Testing Conditional Independence in Psychometric Networks: An Analysis of Three Bayesian Methods.

Network psychometrics uses graphical models to assess the network structure of psychological variables. An important task in their analysis is determining which variables are unrelated in the network, i.e., are independent given the rest of the network variables. This conditional independence structure is a gateway to understanding the causal structure underlying psychological processes. Thus, it is crucial to have an appropriate method for evaluating conditional independence and dependence hypotheses. Bayesian approaches to testing such hypotheses allow researchers to differentiate between absence of evidence and evidence of absence of connections (edges) between pairs of variables in a network. Three Bayesian approaches to assessing conditional independence have been proposed in the network psychometrics literature. We believe that their theoretical foundations are not widely known, and therefore we provide a conceptual review of the proposed methods and highlight their strengths and limitations through a simulation study. We also illustrate the methods using an empirical example with data on Dark Triad Personality. Finally, we provide recommendations on how to choose the optimal method and discuss the current gaps in the literature on this important topic.

A review of applications of the Bayes factor in psychological research.

The last 25 years have shown a steady increase in attention for the Bayes factor as a tool for hypothesis evaluation and model selection. The present review highlights the potential of the Bayes factor in psychological research. We discuss six types of applications: Bayesian evaluation of point null, interval, and informative hypotheses, Bayesian evidence synthesis, Bayesian variable selection and model averaging, and Bayesian evaluation of cognitive models. We elaborate what each application entails, give illustrative examples, and provide an overview of key references and software with links to other applications. The article is concluded with a discussion of the opportunities and pitfalls of Bayes factor applications and a sketch of corresponding future research lines. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Bayesian Estimation of Single-Test Reliability Coefficients.

Popular measures of reliability for a single-test administration include coefficient α, coefficient λ2, the greatest lower bound (glb), and coefficient ω. First, we show how these measures can be easily estimated within a Bayesian framework. Specifically, the posterior distribution for these measures can be obtained through Gibbs sampling - for coefficients α, λ2, and the glb one can sample the covariance matrix from an inverse Wishart distribution; for coefficient ω one samples the conditional posterior distributions from a single-factor CFA-model. Simulations show that - under relatively uninformative priors - the 95% Bayesian credible intervals are highly similar to the 95% frequentist bootstrap confidence intervals. In addition, the posterior distribution can be used to address practically relevant questions, such as "what is the probability that the reliability of this test is between .70 and .90?", or, "how likely is it that the reliability of this test is higher than .80?" In general, the use of a posterior distribution highlights the inherent uncertainty with respect to the estimation of reliability measures.

The JASP guidelines for conducting and reporting a Bayesian analysis.

Despite the increasing popularity of Bayesian inference in empirical research, few practical guidelines provide detailed recommendations for how to apply Bayesian procedures and interpret the results. Here we offer specific guidelines for four different stages of Bayesian statistical reasoning in a research setting: planning the analysis, executing the analysis, interpreting the results, and reporting the results. The guidelines for each stage are illustrated with a running example. Although the guidelines are geared towards analyses performed with the open-source statistical software JASP, most guidelines extend to Bayesian inference in general.

Crowdsourcing hypothesis tests: Making transparent how design choices shape research results.

To what extent are research results influenced by subjective decisions that scientists make as they design studies? Fifteen research teams independently designed studies to answer five original research questions related to moral judgments, negotiations, and implicit cognition. Participants from 2 separate large samples (total N > 15,000) were then randomly assigned to complete 1 version of each study. Effect sizes varied dramatically across different sets of materials designed to test the same hypothesis: Materials from different teams rendered statistically significant effects in opposite directions for 4 of 5 hypotheses, with the narrowest range in estimates being d = -0.37 to + 0.26. Meta-analysis and a Bayesian perspective on the results revealed overall support for 2 hypotheses and a lack of support for 3 hypotheses. Overall, practically none of the variability in effect sizes was attributable to the skill of the research team in designing materials, whereas considerable variability was attributable to the hypothesis being tested. In a forecasting survey, predictions of other scientists were significantly correlated with study results, both across and within hypotheses. Crowdsourced testing of research hypotheses helps reveal the true consistency of empirical support for a scientific claim. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

DstarM: an R package for analyzing two-choice reaction time data with the D∗M method.

