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Preview: Psychological Methods - Vol 11, Iss 3

Psychological Methods - Vol 22, Iss 2

Psychological Methods is devoted to the development and dissemination of methods for collecting, analyzing, understanding, and interpreting psychological data. Its purpose is the dissemination of innovations in research design, measurement, methodology, a

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Copyright: Copyright 2017 American Psychological Association

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. (PsycINFO Database Record (c) 2017 APA, all rights reserved)(image)

A systematic review of Bayesian articles in psychology: The last 25 years.


Although the statistical tools most often used by researchers in the field of psychology over the last 25 years are based on frequentist statistics, it is often claimed that the alternative Bayesian approach to statistics is gaining in popularity. In the current article, we investigated this claim by performing the very first systematic review of Bayesian psychological articles published between 1990 and 2015 (n = 1,579). We aim to provide a thorough presentation of the role Bayesian statistics plays in psychology. This historical assessment allows us to identify trends and see how Bayesian methods have been integrated into psychological research in the context of different statistical frameworks (e.g., hypothesis testing, cognitive models, IRT, SEM, etc.). We also describe take-home messages and provide “big-picture” recommendations to the field as Bayesian statistics becomes more popular. Our review indicated that Bayesian statistics is used in a variety of contexts across subfields of psychology and related disciplines. There are many different reasons why one might choose to use Bayes (e.g., the use of priors, estimating otherwise intractable models, modeling uncertainty, etc.). We found in this review that the use of Bayes has increased and broadened in the sense that this methodology can be used in a flexible manner to tackle many different forms of questions. We hope this presentation opens the door for a larger discussion regarding the current state of Bayesian statistics, as well as future trends. (PsycINFO Database Record (c) 2017 APA, all rights reserved)(image)

Improving transparency and replication in Bayesian statistics: The WAMBS-Checklist.


Bayesian statistical methods are slowly creeping into all fields of science and are becoming ever more popular in applied research. Although it is very attractive to use Bayesian statistics, our personal experience has led us to believe that naively applying Bayesian methods can be dangerous for at least 3 main reasons: the potential influence of priors, misinterpretation of Bayesian features and results, and improper reporting of Bayesian results. To deal with these 3 points of potential danger, we have developed a succinct checklist: the WAMBS-checklist (When to worry and how to Avoid the Misuse of Bayesian Statistics). The purpose of the questionnaire is to describe 10 main points that should be thoroughly checked when applying Bayesian analysis. We provide an account of “when to worry” for each of these issues related to: (a) issues to check before estimating the model, (b) issues to check after estimating the model but before interpreting results, (c) understanding the influence of priors, and (d) actions to take after interpreting results. To accompany these key points of concern, we will present diagnostic tools that can be used in conjunction with the development and assessment of a Bayesian model. We also include examples of how to interpret results when “problems” in estimation arise, as well as syntax and instructions for implementation. Our aim is to stress the importance of openness and transparency of all aspects of Bayesian estimation, and it is our hope that the WAMBS questionnaire can aid in this process. (PsycINFO Database Record (c) 2017 APA, all rights reserved)(image)

Bayesian evaluation of constrained hypotheses on variances of multiple independent groups.


Research has shown that independent groups often differ not only in their means, but also in their variances. Comparing and testing variances is therefore of crucial importance to understand the effect of a grouping variable on an outcome variable. Researchers may have specific expectations concerning the relations between the variances of multiple groups. Such expectations can be translated into hypotheses with inequality and/or equality constraints on the group variances. Currently, however, no methods are available for testing (in)equality constrained hypotheses on variances. This article proposes a novel Bayesian approach to this challenging testing problem. Our approach has the following useful properties: First, it can be used to simultaneously test multiple (non)nested hypotheses with equality as well as inequality constraints on the variances. Second, our approach is fully automatic in the sense that no subjective prior specification is needed. Only the hypotheses need to be provided. Third, a user-friendly software application is included that can be used to perform this Bayesian test in an easy manner. (PsycINFO Database Record (c) 2017 APA, all rights reserved)(image)

Bayesian analyses of cognitive architecture.


