Hierarchical modeling of sequential behavioral data: an empirical Bayesian approach

The authors review the common methods for measuring strength of contingency between 2 behaviors in a behavioral sequence, the binomial z score and the adjusted cell residual, and point out a number of limitations of these approaches. They present a new approach using log odds ratios and empirical Bayes estimation in the context of hierarchical modeling, an approach not constrained by these limitations. A series of hierarchical models is presented to test the stationarity of behavioral sequences, the homogeneity of sequences across a sample of episodes, and whether covariates can account for variation in sequences across the sample. These models are applied to observational data taken from a study of the behavioral interactions of 254 couples to illustrate their use.     

Bayesian techniques for analyzing group differences in the Iowa Gambling Task: A case study of intuitive and deliberate decision-makers

The Iowa Gambling Task (IGT) is one of the most popular experimental paradigms for comparing complex decision-making across groups. Most commonly, IGT behavior is analyzed using frequentist tests to compare performance across groups, and to compare inferred parameters of cognitive models developed for the IGT. Here, we present a Bayesian alternative based on Bayesian repeated-measures ANOVA for comparing performance, and a suite of three complementary model-based methods for assessing the cognitive processes underlying IGT performance. The three model-based methods involve Bayesian hierarchical parameter estimation, Bayes factor model comparison, and Bayesian latent-mixture modeling. We illustrate these Bayesian methods by applying them to test the extent to which differences in intuitive versus deliberate decision style are associated with differences in IGT performance. The results show that intuitive and deliberate decision-makers behave similarly on the IGT, and the modeling analyses consistently suggest that both groups of decision-makers rely on similar cognitive processes. Our results challenge the notion that individual differences in intuitive and deliberate decision styles have a broad impact on decision-making. They also highlight the advantages of Bayesian methods, especially their ability to quantify evidence in favor of the null hypothesis, and that they allow model-based analyses to incorporate hierarchical and latent-mixture structures.     

Bayesian hierarchical modeling of the temporal dynamics of subjective well-being: A 10 year longitudinal analysis

This study demonstrates, for the first time, how Bayesian hierarchical modeling can be applied to yield novel insights into the long-term temporal dynamics of subjective well-being (SWB). Several models were proposed and examined using Bayesian methods. The models were assessed using a sample of Australian adults (n = 1081) who provided annual SWB scores on between 5 and 10 occasions. The best fitting models involved a probit transformation, allowed error variance to vary across participants, and did not include a lag parameter. Including a random linear and quadratic effect resulted in only a small improvement over the intercept only model. Examination of individual-level fits suggested that most participants were stable with a small subset exhibiting patterns of systematic change.     

Semiparametric Thurstonian Models for Recurrent Choices: A Bayesian Analysis

We develop semiparametric Bayesian Thurstonian models for analyzing repeated choice decisions involving multinomial, multivariate binary or multivariate ordinal data. Our modeling framework has multiple components that together yield considerable flexibility in modeling preference utilities, cross-sectional heterogeneity and parameter-driven dynamics. Each component of our model is specified semiparametrically using Dirichlet process (DP) priors. The utility (latent variable) component of our model allows the alternative-specific utility errors to semiparametrically deviate from a normal distribution. This generates a robust alternative to popular Thurstonian specifications that are based on underlying normally distributed latent variables. Our second component focuses on flexibly modeling cross-sectional heterogeneity. The semiparametric specification allows the heterogeneity distribution to mimic either a finite mixture distribution or a continuous distribution such as the normal, whichever is supported by the data. Thus, special features such as multimodality can be readily incorporated without the need to overtly search for the best heterogeneity specification across a series of models. Finally, we allow for parameter-driven dynamics using a semiparametric state-space approach. This specification adds to the literature on robust Kalman filters. The resulting framework is very general and integrates divergent strands of the literatures on flexible choice models, Bayesian nonparametrics and robust time series specifications. Given this generality, we show how several existing Thurstonian models can be obtained as special forms of our model. We describe Markov chain Monte Carlo methods for the inference of model parameters, report results from two simulation studies and apply the model to consumer choice data from a frequently purchased product category. The results from our simulations and application highlight the benefits of using our semiparametric approach.     

