The positive manifold of intelligence has fascinated generations of scholars in human ability. In the past century, various formal explanations have been proposed, including the dominant g factor, the revived sampling theory, and the recent multiplier effect model and mutualism model. In this article, we propose a novel idiographic explanation. We formally conceptualize intelligence as evolving networks in which new facts and procedures are wired together during development. The static model, an extension of the Fortuin-Kasteleyn model, provides a parsimonious explanation of the positive manifold and intelligence's hierarchical factor structure. We show how it can explain the Matthew effect across developmental stages. Finally, we introduce a method for studying growth dynamics. Our truly idiographic approach offers a new view on a century-old construct and ultimately allows the fields of human ability and human learning to coalesce.

https://journals.sagepub.com/doi/pdf/10.1177/1745691619866447

The Wiring of Intelligence

The Ising model is a model for pairwise interactions between binary variables that has become popular in the psychological sciences. It has been first introduced as a theoretical model for the alig...

Interpreting the Ising Model: The Input Matters

Interest in the processes that mediate between stimuli and responses is at the heart of most modern psychology and neuroscience. These processes cannot be directly measured but instead must be inferred from observed responses. Race models, through their ability to account for both response choices and response times, have been a key enabler of such inferences. Examples of such models appeared contemporaneously with the cognitive revolution, and since then have become increasingly prominent and elaborated, so that psychologists now have a powerful array of race models at their disposal. We showcase the state of the art for race models and describe why and how they are used.

Winner Takes All! What Are Race Models, and Why and How Should Psychologists Use Them?

The Ising model is a model for pairwise interactions between binary variables that has become popular in the psychological sciences. It has been first introduced as a theoretical model for the alignment between positive (+1) and negative (-1) atom spins. In many psychological applications, however, the Ising model is defined on the domain $\{0,1\}$ instead of the classical domain $\{-1,1\}$. While it is possible to transform the parameters of a given Ising model in one domain to obtain a statistically equivalent model in the other domain, the parameters in the two versions of the Ising model lend themselves to different interpretations and imply different dynamics, when studying the Ising model as a dynamical system. In this tutorial paper, we provide an accessible discussion of the interpretation of threshold and interaction parameters in the two domains and show how the dynamics of the Ising model depends on the choice of domain. Finally, we provide a transformation that allows to transform the parameters in an Ising model in one domain into a statistically equivalent Ising model in the other domain.

Interpreting the Ising Model: The Input Matters.

In this paper we study the statistical relations between three latent trait models for accuracies and response times: the hierarchical model (HM) of van der Linden (Psychometrika 72(3):287–308, 2007), the signed residual time model (SM) proposed by Maris and van der Maas (Psychometrika 77(4):615–633, 2012), and the drift diffusion model (DM) as proposed by Tuerlinckx and De Boeck (Psychometrika 70(4):629–650, 2005). One important distinction between these models is that the HM and the DM either assume or imply that accuracies and response times are independent given the latent trait variables, while the SM does not. In this paper we investigate the impact of this conditional independence property—or a lack thereof—on the manifest probability distribution for accuracies and response times. We will find that the manifest distributions of the latent trait models share several important features, such as the dependency between accuracy and response time, but we also find important differences, such as in what function of response time is being modeled. Our method for characterizing the manifest probability distributions is related to the Dutch identity (Holland in Psychometrika 55(6):5–18, 1990).

/pdf/characterizing-the-manifest-probability-distributions-of-7qj0053iks.pdf

Characterizing the Manifest Probability Distributions of Three Latent Trait Models for Accuracy and Response Time

In network psychometrics undirected graphical models—such as the Ising model from statistical physics—are used to characterize the manifest probability distribution of psychometric data. In practice, we often find that it is extremely difficult to apply graphical models as the Ising model to educational data because (i) the model’s likelihood is impossible to compute for the big data that we typically observe in educational measurement, and (ii) the model cannot handle the partially observed data that stem from incomplete test designs. In this chapter, we therefore propose to use a simplified Ising model that is known as the Curie-Weiss model. Unlike the more general Ising model, the Curie-Weiss model is computationally tractable, which makes it suitable for applications in educational measurement. The objective of this chapter is to study the statistical properties of the Curie-Weiss model and discuss its estimation with complete or incomplete data. We demonstrate that our procedures work using a simulated example, and illustrate the analysis of fit of the Curie-Weiss model using real data from the 2012 Cito Eindtoets.

/pdf/network-psychometrics-in-educational-practice-4qqkfv8jcd.pdf

Network Psychometrics in Educational Practice

We propose a new approach to cognitive aging research, in which detailed cognitive modelling of a single complex task affords simultaneous measures of the major mechanisms proposed to explain age-related deficits: capacity limits, processing speed, inhibition, and executive function. The validity of these measures rests on their well-defined roles of the model parameters and the model’s precise and comprehensive account of the behaviour of our healthy older (63–78 years) and younger (18–28 years) participants. Processing speed was identified as the primary cause of age-related deficits. Executive control was better for older than younger participants when task demands were lower, but as demands increased this advantage reduced or disappeared, suggesting age-related capacity limitations. These results show that detailed process modelling of a complex task provides a powerful, efficient, and conceptually rich way of gaining new insights into the non-linear interactions among psychological mechanisms that underpin cognitive aging.

Slower processing dominates executive-function deficits in cognitive aging

https://doi.org/10.1016/j.dcn.2022.101191

C. C. Tanis

Papers

Network Psychometrics in Educational Practice

Slower processing dominates executive-function deficits in cognitive aging

A cognitive process modeling framework for the ABCD study stop-signal task