Browsing by Subject "Bayesian modeling"
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Item Bayesian Modeling of Associations in Bivariate Mixed-Effects Models for Segmented Growth Curves(2018-11) Peralta Torres, YadiraDevelopmental processes rarely occur in isolation; often the growth curves of two or more variables are interdependent. In addition, frequently, growth curves do not portray a constant pattern of change. Different stages or segments of development are present in the data. Bivariate piecewise linear mixed-effects models (BPLMEM) are a useful statistical framework to simultaneously describe two processes that portray segmented linear trajectories and to investigate their associations over time. Interrelations between the growth curves are measured by assuming a joint distribution of the random-effects parameters of each outcome variable. Furthermore, associations in the outcome variables collected from the same subject should be taken into account when they are modeled jointly. This association is modeled by correlating the error variance parameters of each outcome variable. There are several drawbacks in the literature of bivariate piecewise mixed-effects models. An important limitation in the BPLMEMs literature is that researchers have assumed uncorrelated residual errors across the two longitudinal processes, which is something unlikely to hold in practice. Also, current modeling choices for the random-effects in bivariate piecewise mixed-effects model have shortcomings. For instance, researchers have unintentionally imposed dependencies among the elements of the covariance matrix associated with the random-effects; or they have modeled only few of its covariance parameters determined by the research interest. In addition, simulation studies using BPLMEMs are scarce. Little is known about the performance of bivariate piecewise mixed-effects models under different correlational scenarios of the random-effects parameters and the error variances. Furthermore, a criticism to the piecewise linear model is a hypothesized abrupt change between one linear segment to another because this performance may not be true for all empirical scenarios. However, although a smooth transition or adaptation period between linear segments might be more realistic, the piecewise linear model is extensively used in practice. Thus, it is natural to wonder under which scenarios this is an acceptable choice. The purpose of the present study was to develop a BPLMEM using a Bayesian inference approach allowing the estimation of the association between error variances and providing a more robust modeling choice for the random-effects. Furthermore, the performance of the BPLMEM was investigated via a Monte Carlo simulation study focusing on the strength of the associations of the error variance parameters and the growth curves (represented by the random-effects’ correlational structure). An additional purpose was to empirically characterize scenarios for which the piecewise linear model gives a reasonable approximation to an underlying smoothed segmented trajectory given by a quadratic bend joining the linear phases of growth. Lastly, the contribution of bivariate mixed-effects modeling approaches is illustrated by using a BPLMEM to investigate the joint development of mathematics and reading achievement and the association between their longitudinal trajectories. This constitutes a novel approach to examine associations between educational domains over time. Simulation results showed that the strength of the association between the growth curves and the sample size had a significant effect on the performance of the BPLMEM. Specifically, lower relative bias of parameter estimates and higher model convergence was related to a stronger correlational structure between the random-effects of the growth curves. Likewise, slightly higher coverage rates and better convergence were associated with a smaller sample size. In addition, it was possible to identify cases for which the piecewise linear model had an acceptable performance when the true underlying trajectory had an adaptation period or bend between linear segments. Scenarios with small or centered bends were accurately described by a piecewise linear model. Results from the illustrative example suggested that mathematics and reading achievement are positively associated all along their segmented trajectories and that the strength of such association decreases over time. In addition, evidence of the same patterns of association of reading over mathematics and mathematics over reading were found.Item Bayesian spatiotemporal modeling using spatial hierarchical priors with applications to functional magnetic resonance imaging(2015-01) Bezener, Martin AndrewFunctional magnetic resonance imaging (fMRI) has recently become a popular tool for studying human brain activity. Despite its widespread use, most existing statistical methods for analyzing fMRI data are problematic. Many methodologies oversimplify the problem for the sake of computational efficiency, often not providing a full statistical model as a result. Other methods are too computationally inefficient to use on large data sets. In this paper, we propose a Bayesian method for analyzing fMRI data that is computationally efficient and provides a full statistical model.Item Contextual Influences on Cognitive and Psychophysiological Mechanisms of Learning in Early Adolescence(2023-06) DeJoseph, MeriahLearning is a central mechanism through which early experiences shape biological and behavioral development across the lifespan. One type of learning, called reinforcement learning, is posited to support youth’s ability to engage and adapt to their unique worlds with links to long-term social and emotional outcomes. Yet, individual differences in reinforcement learning across diverse environmental and experimental contexts remains poorly characterized in developmental samples. The current dissertation study integrated reinforcement learning and dynamic systems frameworks and drew upon newly adapted methodologies to capture how cognitive and psychophysiological processes of learning are modulated by socioemotional context. In a sample of 56 youth aged 12-15-years-old, this study leveraged a within-person experimental design and quantified continuous behavior and heart rate (~700 observations per system, per person) during an adapted reinforcement learning task with stimuli that varied in socioemotional relevance. Findings revealed that compared to traditionally-used benign or non-emotional stimuli, learning from stimuli high in socioemotional arousal enhanced behavioral performance. The use of computational modeling afforded valuable insights into the differential cognitive processes and strategies youth recruited to achieve such a behavioral advantage, demonstrating that socioemotional salience may have elicited faster value-updating processes and qualitative shifts in more exploitative decision-making. Underlying psychophysiological engagement seemed to be particularly modulated not by socioemotional salience as hypothesized, but by heightened sensitivity to learning from rewards, such that faster value-updating in the context of rewards aligned with more optimal psychophysiological flexibility and organization. Taken together, this study provides an important step in clarifying the contexts and modulatory processes that serve to enhance and support the unique ways youth learn and make decisions. Open questions remain about the adaptive utility of these various patterns of behavior, cognition, and psychophysiology across a variety of learning contexts, how they are shaped by prior lived experiences across development, and how they predict later psychosocial adjustment outcomes. Such work will shed light on how youth learn from–and adapt to–different contextual demands, with the potential to inform programs and policies that support youth’s ability to adjust to their dynamically changing ecologies.