Calibrated Bayes Factors Should Not Be Used: A Reply to Hoijtink,van Kooten,and Hulsker

Hoijtink, Kooten, and Hulsker (2016 Hoijtink, H., van Kooten, P., &; Hulsker, K. (2016). Why Bayesian psychologists should change the way they use the Bayes factor. Multivariate Behavioral Research, 51, 1--9. doi: 10.1080/00273171.2014.969364.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) present a method for choosing the prior distribution for an analysis with Bayes factor that is based on controlling error rates, which they advocate as an alternative to our more subjective methods (Morey &; Rouder, 2014 Morey, R.D., &; Rouder, J.N. (2014). Bayesfactor: Computation of Bayes factors for common designs. R package version 0.9.9. Retrieved from http://CRAN.R-project.org/package=BayesFactor [Google Scholar]; Rouder, Speckman, Sun, Morey, &; Iverson, 2009 Rouder, J.N., Speckman, P.L., Sun, D., Morey, R.D., &; Iverson, G. (2009). Bayesian t-tests for accepting and rejecting the null hypothesis. Psychonomic Bulletin and Review, 16, 225–237. doi: 10.3758/PBR.16.2.225[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]; Wagenmakers, Wetzels, Borsboom, &; van der Maas, 2011 Wagenmakers, E.-J., Wetzels, R., Borsboom, D., &; van der Maas, H. (2011). Why psychologists must change the way they analyze their data: The case of psi. A comment on Bem (2011). Journal of Personality and Social Psychology, 100, 426–432. doi: 10.1037/a0022790[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). We show that the method they advocate amounts to a simple significance test, and that the resulting Bayes factors are not interpretable. Additionally, their method fails in common circumstances, and has the potential to yield arbitrarily high Type II error rates. After critiquing their method, we outline the position on subjectivity that underlies our advocacy of Bayes factors.     

Evidence for Mixed Processes in Normal/Mirror Discrimination of Rotated Letters: A Bayesian Model Comparison Between Single- and Mixed-Distribution Models1

When determining whether a rotated letter is normal or mirrored, an observer mentally rotates the letter to its canonical orientation. To account for patterns of response times (RTs) for the normal/mirror discrimination of rotated letters, previous research formulated a model that postulated a mixture of trials with and without mental rotation. While this model could explain the curvilinear relationship that has been found between averaged RT and letter orientations, the curved RT function is still open to alternative explanations without assuming mixed processes. To address this issue and test the mixed-process hypothesis more directly, we analyzed trial-by-trial RT data instead of averaged RTs by employing a Bayesian model comparison technique. If rotation and non-rotation trials are mixed, trial-by-trial RTs for letters in a particular orientation should not follow a single distribution but a mixed one formed from the superposition of two separate distributions, one for rotation and one for non-rotation trials. In the present study, we compared single- and mixed-distribution models. Bayes-factor analysis showed decisive support for the mixed-distribution model over the single-distribution model. In addition, using the widely applicable information criterion (WAIC), the predictive accuracy of the mixed-distribution model was found to be as high as that of the single-distribution model. These results indicated the involvement of mixed processes in normal/mirror discrimination of rotated letters. The usefulness of statistical modeling in psychological study and necessary precautions to take in the interpretation of the parameters of unconfirmed models are also discussed.     

Naïve and Robust: Class‐Conditional Independence in Human Classification Learning

Humans excel in categorization. Yet from a computational standpoint, learning a novel probabilistic classification task involves severe computational challenges. The present paper investigates one way to address these challenges: assuming class‐conditional independence of features. This feature independence assumption simplifies the inference problem, allows for informed inferences about novel feature combinations, and performs robustly across different statistical environments. We designed a new Bayesian classification learning model (the dependence‐independence structure and category learning model, DISC‐LM) that incorporates varying degrees of prior belief in class‐conditional independence, learns whether or not independence holds, and adapts its behavior accordingly. Theoretical results from two simulation studies demonstrate that classification behavior can appear to start simple, yet adapt effectively to unexpected task structures. Two experiments—designed using optimal experimental design principles—were conducted with human learners. Classification decisions of the majority of participants were best accounted for by a version of the model with very high initial prior belief in class‐conditional independence, before adapting to the true environmental structure. Class‐conditional independence may be a strong and useful default assumption in category learning tasks.     

Generic language use reveals domain differences in young children's expectations about animal and artifact categories

The goal of the present study was to explore domain differences in young children's expectations about the structure of animal and artifact categories. We examined 5-year-olds’ and adults’ use of category-referring generic noun phrases (e.g., “Birds fly”) about novel animals and artifacts. The same stimuli served as both animals and artifacts; thus, stimuli were perceptually identical across domains, and domain was indicated exclusively by language. Results revealed systematic domain differences: children and adults produced more generic utterances when items were described as animals than artifacts. Because the stimuli were novel and lacking perceptual cues to domain, these findings must be attributed to higher-order expectations about animal and artifact categories. Overall, results indicate that by age 5, children are able to make knowledge-based domain distinctions between animals and artifacts that may be rooted in beliefs about the coherence and homogeneity of categories within these domains.     