The question of cognitive architecture—how cognitive processes are temporally organized—has arisen in many areas of psychology. This question has proved difficult to answer, with many proposed solutions turning out to be spurious. Systems factorial technology (Townsend & Nozawa, 1995) provided the first rigorous empirical and analytical method of identifying cognitive architecture, using the survivor interaction contrast (SIC) to determine when people are using multiple sources of information in parallel or in series. Although the SIC is based on rigorous nonparametric mathematical modeling of response time distributions, for many years inference about cognitive architecture has relied solely on visual assessment. Houpt and Townsend (2012) recently introduced null hypothesis significance tests, and here we develop both parametric and nonparametric (encompassing prior) Bayesian inference. We show that the Bayesian approaches can have considerable advantages. (PsycINFO Database Record (c) 2017 APA, all rights reserved)(image)

Bayesian analysis of factorial designs.


This article provides a Bayes factor approach to multiway analysis of variance (ANOVA) that allows researchers to state graded evidence for effects or invariances as determined by the data. ANOVA is conceptualized as a hierarchical model where levels are clustered within factors. The development is comprehensive in that it includes Bayes factors for fixed and random effects and for within-subjects, between-subjects, and mixed designs. Different model construction and comparison strategies are discussed, and an example is provided. We show how Bayes factors may be computed with BayesFactor package in R and with the JASP statistical package. (PsycINFO Database Record (c) 2017 APA, all rights reserved)(image)

Sequential hypothesis testing with Bayes factors: Efficiently testing mean differences.


Unplanned optional stopping rules have been criticized for inflating Type I error rates under the null hypothesis significance testing (NHST) paradigm. Despite these criticisms, this research practice is not uncommon, probably because it appeals to researcher’s intuition to collect more data to push an indecisive result into a decisive region. In this contribution, we investigate the properties of a procedure for Bayesian hypothesis testing that allows optional stopping with unlimited multiple testing, even after each participant. In this procedure, which we call Sequential Bayes Factors (SBFs), Bayes factors are computed until an a priori defined level of evidence is reached. This allows flexible sampling plans and is not dependent upon correct effect size guesses in an a priori power analysis. We investigated the long-term rate of misleading evidence, the average expected sample sizes, and the biasedness of effect size estimates when an SBF design is applied to a test of mean differences between 2 groups. Compared with optimal NHST, the SBF design typically needs 50% to 70% smaller samples to reach a conclusion about the presence of an effect, while having the same or lower long-term rate of wrong inference. (PsycINFO Database Record (c) 2017 APA, all rights reserved)(image)

Decision qualities of Bayes factor and p value-based hypothesis testing.


The purpose of this article is to investigate the decision qualities of the Bayes factor (BF) method compared with the p value-based null hypothesis significance testing (NHST). The performance of the 2 methods is assessed in terms of the false- and true-positive rates, as well as the false-discovery rates and the posterior probabilities of the null hypothesis for 2 different models: an independent-samples t test and an analysis of variance (ANOVA) model with 2 random factors. Our simulation study results showed the following: (a) The common BF > 3 criterion is more conservative than the NHST α = .05 criterion, and it corresponds better with the α = .01 criterion. (b) An increasing sample size has a different effect on the false-positive rate and the false-discovery rate, depending on whether the BF or NHST approach is used. (c) When effect sizes are randomly sampled from the prior, power curves tend to be flat compared with when effect sizes are prespecified. (d) The larger the scale factor (or the wider the prior), the more conservative the inferential decision is. (e) The false-positive and true-positive rates of the BF method are very sensitive to the scale factor when the effect size is small. (f) While the posterior probabilities of the null hypothesis ideally follow from the BF value, they can be surprisingly high using NHST. In general, these findings were consistent independent of which of the 2 different models was used. (PsycINFO Database Record (c) 2017 APA, all rights reserved)(image)

A comparison of Bayesian and frequentist model selection methods for factor analysis models.