The course of human events: predicting the timing of primate neural development

A recent model of the timing in which neural developmental events occur in a variety of mammals has shown high predictability of the order and duration of these events across species when appropriately computed. The model, originally derived to study the developmental mechanisms of evolutionary change in the nervous system, is adapted in this paper to predict the course of those events in the developing human, a sequence that has been difficult to determine using non‐invasive neuroanatomical techniques. Using a modified version of our original regression model, we generate predicted times of occurrence for a large number of developmental events in the human embryo and fetus, and include a chart of comparable events for macaque monkeys. We discuss a bidirectional variability in the original model which allowed us to identify limbic and cortical primate neural events that are significantly deviant from the general mammalian norm, but which also proved predictable following modification. We test the modified model against empirically derived values for neural events not included in the original model, as well as through comparisons with human developmental sequences inferred by other methods. In view of the remarkable stability in the course of development across species, knowledge of the timing of human neural events need not be entirely restricted to the limited existent embryonic and infant data. Although the primate neural development sequence is somewhat more complex than that for other mammals, primate data continue to support a theory of developmental conservation across evolution.     

Hierarchical control of rapid movement sequences

Are movement sequences executed in a hierarchically controlled fashion? We first state explicitly what such control would entail, and we observe that if a movement sequence is planned hierarchically, that does not imply that its execution is hierarchical. To find evidence for hierarchically controlled execution, we require subjects to perform memorized sequences of finger responses like those used in playing the piano. The error data we obtain are consistent with a hierarchical planning as well as execution model, but the interresponse-time data provide strong support for a hierarchical execution model. We consider three alternatives to the hierarchical execution model and reject them. We also consider the implications of our results for the role of timing in motor programs, the characteristics of motor buffers, and the relations between memory for symbolic and motor information.     

A Bayesian hierarchical diffusion model decomposition of performance in Approach–Avoidance Tasks

Common methods for analysing response time (RT) tasks, frequently used across different disciplines of psychology, suffer from a number of limitations such as the failure to directly measure the underlying latent processes of interest and the inability to take into account the uncertainty associated with each individual's point estimate of performance. Here, we discuss a Bayesian hierarchical diffusion model and apply it to RT data. This model allows researchers to decompose performance into meaningful psychological processes and to account optimally for individual differences and commonalities, even with relatively sparse data. We highlight the advantages of the Bayesian hierarchical diffusion model decomposition by applying it to performance on Approach–Avoidance Tasks, widely used in the emotion and psychopathology literature. Model fits for two experimental data-sets demonstrate that the model performs well. The Bayesian hierarchical diffusion model overcomes important limitations of current analysis procedures and provides deeper insight in latent psychological processes of interest.     

A hierarchical state space approach to affective dynamics

Linear dynamical system theory is a broad theoretical framework that has been applied in various research areas such as engineering, econometrics and recently in psychology. It quantifies the relations between observed inputs and outputs that are connected through a set of latent state variables. State space models are used to investigate the dynamical properties of these latent quantities. These models are especially of interest in the study of emotion dynamics, with the system representing the evolving emotion components of an individual. However, for simultaneous modeling of individual and population differences, a hierarchical extension of the basic state space model is necessary. Therefore, we introduce a Bayesian hierarchical model with random effects for the system parameters. Further, we apply our model to data that were collected using the Oregon adolescent interaction task: 66 normal and 67 depressed adolescents engaged in a conflict-oriented interaction with their parents and second-to-second physiological and behavioral measures were obtained. System parameters in normal and depressed adolescents were compared, which led to interesting discussions in the light of findings in recent literature on the links between cardiovascular processes, emotion dynamics and depression. We illustrate that our approach is flexible and general: The model can be applied to any time series for multiple systems (where a system can represent any entity) and moreover, one is free to focus on various components of this versatile model.     

A Hierarchical Modeling Approach to Data Analysis and Study Design in a Multi-site Experimental fMRI Study

We propose a hierarchical Bayesian model for analyzing multi-site experimental fMRI studies. Our method takes the hierarchical structure of the data (subjects are nested within sites, and there are multiple observations per subject) into account and allows for modeling between-site variation. Using posterior predictive model checking and model selection based on the deviance information criterion (DIC), we show that our model provides a good fit to the observed data by sharing information across the sites. We also propose a simple approach for evaluating the efficacy of the multi-site experiment by comparing the results to those that would be expected in hypothetical single-site experiments with the same sample size.     

On the importance of avoiding shortcuts in applying cognitive models to hierarchical data

Psychological experiments often yield data that are hierarchically structured. A number of popular shortcut strategies in cognitive modeling do not properly accommodate this structure and can result in biased conclusions. To gauge the severity of these biases, we conducted a simulation study for a two-group experiment. We first considered a modeling strategy that ignores the hierarchical data structure. In line with theoretical results, our simulations showed that Bayesian and frequentist methods that rely on this strategy are biased towards the null hypothesis. Secondly, we considered a modeling strategy that takes a two-step approach by first obtaining participant-level estimates from a hierarchical cognitive model and subsequently using these estimates in a follow-up statistical test. Methods that rely on this strategy are biased towards the alternative hypothesis. Only hierarchical models of the multilevel data lead to correct conclusions. Our results are particularly relevant for the use of hierarchical Bayesian parameter estimates in cognitive modeling.     