Bayesian Analysis of Nonlinear Structural Equation Models with Nonignorable Missing Data

A Bayesian approach is developed for analyzing nonlinear structural equation models with nonignorable missing data. The nonignorable missingness mechanism is specified by a logistic regression model. A hybrid algorithm that combines the Gibbs sampler and the Metropolis–Hastings algorithm is used to produce the joint Bayesian estimates of structural parameters, latent variables, parameters in the nonignorable missing model, as well as their standard errors estimates. A goodness-of-fit statistic for assessing the plausibility of the posited nonlinear structural equation model is introduced, and a procedure for computing the Bayes factor for model comparison is developed via path sampling. Results obtained with respect to different missing data models, and different prior inputs are compared via simulation studies. In particular, it is shown that in the presence of nonignorable missing data, results obtained by the proposed method with a nonignorable missing data model are significantly better than those that are obtained under the missing at random assumption. A real example is presented to illustrate the newly developed Bayesian methodologies. This research is fully supported by a grant (CUHK 4243/03H) from the Research Grant Council of the Hong Kong Special Administration Region. The authors are thankful to the editor and reviewers for valuable comments for improving the paper, and also to ICPSR and the relevant funding agency for allowing the use of the data. Requests for reprints should be sent to Professor S.Y. Lee, Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong.     

泛文化的自尊需要：基于中国人的研究证据

自尊需要是否具有跨文化普遍性是文化心理学领域近10年来争论最为激烈的问题之一。围绕这一争议, 本文从6个方面对国内外基于中国人的自尊研究进行了梳理、整合和解读。结果显示：1)自尊作为一种结构在中国和西方是类似的; 2)中国人的自尊是存在积极偏差的; 3)高自尊对中国人是有益的; 4)中国人需要、努力且策略性地维护和促进自尊; 5)中国人只是在自尊的认知成分上水平比西方人低, 情感成分上不低; 6)自尊的文化差异可以由动机或需要本身以外的与文化密切相关的因素解释, 比如：谦虚、趋中的反应偏向、朴素的辩证认知风格等。这些证据表明：自尊需要具有跨文化普遍性, 但其表达、促进和维护因文化而异。     

Towards a cognitive theory of existential meaning

The capacity to attribute meaning to personal experiences may rest on a specialized cognitive system enabling this form of causal reasoning. Close examination of these attributional tendencies suggests that this system may be distinct from those underlying other forms of causal reasoning such as a “theory of mind” system in the behavioral domain, a folk physics system in the physical domain, and a folk biology system in the biological domain. A fourth, existential domain, an abstract ontological frame within which the subjective, narrative self is envisioned to be contained, may have driven the construction of an intuitive capacity in humans that encourages them to search for the underlying purpose or reason for having had certain life experiences. This system likely has specific, definable operational rules that are responsible for activating such explanatory searches. In addition, it appears anchored to a general intentionality system that promotes the attribution of teleological purpose and higher-order mental states to an abstract agency that is envisioned to cause events and personal experiences. Identifying the component parts of this specialized cognitive system through empirical investigations can help researchers to reconstruct both its evolutionary phylogeny and to track its developmental emergence.     

Routes to Triviality

It is known that a number of inference principles can be used to trivialise the axioms of naïve comprehension – the axioms underlying the naïve theory of sets. In this paper we systematise and extend these known results, to provide a number of general classes of axioms responsible for trivialising naïve comprehension.     

Naïve Comprehension and Contracting Implications

In his paper [6], Greg Restall conjectured that a logic supports a naïve comprehension scheme if and only if it is robustly contraction free, that is, if and only if no contracting connective is definable in terms of the primitive connectives of the logic. In this paper, we present infinitely many counterexamples to Restall's conjecture, in the form of purely implicational logics which are robustly contraction free, but which trivialize naïve comprehension.     

A developmental examination of the conceptual structure of animal, artifact, and human social categories across two cultural contexts

Previous research indicates that the ontological status that adults attribute to categories varies systematically by domain. For example, adults view distinctions between different animal species as natural and objective, but view distinctions between different kinds of furniture as more conventionalized and subjective. The present work (N = 435; ages 5-18) examined the effects of domain, age, and cultural context on beliefs about the naturalness vs. conventionality of categories. Results demonstrate that young children, like adults, view animal categories as natural kinds, but artifact categories as more conventionalized. For human social categories (gender and race), beliefs about naturalness and conventionality were predicted by interactions between cultural context and age. Implications for the origins of social categories and theories of conceptual development will be discussed.