Francis Tuerlinckx

Estimating parameters of the diffusion model: Approaches to dealing with contaminant reaction times and parameter variability

Three methods for fitting the diffusion model (Ratcliff, 1978) to experimental data are examined. Sets of simulated data were generated with known parameter values, and from fits of the model, we found that the maximum likelihood method was better than the chi-square and weighted least squares methods by criteria of bias in the parameters relative to the parameter values used to generate the data and standard deviations in the parameter estimates. The standard deviations in the parameter values can be used as measures of the variability in parameter estimates from fits to experimental data. We introduced contaminant reaction times and variability into the other components of processing besides the decision process and found that the maximum likelihood and chi-square methods failed, sometimes dramatically. But the weighted least squares method was robust to these two factors. We then present results from modifications of the maximum likelihood and chi-square methods, in which these factors are explicitly modeled, and show that the parameter values of the diffusion model are recovered well. We argue that explicit modeling is an important method for addressing contaminants and variability in nondecision processes and that it can be applied in any theoretical approach to modeling reaction time.

A nonlinear mixed model framework for item response theory

Mixed models take the dependency between observations based on the same cluster into account by introducing 1 or more random effects. Common item response theory (IRT) models introduce latent person variables to model the dependence between responses of the same participant. Assuming a distribution for the latent variables, these IRT models are formally equivalent with nonlinear mixed models. It is shown how a variety of IRT models can be formulated as particular instances of nonlinear mixed models. The unifying framework offers the advantage that relations between different IRT models become explicit and that it is rather straightforward to see how existing IRT models can be adapted and extended. The approach is illustrated with a self-report study on anger.

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 the Ratcliff diffusion model to experimental data.

Many experiments in psychology yield both reaction time and accuracy data. However, no off-the-shelf methods yet exist for the statistical analysis of such data. One particularly successful model has been the diffusion process, but using it is difficult in practice because of numerical, statistical, and software problems. We present a general method for performing diffusion model analyses on experimental data. By implementing design matrices, a wide range of across-condition restrictions can be imposed on model parameters, in a flexible way. It becomes possible to fit models with parameters regressed onto predictors. Moreover, data analytical tools are discussed that can be used to handle various types of outliers and contaminants. We briefly present an easy-touse software tool that helps perform diffusion model analyses.

Feelings change: accounting for individual differences in the temporal dynamics of affect.

People display a remarkable variability in the patterns and trajectories with which their feelings change over time. In this article, we present a theoretical account for the dynamics of affect (DynAffect) that identifies the major processes underlying individual differences in the temporal dynamics of affective experiences. It is hypothesized that individuals are characterized by an affective home base, a baseline attractor state around which affect fluctuates. These fluctuations vary as the result of internal or external processes to which an individual is more or less sensitive and are regulated and tied back to the home base by the attractor strength. Individual differences in these 3 processes--affective home base, variability, and attractor strength--are proposed to underlie individual differences in affect dynamics. The DynAffect account is empirically evaluated by means of a diffusion modeling approach in 2 extensive experience-sampling studies on peoples core affective experiences. The findings show that the model is capable of adequately capturing the observed dynamics in core affect across both large (Study 1) and shorter time scales (Study 2) and illuminate how the key processes are related to personality and emotion dispositions. Implications for the understanding of affect dynamics and affective dysfunctioning in psychopathology are also discussed.

A Network Approach to Psychopathology: New Insights into Clinical Longitudinal Data

In the network approach to psychopathology, disorders are conceptualized as networks of mutually interacting symptoms (e.g., depressed mood) and transdiagnostic factors (e.g., rumination). This suggests that it is necessary to study how symptoms dynamically interact over time in a network architecture. In the present paper, we show how such an architecture can be constructed on the basis of time-series data obtained through Experience Sampling Methodology (ESM). The proposed methodology determines the parameters for the interaction between nodes in the network by estimating a multilevel vector autoregression (VAR) model on the data. The methodology allows combining between-subject and within-subject information in a multilevel framework. The resulting network architecture can subsequently be analyzed through network analysis techniques. In the present study, we apply the method to a set of items that assess mood-related factors. We show that the analysis generates a plausible and replicable network architecture, the structure of which is related to variables such as neuroticism; that is, for subjects who score high on neuroticism, worrying plays a more central role in the network. Implications and extensions of the methodology are discussed.

Diffusion model analysis with MATLAB: A DMAT primer

The Ratcliff diffusion model has proved to be a useful tool in reaction time analysis. However, its use has been limited by the practical difficulty of estimating the parameters. We present a software tool, the Diffusion Model Analysis Toolbox (DMAT), intended to make the Ratcliff diffusion model for reaction time and accuracy data more accessible to experimental psychologists. The tool takes the form of a MATLAB toolbox and can be freely downloaded from ppw.kuleuven.be/okp/dmatoolbox. Using the program does not require a background in mathematics, nor any advanced programming experience (but familiarity with MATLAB is useful). We demonstrate the basic use of DMAT with two examples.

The Relation Between Valence and Arousal in Subjective Experience

Affect is basic to many if not all psychological phenomena. This article examines 2 of the most fundamental properties of affective experience--valence and arousal--asking how they are related to each other on a moment to moment basis. Over the past century, 6 distinct types of relations have been suggested or implicitly presupposed in the literature. We critically review the available evidence for each proposal and argue that the evidence does not provide a conclusive answer. Next, we use statistical modeling to verify the different proposals in 8 data sets (with Ns ranging from 80 to 1,417) where participants reported their affective experiences in response to experimental stimuli in laboratory settings or as momentary or remembered in natural settings. We formulate 3 key conclusions about the relation between valence and arousal: (a) on average, there is a weak but consistent V-shaped relation of arousal as a function of valence, but (b) there is large variation at the individual level, so that (c) valence and arousal can in principle show a variety of relations depending on person or circumstances. This casts doubt on the existence of a static, lawful relation between valence and arousal. The meaningfulness of the observed individual differences is supported by their personality and cultural correlates. The malleability and individual differences found in the structure of affect must be taken into account when studying affect and its role in other psychological phenomena.

Hierarchical diffusion models for two-choice response times

Two-choice response times are a common type of data, and much research has been devoted to the development of process models for such data. However, the practical application of these models is notoriously complicated, and flexible methods are largely nonexistent. We combine a popular model for choice response times-the Wiener diffusion process-with techniques from psychometrics in order to construct a hierarchical diffusion model. Chief among these techniques is the application of random effects, with which we allow for unexplained variability among participants, items, or other experimental units. These techniques lead to a modeling framework that is highly flexible and easy to work with. Among the many novel models this statistical framework provides are a multilevel diffusion model, regression diffusion models, and a large family of explanatory diffusion models. We provide examples and the necessary computer code.

A Hierarchical IRT Model for Criterion-Referenced Measurement

A hierarchical IRT model is proposed for mastery classification in criterion-referenced measurement. In this model, items measuring the same criterion are grouped, and a difficulty and discrimination parameter of the criterion is estimated on the same scale as the person and item parameters. The level of proficiency of a student with respect to the criterion is determined by the probability of success on the criterion. Cutoff points on the probability scale can be used to classify respondents into masters and nonmasters. The hierarchical IRT model is estimated using the Gibbs sampler and tested using posterior predictive checks. The model is illustrated with a test measuring the attainment targets of reading comprehension (in Dutch) at the end of primary education.