ELM-HTM guided bio-inspired unsupervised learning for anomalous trajectory classification

Artificial intelligent systems often model the solutions of typical machine learning problems, inspired by biological processes, because of the biological system is faster and much adaptive than deep learning. The utility of bio-inspired learning methods lie in its ability to discover unknown patterns, and its less dependence on mathematical modeling or exhaustive training. In this paper, we propose a new bio-inspired learning model for a single-class classifier to detect abnormality in video object trajectories. The method uses a simple but dynamic extreme learning machine (ELM) and hierarchical temporal memory (HTM) together referred to as ELM-HTM in an unsupervised way to learn and classify time series patterns. The method has been tested on trajectory sequences in traffic surveillance to find abnormal behaviors such as high-speed, unusual stops, driving in wrong directions, loitering, etc. Experiments have also been performed with 3D air signatures captured using sensors and used for biometric authentication(forged/genuine). The results indicate a significant gain over training time and classification accuracy. The proposed method outperforms in predicting long-time patterns by observing small steps with an average accuracy gain of 15% as compared to the state-of-the-art HTM. The method has applications in detecting abnormal activities in videos by learning the movement patterns as well as in biometric authentication.     

多项式加工树模型在再认启发式中的应用

摘 要 再认启发式利用再认线索进行决策。以往研究采用一致率、击中率、虚报率和区分指数来表示再认启发式使用,然而这些方法都存在局限。多项式加工树模型能够分离不同的认知加工过程,为了解决再认使用与知识使用的混淆,研究者提出一种多项式加工树模型 r-model 测量再认启发式的使用。本文将重 点介绍 r-model,具体包括 r-model 的内容、数据分析以及考虑个体差异的分层 r-model。最后,从 r-model 的模型修正和边界条件两个方面提出未来研究方向。 关键词 再认启发式;流畅启发式;多项式加工树;贝叶斯分层模型     

问题解决测验中过程数据的特征抽取与能力评估

基于计算机的问题解决测验可以实时记录被试探索环境和解决问题时的详细行动痕迹,并保存为过程数据。首先介绍了过程数据的分析流程,然后从问题解决测验入手,分别对过程数据的特征抽取和能力估计建模两方面的研究进行了梳理和评价。未来研究应注意：提高分析结果的可解释性;特征提取时纳入更多信息;实现更复杂问题情景下的能力评估;注重方法的实用性;以及融合与借鉴不同领域的分析方法。     

Exploring Factor Model Parameters across Continuous Variables with Local Structural Equation Models

Using an empirical data set, we investigated variation in factor model parameters across a continuous moderator variable and demonstrated three modeling approaches: multiple-group mean and covariance structure (MGMCS) analyses, local structural equation modeling (LSEM), and moderated factor analysis (MFA). We focused on how to study variation in factor model parameters as a function of continuous variables such as age, socioeconomic status, ability levels, acculturation, and so forth. Specifically, we formalized the LSEM approach in detail as compared with previous work and investigated its statistical properties with an analytical derivation and a simulation study. We also provide code for the easy implementation of LSEM. The illustration of methods was based on cross-sectional cognitive ability data from individuals ranging in age from 4 to 23 years. Variations in factor loadings across age were examined with regard to the age differentiation hypothesis. LSEM and MFA converged with respect to the conclusions. When there was a broad age range within groups and varying relations between the indicator variables and the common factor across age, MGMCS produced distorted parameter estimates. We discuss the pros of LSEM compared with MFA and recommend using the two tools as complementary approaches for investigating moderation in factor model parameters.     

Residual Normality Assumption and the Estimation of Multiple Membership Random Effects Models

While conventional hierarchical linear modeling is applicable to purely hierarchical data, a multiple membership random effects model (MMrem) is appropriate for nonpurely nested data wherein some lower-level units manifest mobility across higher-level units. Although a few recent studies have investigated the influence of cluster-level residual nonnormality on hierarchical linear modeling estimation for purely hierarchical data, no research has examined the statistical performance of an MMrem given residual non-normality. The purpose of the present study was to extend prior research on the influence of residual non-normality from purely nested data structures to multiple membership data structures. Employing a Monte Carlo simulation study, this research inquiry examined two-level MMrem parameter estimate biases and inferential errors. Simulation factors included the level-two residual distribution, sample sizes, intracluster correlation coefficient, and mobility rate. Results showed that estimates of fixed effect parameters and the level-one variance component were robust to level-two residual non-normality. The level-two variance component, however, was sensitive to level-two residual non-normality and sample size. Coverage rates of the 95% credible intervals deviated from the nominal value assumed when level-two residuals were non-normal. These findings can be useful in the application of an MMrem to account for the contextual effects of multiple higher-level units.     

