant latent variable, the g factor, associated with a single quantitative cognitive or biological process or capacity. In this article, a new explanation of the positive manifold based on a dynamical model is proposed, in which reciprocal causation or mutualism plays a central role. It is shown that the positive manifold emerges purely by positive beneficial interactions between cognitive processes during development. A single underlying g factor plays no role in the model. The model offers explanations of important findings in intelligence research, such as the hierarchical factor structure of intelligence, the low predictability of intelligence from early childhood performance, the integration/differentiation effect, the increase in heritability of g, and the Jensen effect, and is consistent with current explanations of the Flynn effect.

Comorbidity: A network perspective

The pivotal problem of comorbidity research lies in the psychometric foundation it rests on, that is, latent variable theory, in which a mental disorder is viewed as a latent variable that causes a constellation of symptoms. From this perspective, comorbidity is a (bi)directional relationship between multiple latent variables. We argue that such a latent variable perspective encounters serious problems in the study of comorbidity, and offer a radically different conceptualization in terms of a network approach, where comorbidity is hypothesized to arise from direct relations between symptoms of multiple disorders. We propose a method to visualize comorbidity networks and, based on an empirical network for major depression and generalized anxiety, we argue that this approach generates realistic hypotheses about pathways to comorbidity, overlapping symptoms, and diagnostic boundaries, that are not naturally accommodated by latent variable models: Some pathways to comorbidity through the symptom space are more likely than others; those pathways generally have the same direction (i.e., from symptoms of one disorder to symptoms of the other); overlapping symptoms play an important role in comorbidity; and boundaries between diagnostic categories are necessarily fuzzy.

Why psychologists must change the way they analyze their data: The case of psi: Comment on Bem (2011).

Does psi exist? D. J. Bem (2011) conducted 9 studies with over 1,000 participants in an attempt to demonstrate that future events retroactively affect peoples responses. Here we discuss several limitations of Bems experiments on psi; in particular, we show that the data analysis was partly exploratory and that one-sided p values may overstate the statistical evidence against the null hypothesis. We reanalyze Bems data with a default Bayesian t test and show that the evidence for psi is weak to nonexistent. We argue that in order to convince a skeptical audience of a controversial claim, one needs to conduct strictly confirmatory studies and analyze the results with statistical tests that are conservative rather than liberal. We conclude that Bems p values do not indicate evidence in favor of precognition; instead, they indicate that experimental psychologists need to change the way they conduct their experiments and analyze their data.

An Agenda for Purely Confirmatory Research

The veracity of substantive research claims hinges on the way experimental data are collected and analyzed. In this article, we discuss an uncomfortable fact that threatens the core of psychology’s academic enterprise: almost without exception, psychologists do not commit themselves to a method of data analysis before they see the actual data. It then becomes tempting to fine tune the analysis to the data in order to obtain a desired result—a procedure that invalidates the interpretation of the common statistical tests. The extent of the fine tuning varies widely across experiments and experimenters but is almost impossible for reviewers and readers to gauge. To remedy the situation, we propose that researchers preregister their studies and indicate in advance the analyses they intend to conduct. Only these analyses deserve the label “confirmatory,” and only for these analyses are the common statistical tests valid. Other analyses can be carried out but these should be labeled “exploratory.” We illustrate our proposal with a confirmatory replication attempt of a study on extrasensory perception.

An EZ-diffusion model for response time and accuracy

The EZ-diffusion model for two-choice response time tasks takes mean response time, the variance of response time, and response accuracy as inputs. The model transforms these data via three simple equations to produce unique values for the quality of information, response conservativeness, and nondecision time. This transformation of observed data in terms of unobserved variables addresses the speed—accuracy trade-off and allows an unambiguous quantification of performance differences in two-choice response time tasks. The EZ-diffusion model can be applied to data-sparse situations to facilitate individual subject analysis. We studied the performance of the EZ-diffusion model in terms of parameter recovery and robustness against misspecification by using Monte Carlo simulations. The EZ model was also applied to a real-world data set.

Critical slowing down as early warning for the onset and termination of depression

Significance As complex systems such as the climate or ecosystems approach a tipping point, their dynamics tend to become dominated by a phenomenon known as critical slowing down. Using time series of autorecorded mood, we show that indicators of slowing down are also predictive of future transitions in depression. Specifically, in persons who are more likely to have a future transition, mood dynamics are slower and different aspects of mood are more correlated. This supports the view that the mood system may have tipping points where reinforcing feedbacks among a web of symptoms can propagate a person into a disorder. Our findings suggest the possibility of early warning systems for psychiatric disorders, using smartphone-based mood monitoring. About 17% of humanity goes through an episode of major depression at some point in their lifetime. Despite the enormous societal costs of this incapacitating disorder, it is largely unknown how the likelihood of falling into a depressive episode can be assessed. Here, we show for a large group of healthy individuals and patients that the probability of an upcoming shift between a depressed and a normal state is related to elevated temporal autocorrelation, variance, and correlation between emotions in fluctuations of autorecorded emotions. These are indicators of the general phenomenon of critical slowing down, which is expected to occur when a system approaches a tipping point. Our results support the hypothesis that mood may have alternative stable states separated by tipping points, and suggest an approach for assessing the likelihood of transitions into and out of depression.

FITTING MULTIVARIAGE NORMAL FINITE MIXTURES SUBJECT TO STRUCTURAL EQUATION MODELING

This paper is about fitting multivariate normal mixture distributions subject to structural equation modeling. The general model comprises common factor and structural regression models. The introduction of covariance and mean structure models reduces the number of parameters to be estimated in fitting the mixture and enables one to investigate a variety of substantive hypotheses concerning the differences between the components in the mixture. Within the general model, individual parameters can be subjected to equality, nonlinear and simple bounds constraints. Confidence intervals are based on the inverse of the Hessian and on the likelihood profile. Several illustrations are given and results of a simulation study concerning the confidence intervals are reported.

Cognitive psychology meets psychometric theory: on the relation between process models for decision making and latent variable models for individual differences.

This article analyzes latent variable models from a cognitive psychology perspective. We start by discussing work by Tuerlinckx and De Boeck (2005), who proved that a diffusion model for 2-choice response processes entails a 2-parameter logistic item response theory (IRT) model for individual differences in the response data. Following this line of reasoning, we discuss the appropriateness of IRT for measuring abilities and bipolar traits, such as pro versus contra attitudes. Surprisingly, if a diffusion model underlies the response processes, IRT models are appropriate for bipolar traits but not for ability tests. A reconsideration of the concept of ability that is appropriate for such situations leads to a new item response model for accuracy and speed based on the idea that ability has a natural zero point. The model implies fundamentally new ways to think about guessing, response speed, and person fit in IRT. We discuss the relation between this model and existing models as well as implications for psychology and psychometrics.

Sudden Transitions in Attitudes

Both the dynamic approach and catastrophe modeling have been warmly welcomed in research on attitudes and opinions. In this article, the authors discuss a general methodology for testing catastrophe models and apply it to the dynamics of attitude formation and change. First, by making use of the so-called catastrophe flags, converging support for the catastrophe model can be attained. Each flag relates to a specific hypothesis about attitudinal change. Second, fitting stochastic catastrophe models to data enables one to carry out a direct test of catastrophe models. Results of analyzing large data sets on political attitudes support the validity of the general catastrophe model of attitude change in which transitions in attitudes are a function of involvement and information. Present results suggest that in the case of political attitudes, involvement might well be correlated with attitude. A more refined approach to the measurement of information and involvement is suggested.