We compare the performances of well-known frequentist model fit indices (MFIs) and several Bayesian model selection criteria (MCC) as tools for cross-loading selection in factor analysis under low to moderate sample sizes, cross-loading sizes, and possible violations of distributional assumptions. The Bayesian criteria considered include the Bayes factor (BF), Bayesian Information Criterion (BIC), Deviance Information Criterion (DIC), a Bayesian leave-one-out with Pareto smoothed importance sampling (LOO-PSIS), and a Bayesian variable selection method using the spike-and-slab prior (SSP; Lu, Chow, & Loken, 2016). Simulation results indicate that of the Bayesian measures considered, the BF and the BIC showed the best balance between true positive rates and false positive rates, followed closely by the SSP. The LOO-PSIS and the DIC showed the highest true positive rates among all the measures considered, but with elevated false positive rates. In comparison, likelihood ratio tests (LRTs) are still the preferred frequentist model comparison tool, except for their higher false positive detection rates compared to the BF, BIC and SSP under violations of distributional assumptions. The root mean squared error of approximation (RMSEA) and the Tucker-Lewis index (TLI) at the conventional cut-off of approximate fit impose much more stringent “penalties” on model complexity under conditions with low cross-loading size, low sample size, and high model complexity compared with the LRTs and all other Bayesian MCC. Nevertheless, they provided a reasonable alternative to the LRTs in cases where the models cannot be readily constructed as nested within each other. (PsycINFO Database Record (c) 2017 APA, all rights reserved)(image)

Posterior calibration of posterior predictive p values.


In order to accurately control the Type I error rate (typically .05), a p value should be uniformly distributed under the null model. The posterior predictive p value (ppp), which is commonly used in Bayesian data analysis, generally does not satisfy this property. For example there have been reports where the sampling distribution of the ppp under the null model was highly concentrated around .50. In this case, a ppp of .20 would indicate model misfit, but when comparing it with a significance level of .05, which is standard statistical practice, the null model would not be rejected. Therefore, the ppp has very little power to detect model misfit. A solution has been proposed in the literature, which involves calibrating the ppp using the prior distribution of the parameters under the null model. A disadvantage of this “prior-cppp” is that it is very sensitive to the prior of the model parameters. In this article, an alternative solution is proposed where the ppp is calibrated using the posterior under the null model. This “posterior-cppp” (a) can be used when prior information is absent, (b) allows one to test any type of misfit by choosing an appropriate discrepancy measure, and (c) has a uniform distribution under the null model. The methodology is applied in various testing problems: testing independence of dichotomous variables, checking misfit of linear regression models in the presence of outliers, and assessing misfit in latent class analysis. (PsycINFO Database Record (c) 2017 APA, all rights reserved)(image)

Assessing fit of alternative unidimensional polytomous IRT models using posterior predictive model checking.


This article explored the application of the posterior predictive model checking (PPMC) method in assessing fit for unidimensional polytomous item response theory (IRT) models, specifically the divide-by-total models (e.g., the generalized partial credit model). Previous research has primarily focused on using PPMC in model checking for unidimensional and multidimensional IRT models for dichotomous data, and has paid little attention to polytomous models. A Monte Carlo simulation was conducted to investigate the performance of PPMC in detecting different sources of misfit for the partial credit model family. Results showed that the PPMC method, in combination with appropriate discrepancy measures, had adequate power in detecting different sources of misfit for the partial credit model family. Global odds ratio and item total correlation exhibited specific patterns in detecting the absence of the slope parameter, whereas Yen’s Q1 was found to be promising in the detection of misfit caused by the constant category intersection parameter constraint across items. (PsycINFO Database Record (c) 2017 APA, all rights reserved)(image)