Learning Orthographic Structure With Sequential Generative Neural Networks

Learning the structure of event sequences is a ubiquitous problem in cognition and particularly in language. One possible solution is to learn a probabilistic generative model of sequences that allows making predictions about upcoming events. Though appealing from a neurobiological standpoint, this approach is typically not pursued in connectionist modeling. Here, we investigated a sequential version of the restricted Boltzmann machine (RBM), a stochastic recurrent neural network that extracts high‐order structure from sensory data through unsupervised generative learning and can encode contextual information in the form of internal, distributed representations. We assessed whether this type of network can extract the orthographic structure of English monosyllables by learning a generative model of the letter sequences forming a word training corpus. We show that the network learned an accurate probabilistic model of English graphotactics, which can be used to make predictions about the letter following a given context as well as to autonomously generate high‐quality pseudowords. The model was compared to an extended version of simple recurrent networks, augmented with a stochastic process that allows autonomous generation of sequences, and to non‐connectionist probabilistic models (n‐grams and hidden Markov models). We conclude that sequential RBMs and stochastic simple recurrent networks are promising candidates for modeling cognition in the temporal domain.     

Using system dynamics modeling to understand the impact of social change initiatives

Community psychologists have a long history of interest in understanding social systems and how to bring about enduring positive change in these systems. However, the methods that community psychologists use to anticipate and evaluate the changes that result from system change efforts are less well developed. In the current paper, we introduce readers to system dynamics modeling, an action research approach to studying complex systems and the consequences of system change. We illustrate this approach by describing a system dynamics model of educational reform. We provide readers with an introduction to system dynamics modeling, as well as describe the strengths and limitations of the approach for application to community psychology.     

A statistical model for discriminating between subliminal and near-liminal performance

The concept of a psychophysical threshold is foundational in perceptual psychology. In practice, thresholds are operationalized as stimulus values that lead to a fairly high level of performance such as .75 or .707 in two-choice tasks. These operationalizations are not useful for assessing subliminality—the state in which a stimulus is so weak that performance is at chance. We present a hierarchical Bayesian model of performance that incorporates a threshold that divides subliminal from near-liminal performance. The model provides a convenient means to measure at-chance thresholds and therefore is useful for testing theories of subliminal priming. The hierarchical nature of the model is critical for efficient analysis as strength is pooled across people and stimulus values. A comparison to Rasch psychometric models is provided.     

An Investigation of the Structural Validity of Loevinger's Model and Measure of Ego Development

This study demonstrates the use of structural equation modeling for investigating a hierarchical model of personality based on Loevinger's (1976) conceptualization. This model was constructed to have a multifactorial and hierarchical structure in which the ego development construct served as the source of covariation for specific personality constructs of impulse control, interpersonal style, conscious preoccupations, and cognitive style. This model and three other conceivable models were investigated to determine which structure best represented the relations among specific personality constructs and ego development. The specific personality constructs were identified by measures chosen from the available pool of measures that were compatible with Loevinger's conceptualization. The four conceivable models were fitted to sample data from 267 adult subjects using confirmatory factor analysis and were compared with indices of model fit and methods for comparison of nested models. Results suggested that the four specific personality constructs and ego development are part of the same process. Although a hierarchical structure appeared tenable for this process, the role of ego development perhaps is not as dominant as envisioned by Loevinger. These results must be considered tentative due to measurement limitations.     

Bayesian and maximum likelihood estimation of hierarchical response time models

Hierarchical (or multilevel) statistical models have become increasingly popular in psychology in the last few years. In this article, we consider the application of multilevel modeling to the ex-Gaussian, a popular model of response times. We compare single-level and hierarchical methods for estimation of the parameters of ex-Gaussian distributions. In addition, for each approach, we compare maximum likelihood estimation with Bayesian estimation. A set of simulations and analyses of parameter recovery show that although all methods perform adequately well, hierarchical methods are better able to recover the parameters of the ex-Gaussian, by reducing variability in the recovered parameters. At each level, little overall difference was observed between the maximum likelihood and Bayesian methods.