Secondary motor integration as a final arbiter in sensorimotor decision-making.

Sensorimotor decision-making is believed to involve a process of accumulating sensory evidence over time. While current theories posit a single accumulation process prior to planning an overt motor response, here, we propose an active role of motor processes in decision formation via a secondary leaky motor accumulation stage. The motor leak adapts the "memory" with which this secondary accumulator reintegrates the primary accumulated sensory evidence, thus adjusting the temporal smoothing in the motor evidence and, correspondingly, the lag between the primary and motor accumulators. We compare this framework against different single accumulator variants using formal model comparison, fitting choice, and response times in a task where human observers made categorical decisions about a noisy sequence of images, under different speed-accuracy trade-off instructions. We show that, rather than boundary adjustments (controlling the amount of evidence accumulated for decision commitment), adjustment of the leak in the secondary motor accumulator provides the better description of behavior across conditions. Importantly, we derive neural correlates of these 2 integration processes from electroencephalography data recorded during the same task and show that these neural correlates adhere to the neural response profiles predicted by the model. This framework thus provides a neurobiologically plausible description of sensorimotor decision-making that captures emerging evidence of the active role of motor processes in choice behavior.

Efficient estimation of bounded gradient-drift diffusion models for affect on CPU and GPU.

Computational modeling plays an important role in a gamut of research fields. In affect research, continuous-time stochastic models are becoming increasingly popular. Recently, a non-linear, continuous-time, stochastic model has been introduced for affect dynamics, called the Affective Ising Model (AIM). The drawback of non-linear models like the AIM is that they generally come with serious computational challenges for parameter estimation and related statistical analyses. The likelihood function of the AIM does not have a closed form expression. Consequently, simulation based or numerical methods have to be considered in order to evaluate the likelihood function. Additionally, the likelihood function can have multiple local minima. Consequently, a global optimization heuristic is required and such heuristics generally require a large number of likelihood function evaluations. In this paper, a Julia software package is introduced that is dedicated to fitting the AIM. The package includes an implementation of a numeric algorithm for fast computations of the likelihood function, which can be run both on graphics processing units (GPU) and central processing units (CPU). The numerical method introduced in this paper is compared to the more traditional Euler-Maruyama method for solving stochastic differential equations. Furthermore, the estimation software is tested by means of a recovery study and estimation times are reported for benchmarks that were run on several computing devices (two different GPUs and three different CPUs). According to these results, a single parameter estimation can be obtained in less than thirty seconds using a mainstream NVIDIA GPU.

The Affective Ising Model: A computational account of human affect dynamics.

The human affect system is responsible for producing the positive and negative feelings that color and guide our lives. At the same time, when disrupted, its workings lie at the basis of the occurrence of mood disorder. Understanding the functioning and dynamics of the affect system is therefore crucial to understand the feelings that people experience on a daily basis, their dynamics across time, and how they can become dysregulated in mood disorder. In this paper, a nonlinear stochastic model for the dynamics of positive and negative affect is proposed called the Affective Ising Model (AIM). It incorporates principles of statistical mechanics, is inspired by neurophysiological and behavioral evidence about auto-excitation and mutual inhibition of the positive and negative affect dimensions, and is intended to better explain empirical phenomena such as skewness, multimodality, and non-linear relations of positive and negative affect. The AIM is applied to two large experience sampling studies on the occurrence of positive and negative affect in daily life in both normality and mood disorder. It is examined to what extent the model is able to reproduce the aforementioned non-Gaussian features observed in the data, using two sightly different continuous-time vector autoregressive (VAR) models as benchmarks. The predictive performance of the models is also compared by means of leave-one-out cross-validation. The results indicate that the AIM is better at reproducing non-Gaussian features while their performance is comparable for strictly Gaussian features. The predictive performance of the AIM is also shown to be better for the majority of the affect time series. The potential and limitations of the AIM as a computational model approximating the workings of the human affect system are discussed.

Prepaid parameter estimation without likelihoods.

In various fields, statistical models of interest are analytically intractable and inference is usually performed using a simulation-based method. However elegant these methods are, they are often painstakingly slow and convergence is difficult to assess. As a result, statistical inference is greatly hampered by computational constraints. However, for a given statistical model, different users, even with different data, are likely to perform similar computations. Computations done by one user are potentially useful for other users with different data sets. We propose a pooling of resources across researchers to capitalize on this. More specifically, we preemptively chart out the entire space of possible model outcomes in a prepaid database. Using advanced interpolation techniques, any individual estimation problem can now be solved on the spot. The prepaid method can easily accommodate different priors as well as constraints on the parameters. We created prepaid databases for three challenging models and demonstrate how they can be distributed through an online parameter estimation service. Our method outperforms state-of-the-art estimation techniques in both speed (with a 23,000 to 100,000-fold speed up) and accuracy, and is able to handle previously quasi inestimable models.

Stimulus-Driven Affective Change: Evaluating Computational Models of Affect Dynamics in Conjunction with Input.

