An elicitation method for multiple linear regression models

This paper describes a method of quantifying subjective opinion about a normal linear regression model. Opinion about the regression coefficients and experimental error is elicited and modeled by a multivariate probability distribution (a Bayesian conjugate prior distribution). The distribution model is richly parameterized and various assessment tasks are used to estimate its parameters. These tasks include the revision of opinion in the light of hypothetical data, the assessment of credible intervals, and a task commonly performed in cue-weighting experiments. A new assessment task is also introduced. In addition, implementation of the method in an interactive computer program is described and the method is illustrated with a practical example.     

Bayesian Extended Redundancy Analysis: A Bayesian Approach to Component-based Regression with Dimension Reduction

Abstract

Extended redundancy analysis (ERA) combines linear regression with dimension reduction to explore the directional relationships between multiple sets of predictors and outcome variables in a parsimonious manner. It aims to extract a component from each set of predictors in such a way that it accounts for the maximum variance of outcome variables. In this article, we extend ERA into the Bayesian framework, called Bayesian ERA (BERA). The advantages of BERA are threefold. First, BERA enables to make statistical inferences based on samples drawn from the joint posterior distribution of parameters obtained from a Markov chain Monte Carlo algorithm. As such, it does not necessitate any resampling method, which is on the other hand required for (frequentist’s) ordinary ERA to test the statistical significance of parameter estimates. Second, it formally incorporates relevant information obtained from previous research into analyses by specifying informative power prior distributions. Third, BERA handles missing data by implementing multiple imputation using a Markov Chain Monte Carlo algorithm, avoiding the potential bias of parameter estimates due to missing data. We assess the performance of BERA through simulation studies and apply BERA to real data regarding academic achievement.     

The influence of chemical cues on the territorial prior residence effect in convict cichlids (cichlasoma nigrofasciatum Günther)

The importance of accumulated chemical cues on the occurrence of the territorial prior residence effect was investigated in two experiments using adult convict cichlids (Cichlasonul nigrofasciatum). In the first experiment, pairs of fish, matched on a number of criteria, were randomly assigned to three independent treatment conditions in which (1) the territorial marker (pot or clump of plants) was removed just prior to a direct encounter in the aquarium of the resident (pair member in whose aquarium the encounter took place) with accumulated chemical cues remaining intact; (2) the marker was removed, as well as the chemical cues; or (3) the marker was present, but the chemical cues were removed. Results showed that a significant prior residence effect occurred when the marker was present, but did not occur in either condition in which the marker was removed. A second experiment, in which the marker was removed and the gravel substrate altered, also did not reveal a signficant prior residence effect. Apparently, the territorial resident recognizes his territory by using certain visual cues, with accumulated chemical cues being neither necessary nor sufficient in this process.     

儿童对他人情绪与过去经验的关系的认知

用设置故事情景的方法对儿童对他人情绪与过去经验的关系的认知进行了实验研究。研究表明,4～7岁儿童能够认知他人情绪与过去经验的关系,认知能力随年龄的增长不断提高。情绪效价和情绪情景的匹配性影响儿童对他人情绪与过去经验关系的认知。4、5岁儿童更能认识到正性情绪情景条件下体验到负性情绪的他人情绪与过去经验的关系,其得分显著高于其它情绪情景故事和行为故事。     

Why Bayesian Psychologists Should Change the Way They Use the Bayes Factor

The discussion following Bem’s (2011 Bem, D. J. (2011). Feeling the future: Experimental evidence for anomalous retroactive influences on cognition and affect. Journal of Personality and Social Psychology, 100, 407–425. doi: 10.1037/a0021524[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) psi research highlights that applications of the Bayes factor in psychological research are not without problems. The first problem is the omission to translate subjective prior knowledge into subjective prior distributions. In the words of Savage (1961 Savage, L. J. (1961). The foundations of statistical inference reconsidered. In J. Neyman, (Ed.), Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Contributions to the Theory of Statistics, pp. 575–586. BerkeleyCA: University of California. [Google Scholar]): “they make the Bayesian omelet without breaking the Bayesian egg.” The second problem occurs if the Bayesian egg is not broken: the omission to choose default prior distributions such that the ensuing inferences are well calibrated. The third problem is the adherence to inadequate rules for the interpretation of the size of the Bayes factor. The current paper will elaborate these problems and show how to avoid them using the basic hypotheses and statistical model used in the first experiment described in Bem (2011 Bem, D. J. (2011). Feeling the future: Experimental evidence for anomalous retroactive influences on cognition and affect. Journal of Personality and Social Psychology, 100, 407–425. doi: 10.1037/a0021524[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). It will be argued that a thorough investigation of these problems in the context of more encompassing hypotheses and statistical models is called for if Bayesian psychologists want to add a well-founded Bayes factor to the tool kit of psychological researchers.     

A Comparison of Inverse-Wishart Prior Specifications for Covariance Matrices in Multilevel Autoregressive Models

Multilevel autoregressive models are especially suited for modeling between-person differences in within-person processes. Fitting these models with Bayesian techniques requires the specification of prior distributions for all parameters. Often it is desirable to specify prior distributions that have negligible effects on the resulting parameter estimates. However, the conjugate prior distribution for covariance matrices—the Inverse-Wishart distribution—tends to be informative when variances are close to zero. This is problematic for multilevel autoregressive models, because autoregressive parameters are usually small for each individual, so that the variance of these parameters will be small. We performed a simulation study to compare the performance of three Inverse-Wishart prior specifications suggested in the literature, when one or more variances for the random effects in the multilevel autoregressive model are small. Our results show that the prior specification that uses plug-in ML estimates of the variances performs best. We advise to always include a sensitivity analysis for the prior specification for covariance matrices of random parameters, especially in autoregressive models, and to include a data-based prior specification in this analysis. We illustrate such an analysis by means of an empirical application on repeated measures data on worrying and positive affect.     

When does prior knowledge disproportionately benefit older adults’ memory?

Material consistent with knowledge/experience is generally more memorable than material inconsistent with knowledge/experience – an effect that can be more extreme in older adults. Four experiments investigated knowledge effects on memory with young and older adults. Memory for familiar and unfamiliar proverbs (Experiment 1) and for common and uncommon scenes (Experiment 2) showed similar knowledge effects across age groups. Memory for person-consistent and person-neutral actions (Experiment 3) showed a greater benefit of prior knowledge in older adults. For cued recall of related and unrelated word pairs (Experiment 4), older adults benefited more from prior knowledge only when it provided uniquely useful additional information beyond the episodic association itself. The current data and literature suggest that prior knowledge has the age-dissociable mnemonic properties of (1) improving memory for the episodes themselves (age invariant), and (2) providing conceptual information about the tasks/stimuli extrinsically to the actual episodic memory (particularly aiding older adults).     

'You’re Being Unreasonable’: Prior and Passing Theories of Critical Discussion

A key and continuing concern within the pragma-dialectical theory of argumentation is how to account for effective persuasion disciplined by dialectical rationality. Currently, van Eemeren and Houtlosser offer one response to this concern in the form of strategic manoeuvring. This paper offers a prior/passing theory of communicative interaction as a supplement to the strategic manoeuvring approach. Our use of a prior/passing model investigates how a difference of opinion can be resolved while both dialectic obligations of reasonableness and rhetorical ambitions of argumentative success are simultaneously accommodated. The paper explores the model with particular reference to the pragma-dialectical rules of critical discussion, strategic manoeuvring and fallacious reasoning.