Raoul P. P. P. Grasman

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.

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.

Bayesian hypothesis testing for psychologists: A tutorial on the Savage–Dickey method

In the field of cognitive psychology, the p-value hypothesis test has established a stranglehold on statistical reporting. This is unfortunate, as the p-value provides at best a rough estimate of the evidence that the data provide for the presence of an experimental effect. An alternative and arguably more appropriate measure of evidence is conveyed by a Bayesian hypothesis test, which prefers the model with the highest average likelihood. One of the main problems with this Bayesian hypothesis test, however, is that it often requires relatively sophisticated numerical methods for its computation. Here we draw attention to the Savage-Dickey density ratio method, a method that can be used to compute the result of a Bayesian hypothesis test for nested models and under certain plausible restrictions on the parameter priors. Practical examples demonstrate the methods validity, generality, and flexibility.

A critique of the cross-lagged panel model.

The cross-lagged panel model (CLPM) is believed by many to overcome the problems associated with the use of cross-lagged correlations as a way to study causal influences in longitudinal panel data. The current article, however, shows that if stability of constructs is to some extent of a trait-like, time-invariant nature, the autoregressive relationships of the CLPM fail to adequately account for this. As a result, the lagged parameters that are obtained with the CLPM do not represent the actual within-person relationships over time, and this may lead to erroneous conclusions regarding the presence, predominance, and sign of causal influences. In this article we present an alternative model that separates the within-person process from stable between-person differences through the inclusion of random intercepts, and we discuss how this model is related to existing structural equation models that include cross-lagged relationships. We derive the analytical relationship between the cross-lagged parameters from the CLPM and the alternative model, and use simulations to demonstrate the spurious results that may arise when using the CLPM to analyze data that include stable, trait-like individual differences. We also present a modeling strategy to avoid this pitfall and illustrate this using an empirical data set. The implications for both existing and future cross-lagged panel research are discussed.

Intra-Individual Variability in ADHD, Autism Spectrum Disorders and Tourette's Syndrome.

The potential for response variability to serve as an endophenotype for attention deficit hyperactivity disorders (ADHD) rests, in part, upon the development of reliable and valid methods to decompose variability. This study investigated the specificity of intra-individual variability (IIV) in 53 children with ADHD by comparing them with 25 children with high functioning autism (HFA), 32 children with autism spectrum disorders (ASD), who also were comorbid for ADHD (ASD+ADHD), 21 children with Tourettes syndrome (TS), and 85 typically developing controls (TD). In order to decompose the variability of the reaction times, we applied three distinct techniques: ex-Gaussian modeling, intra-individual variability analysis, and spectral analysis. Our data revealed that children with HFA and children with ASD+ADHD exhibited substantial IIV compared with ADHD and TD children. We argue that: (1) all three methods lead to a single consistent conclusion; (2) careful documentation of the analytic steps used in spectral analysis is mandatory for comparison between studies; (3) the presence of comorbidities may constitute an important factor in the observed response variability in previous studies of ADHD.

Spatiotemporal EEG/MEG source analysis based on a parametric noise covariance model

A method is described to incorporate the spatiotemporal noise covariance matrix into a spatiotemporal source analysis. The essential feature is that the estimation problem is split into two parts. First, a model is fitted to the observed noise covariance matrix. This model is a Kronecker product of a spatial and a temporal matrix. The spatial matrix models the spatial covariances by a function dependent on sensor distance. The temporal matrix models the temporal covariances as lag dependent. In the second part, sources are estimated given this noise model, which can be done very efficiently due to the Kronecker formulation. An application to real electroencephalogram (EEG) data shows that the noise model fits the data very well. Simulation results show that the resulting source estimates are more precise than those obtained from a standard analysis neglecting the noise covariance. In addition, the estimated standard errors of the source parameter estimates are far more precise than those obtained from a standard analysis. Finally, the source parameter standard errors are used to investigate the effects of temporal sampling. It is shown that increasing the sampling by a factor x, decreases the standard errors of all source parameters with the square root of x.

EZ does it! Extensions of the EZ-diffusion model

In this rejoinder, we address two of Ratcliff’s main concerns with respect to the EZ-diffusion model (Ratcliff, 2008). First, we introduce “robust-EZ,” a mixture model approach to achieve robustness against the presence of response contaminants that might otherwise distort parameter estimates. Second, we discuss an extension of the EZ model that allows the estimation of starting point as an additional parameter. Together with recently developed, user-friendly software programs for fitting the full diffusion model (Vandekerckhove & Tuerlinckx, 2007; Voss & Voss, 2007), the development of the EZ model and its extensions is part of a larger effort to make diffusion model analyses accessible to a broader audience, an effort that is long overdue.

A Default Bayesian Hypothesis Test for ANOVA Designs

This article presents a Bayesian hypothesis test for analysis of variance (ANOVA) designs. The test is an application of standard Bayesian methods for variable selection in regression models. We illustrate the effect of various g-priors on the ANOVA hypothesis test. The Bayesian test for ANOVA designs is useful for empirical researchers and for students; both groups will get a more acute appreciation of Bayesian inference when they can apply it to practical statistical problems such as ANOVA. We illustrate the use of the test with two examples, and we provide R code that makes the test easy to use.

An Introduction to Bayesian Hypothesis Testing for Management Research

In management research, empirical data are often analyzed using p-value null hypothesis significance testing (pNHST). Here we outline the conceptual and practical advantages of an alternative analysis method: Bayesian hypothesis testing and model selection using the Bayes factor. In contrast to pNHST, Bayes factors allow researchers to quantify evidence in favor of the null hypothesis. Also, Bayes factors do not require adjustment for the intention with which the data were collected. The use of Bayes factors is demonstrated through an extended example for hierarchical regression based on the design of an experiment recently published in the Journal of Management. This example also highlights the fact that p values overestimate the evidence against the null hypothesis, misleading researchers into believing that their findings are more reliable than is warranted by the data.

Multivariate normative comparisons.

In neuropsychological evaluations and single case research generally a number of tests are administered, since the interest is not in a single, but in multiple characteristics of a patient. The typical problem is to decide whether or not a patient is different from normal controls with respect to one or more of these characteristics. Consideration of each characteristic separately entails an increased risk of a false positive decision (a wrongful decision that the patient is abnormal, or a type 1 error). From a statistical point of view this calls for a multivariate analysis. In this paper, we propose two approaches to perform normative comparisons for such multivariate data: Bonferroni corrected univariate comparisons and a multivariate comparison. Both approaches allow for the testing of unidirectional (two-sided) as well as directional (one-sided) hypothesis, i.e. the hypothesis that a patient deviates in a negative sense from the norm. Monte Carlo simulations were performed to check if the type I error of both approaches is adequately controlled, and to investigate the power of both approaches to detect deviation from the norm. The results indicate that the type I error rate of both approaches is correct, even in small samples. The results also indicate that the power is higher for the univariate approach if the normative sample size is very small (i.e. just exceeds the number of tests administered). In larger samples, the multivariate comparison has in general increased power. We illustrate both approaches with a clinical example of patients with Parkinson disease, who received deep brain stimulation to alleviate motor symptoms, and who were neuropsychologically evaluated to detect possible cognitive side effects.