Bayesian hypothesis testing: Editorial to the Special Issue on Bayesian data analysis

In the past 20 years, there has been a steadily increasing attention and demand for Bayesian data analysis across multiple scientific disciplines, including psychology. Bayesian methods and the related Markov chain Monte Carlo sampling techniques offered renewed ways of handling old and challenging new problems that may be difficult or impossible to handle using classical approaches. Yet, such opportunities and potential improvements have not been sufficiently explored and investigated. This is 1 of 2 special issues in Psychological Methods dedicated to the topic of Bayesian data analysis, with an emphasis on Bayesian hypothesis testing, model comparison, and general guidelines for applications in psychology. In this editorial, we provide an overview of the use of Bayesian methods in psychological research and a brief history of the Bayes factor and the posterior predictive p value. Translational abstracts that summarize the articles in this issue in very clear and understandable terms are included in the Appendix.https://deepblue.lib.umich.edu/bitstream/2027.42/136926/1/Bayesian Hypothesis Testing Editorial to the Special Issue on Bayesian.pdfDescription of Bayesian Hypothesis Testing Editorial to the Special Issue on Bayesian.pdf : Main Articl

Fitting Nonlinear Ordinary Differential Equation Models with Random Effects and Unknown Initial Conditions Using the Stochastic Approximation Expectation–Maximization (SAEM) Algorithm

The past decade has evidenced the increased prevalence of irregularly spaced longitudinal data in social sciences. Clearly lacking, however, are modeling tools that allow researchers to fit dynamic models to irregularly spaced data, particularly data that show nonlinearity and heterogeneity in dynamical structures. We consider the issue of fitting multivariate nonlinear differential equation models with random effects and unknown initial conditions to irregularly spaced data. A stochastic approximation expectation–maximization algorithm is proposed and its performance is evaluated using a benchmark nonlinear dynamical systems model, namely, the Van der Pol oscillator equations. The empirical utility of the proposed technique is illustrated using a set of 24-h ambulatory cardiovascular data from 168 men and women. Pertinent methodological challenges and unresolved issues are discussed

Developmental family processes and interparental conflict: Patterns of microlevel influences.

Although frequent calls are made for the study of effects of children on families and mutual influence processes within families, little empirical progress has been made. We address these questions at the level of micro processes during marital conflict, including children’s influence on marital conflict and parents’ influence on each other. Participants were 111 cohabiting couples with a child (55 males, 56 females) aged 8 – 16 years. Data were drawn from parents’ diary reports of interparental conflict over 15 days, analyzed using dynamic systems modeling tools. Child emotions and behavior during conflicts were associated with interparental positivity, negativity, and resolution at the end of the same conflicts. For example, children’s agentic behavior was associated with more marital conflict resolution whereas child negativity was linked with more marital negativity. Regarding parents’ influence on each other, among the findings, husbands’ and wives’ influence on themselves from one conflict to the next was indicated, and total number of conflicts predicted greater influence of wives’ positivity on husbands’ positivity. Contributions of these findings to the understanding of developmental family processes are discussed, including implications for advanced understanding of interrelations between child and adult functioning and development

Dynamic infant–parent affect coupling during the face-to-face/still-face.

We examined dynamic infant-parent affect coupling using the Face-to-Face/Still-Face (FFSF) paradigm. The sample included 20 infants whose older siblings had been diagnosed with Autism Spectrum Disorders (ASD-sibs), and 18 infants with comparison siblings (COMP-sibs). A series of extended autoregressive models was used to represent the self-regulation and interactive dynamics of infants and parents during FFSF. Significant bidirectional affective coupling was found between infants and parents, with the former serving as the “leading members” of the dyads. Further analysis of within-dyad dynamics revealed ongoing changes in concurrent infant-parent linkages both within and across different FFSF episodes. The importance of considering both inter- and intra-dyad differences is discussed

Bayesian analysis of ambulatory blood pressure dynamics with application to irregularly spaced sparse data

Ambulatory cardiovascular (CV) measurements provide valuable insights into individuals' health conditions in “real-life,” everyday settings. Current methods of modeling ambulatory CV data do not consider the dynamic characteristics of the full data set and their relationships with covariates such as caffeine use and stress. We propose a stochastic differential equation (SDE) in the form of a dual nonlinear Ornstein-Uhlenbeck (OU) model with person-specific covariates to capture the morning surge and nighttime dipping dynamics of ambulatory CV data. To circumvent the data analytic constraint that empirical measurements are typically collected at irregular and much larger time intervals than those evaluated in simulation studies of SDEs, we adopt a Bayesian approach with a regularized Brownian Bridge sampler (RBBS) and an efficient multiresolution (MR) algorithm to fit the proposed SDE. The MR algorithm can produce more efficient MCMC samples that is crucial for valid parameter estimation and inference. Using this model and algorithm to data from the Duke Behavioral Investigation of Hypertension Study, results indicate that age, caffeine intake, gender and race have effects on distinct dynamic characteristics of the participants' CV trajectories

Bayesian Lasso for Semiparametric Structural Equation Models

There has been great interest in developing nonlinear structural equation models and associated statistical inference procedures, including estimation and model selection methods. In this paper a general semiparametric structural equation model (SSEM) is developed in which the structural equation is composed of nonparametric functions of exogenous latent variables and fixed covariates on a set of latent endogenous variables. A basis representation is used to approximate these nonparametric functions in the structural equation and the Bayesian Lasso method coupled with a Markov Chain Monte Carlo (MCMC) algorithm is used for simultaneous estimation and model selection. The proposed method is illustrated using a simulation study and data from the Affective Dynamics and Individual Differences (ADID) study. Results demonstrate that our method can accurately estimate the unknown parameters and correctly identify the true underlying model

Bayesian estimation of semiparametric nonlinear dynamic factor analysis models using the Dirichlet process prior: Semiparametric nonlinear DFA models with the DP prior

Parameters in time series and other dynamic models often show complex range restrictions and their distributions may deviate substantially from multivariate normal or other standard parametric distributions. We use the truncated Dirichlet process (DP) as a non-parametric prior for such dynamic parameters in a novel nonlinear Bayesian dynamic factor analysis model. This is equivalent to specifying the prior distribution to be a mixture distribution composed of an unknown number of discrete point masses (or clusters). The stick-breaking prior and the blocked Gibbs sampler are used to enable efficient simulation of posterior samples. Using a series of empirical and simulation examples, we illustrate the flexibility of the proposed approach in approximating distributions of very diverse shapes