The way in which emotional experiences change over time can be studied through the use of computational models. An important question with regard to such models is which characteristics of the data a model should account for in order to adequately describe these data. Recently, attention has been drawn on the potential importance of nonlinearity as a characteristic of affect dynamics. However, this conclusion was reached through the use of experience sampling data in which no information was available about the context in which affect was measured. However, affective stimuli may induce some or all of the observed nonlinearity. This raises the question of whether computational models of affect dynamics should account for nonlinearity, or whether they just need to account for the affective stimuli a person encounters. To investigate this question, we used a probabilistic reward task in which participants either won or lost money at each trial. A number of plausible ways in which the experimental stimuli played a role were considered and applied to the nonlinear Affective Ising Model (AIM) and the linear Bounded Ornstein-Uhlenbeck (BOU) model. In order to reach a conclusion, the relative and absolute performance of these models were assessed. Results suggest that some of the observed nonlinearity could indeed be attributed to the experimental stimuli. However, not all nonlinearity was accounted for by these stimuli, suggesting that nonlinearity may present an inherent feature of affect dynamics. As such, nonlinearity should ideally be accounted for in the computational models of affect dynamics. Supplementary Information: The online version contains supplementary material available at 10.1007/s42761-022-00118-5.

Informing VAR(1) with qualitative dynamical features improves predictive accuracy.

The AR(1) model has been shown to outperform the general VAR(1) model on typical affective time series. Even in combination with a lasso penalty, the reduced VAR(1) model (VAR-lasso) is generally outperformed. A reason for the AR dominance is that the VAR-lasso selects models that are still too complex-the space of all possible VAR models includes simpler models but these are hard to select with a traditional lasso penalty. In this article, we propose a reparametrization of the VAR model by decomposing its transition matrix into a symmetric and antisymmetric component (denoted as SAD), allowing us to construct a hierarchy of meaningful signposts in the VAR model space ranging from simple to complex. The decomposition enables the lasso procedure to pick up qualitatively distinct dynamical features in a more targeted way (like relaxation, shearing, and oscillations); this procedure is called SAD-lasso. This leads to a more intuitive interpretation of the reduced models. By removing the antisymmetric component altogether, we obtain a subclass of symmetric VAR models that form a natural extension of the AR model with the same simple relaxation dynamics but allowing for interactions between the system components. We apply these reparametrized and constrained VAR models to 1,391 psychological time series of affect, and compare their predictive accuracy. This analysis indicates that the SAD-lasso is a better regularization technique than the VAR-lasso. Additionally, the results of an extensive simulation study suggest the existence of symmetric interactions for almost half of the time series considered in this article. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

A comparison of continuous and discrete time modeling of affective processes in terms of predictive accuracy.

Intra-individual processes are thought to continuously unfold across time. For equally spaced time intervals, the discrete-time lag-1 vector autoregressive (VAR(1)) model and the continuous-time Ornstein-Uhlenbeck (OU) model are equivalent. It is expected that by taking into account the unequal spacings of the time intervals in real data between observations will lead to an advantage for the OU in terms of predictive accuracy. In this paper, this is claim is being investigated by comparing the predictive accuracy of the OU model to that of the VAR(1) model on typical ESM data obtained in the context of affect research. It is shown that the VAR(1) model outperforms the OU model for the majority of the time series, even though time intervals in the data are unequally spaced. Accounting for measurement error does not change the result. Deleting large abrupt changes on short time intervals (that may be caused by externally driven events) does however lead to a significant improvement for the OU model. This suggests that processes in psychology may be continuously evolving, but that there are factors, like external events, which can disrupt the continuous flow.

The Leaky Integrating Threshold and its impact on evidence accumulation models of choice response time (RT).

A common assumption in choice response time (RT) modeling is that after evidence accumulation reaches a certain decision threshold, the choice is categorically communicated to the motor system that then executes the response. However, neurophysiological findings suggest that motor preparation partly overlaps with evidence accumulation, and is not independent from stimulus difficulty level. We propose to model this entanglement by changing the nature of the decision criterion from a simple threshold to an actual process. More specifically, we propose a secondary, motor preparation related, leaky accumulation process that takes the accumulated evidence of the original decision process as a continuous input, and triggers the actual response when it reaches its own threshold. We analytically develop this Leaky Integrating Threshold (LIT), applying it to a simple constant drift diffusion model, and show how its parameters can be estimated with the D*M method. Reanalyzing 3 different data sets, the LIT extension is shown to outperform a standard drift diffusion model using multiple statistical approaches. Further, the LIT leak parameter is shown to be better at explaining the speed/accuracy trade-off manipulation than the commonly used boundary separation parameter. These improvements can also be verified using traditional diffusion model analyses, for which the LIT predicts the violation of several common selective parameter influence assumptions. These predictions are consistent with what is found in the data and with what is reported experimentally in the literature. Crucially, this work offers a new benchmark against which to compare neural data to offer neurobiological validation for the proposed processes. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Optimal sampling rates for reliable continuous-time first-order autoregressive and vector autoregressive modeling.

Autoregressive and vector autoregressive models are a driving force in current psychological research. In affect research they are, for instance, frequently used to formalize affective processes and estimate affective dynamics. Discrete-time model variants are most commonly used, but continuous-time formulations are gaining popularity, because they can handle data from longitudinal studies in which the sampling rate varies within the study period, and yield results that can be compared across data sets from studies with different sampling rates. However, whether and how the sampling rate affects the quality with which such continuous-time models can be estimated, has largely been ignored in the literature. In the present article, we show how the sampling rate affects the estimation reliability (i.e., the standard errors of the parameter estimators, with smaller values indicating higher reliability) of continuous-time autoregressive and vector autoregressive models. Moreover, we determine which sampling rates are optimal in the sense that they lead to standard errors of minimal size (subject to the assumption that the models are correct). Our results are based on the theories of optimal design and maximum likelihood estimation. We illustrate them making use of data from the COGITO Study. We formulate recommendations for study planning, and elaborate on strengths and limitations of our approach. (PsycInfo Database Record (c) 2022 APA, all rights reserved).