The decision process in choice reaction time data is traditionally described in detail with diffusion models. However, the total reaction time is assumed to consist of the sum of a decision time (as modeled by the diffusion process) and the time devoted to nondecision processes (e.g., perceptual and motor processes). It has become standard practice to assume that the nondecision time is uniformly distributed. However, a misspecification of the nondecision time distribution introduces bias in the parameter estimates for the decision model. Recently, a new method has been proposed (called the D∗M method) that allows the estimation of the decision model parameters, while leaving the nondecision time distribution unspecified. In a second step, a nonparametric estimate of the nondecision time distribution may be retrieved. In this paper, we present an R package that estimates parameters of several diffusion models via the D∗M method. Moreover, it is shown in a series of extensive simulation studies that the parameters of the decision model and the nondecision distributions are correctly retrieved.

Outcome measurement in mental health services: insights from symptom networks.

BACKGROUND: In mental health, outcomes are currently measured by changes of individual scores. However, such an analysis on individual scores does not take into account the interaction between symptoms, which could yield crucial information while investigating outcomes. Network analysis techniques can be used to routinely study these systems of interacting symptoms. The present study aimed at comparing outcomes using individual scores vs. symptom networks, after a 1 year intervention at a local community mental health centre. METHODS: We used the Health of the Nation Outcomes Scales, which defines a set of 12 scales investigating mental health and social functioning. We first assessed how individual scores varied from baseline to end point and which items were associated to treatment response. Second, using network analysis techniques, we measured the overall connectivity of the networks and determined the most important symptoms. RESULTS: The individual scores analysis revealed a significant improvement amongst most scales. No specific factors were related to treatment response at end point. At end point, network analysis revealed a very densely connected network while agitation and substance use were the most connected symptoms. CONCLUSIONS: Individual scores and symptom network analysis resulted in very different outcomes, with network analysis toning down positive results gained from individual scores analysis. The strong connectivity of patients' network at end point may reflect their increased complexity. Allocating more resources to interventions tailored to symptoms that are the most connected would decrease network connectivity and improve patients' prognosis. When investigating outcomes, network analysis could give insights complementary to standard analysis on individual scores.

Parsimonious estimation of signal detection models from confidence ratings.

Signal detection theory (SDT) is used to quantify people's ability and bias in discriminating stimuli. The ability to detect a stimulus is often measured through confidence ratings. In SDT models, the use of confidence ratings necessitates the estimation of confidence category thresholds, a requirement that can easily result in models that are overly complex. As a parsimonious alternative, we propose a threshold SDT model that estimates these category thresholds using only two parameters. We fit the model to data from Pratte et al. (Journal of Experimental Psychology: Learning, Memory, and Cognition, 36, 224-232 2010) and illustrate its benefits over previous threshold SDT models.

Bayesian inference for psychology. Part II: Example applications with JASP.

Bayesian hypothesis testing presents an attractive alternative to p value hypothesis testing. Part I of this series outlined several advantages of Bayesian hypothesis testing, including the ability to quantify evidence and the ability to monitor and update this evidence as data come in, without the need to know the intention with which the data were collected. Despite these and other practical advantages, Bayesian hypothesis tests are still reported relatively rarely. An important impediment to the widespread adoption of Bayesian tests is arguably the lack of user-friendly software for the run-of-the-mill statistical problems that confront psychologists for the analysis of almost every experiment: the t-test, ANOVA, correlation, regression, and contingency tables. In Part II of this series we introduce JASP ( http://www.jasp-stats.org ), an open-source, cross-platform, user-friendly graphical software package that allows users to carry out Bayesian hypothesis tests for standard statistical problems. JASP is based in part on the Bayesian analyses implemented in Morey and Rouder's BayesFactor package for R. Armed with JASP, the practical advantages of Bayesian hypothesis testing are only a mouse click away.