A Bayesian psychophysical model for angular variables

Bayesian theories of perception provide a link between observed response distributions and theoretical constructs from Bayesian decision theory. Using Bayesian psychophysics we derive response distributions for two cases, one based on a normal distribution and one on a von Mises distribution for angular variables. Interestingly, where the theoretical response distribution is always unimodal in the case of normal distributions, it can become bimodal in the angular setting in the case when prior and likelihood are about equally strong.     

Simple use of BIC to Assess Model Selection Uncertainty: An Illustration using Mediation and Moderation Models

Abstract

The Bayesian information criterion (BIC) has been used sometimes in SEM, even adopting a frequentist approach. Using simple mediation and moderation models as examples, we form posterior probability distribution via using BIC, which we call the BIC posterior, to assess model selection uncertainty of a finite number of models. This is simple but rarely used. The posterior probability distribution can be used to form a credibility set of models and to incorporate prior probabilities for model comparisons and selections. This was validated by a large scale simulation and results showed that the approximation via the BIC posterior is very good except when both the sample sizes and magnitude of parameters are small. We applied the BIC posterior to a real data set, and it has the advantages of flexibility in incorporating prior, addressing overfitting problems, and giving a full picture of posterior distribution to assess model selection uncertainty.     

The effect of information distribution on collaborative inhibition

Two experiments examined collaborative memory for information that was studied by all group members (shared items) and information that was studied by only a subset of group members (unshared items). In both experiments significant collaborative inhibition (reduced output of the collaborative groups relative to the pooled output of individuals) was obtained for both shared and unshared information. In Experiment 1 the magnitude of collaborative inhibition was larger for unshared items than for shared items, possibly because unshared items were less likely to be acknowledged and thus incorporated into the groups’ recall. In Experiment 2 the magnitude of collaborative inhibition for shared and unshared information was equivalent once all participants were provided with the category name associated with the shared and unshared items. The results of the experiments are discussed in relation to the retrieval strategy disruption hypothesis of collaborative inhibition and the role of social process variables, such as acknowledgement, in influencing collaborative inhibition across situations involving memory of shared and unshared information.     

非正态分布测量数据对克隆巴赫信度α系数的影响

对“增大被试群体异质性,能提高测验信度”观点提出质疑。讨论非正态分布测量数据的偏度对克隆巴赫信度α系数的影响,以模拟方法验证Box—COX正态化变换对信度的高估现象,进而给出对克隆巴赫信度α系数估计的改进方法。     

An EM algorithm for fitting two-level structural equation models

Maximum likelihood is an important approach to analysis of two-level structural equation models. Different algorithms for this purpose have been available in the literature. In this paper, we present a new formulation of two-level structural equation models and develop an EM algorithm for fitting this formulation. This new formulation covers a variety of two-level structural equation models. As a result, the proposed EM algorithm is widely applicable in practice. A practical example illustrates the performance of the EM algorithm and the maximum likelihood statistic.We are thankful to the reviewers for their constructive comments that have led to significant improvement on the first version of this paper. Special thanks are due to the reviewer who suggested a comparison with the LISREL program in the saturated means model, and provided its setup and output. This work was supported by National Institute on Drug Abuse grants DA01070, DA00017, and a UNH 2002 Summer Faculty Fellowship.     

An approach to combine the logistic threshold model of psychophysics with the Bradley-Terry-Luce models of choice theory

The paper presents a straightforward extension of the Bradley-Terry-Luce model (BTL model) that can be derived from the logistic threshold model of psychophysics which assumes that psychometric functions are logistic probability functions. It is shown that (under weak side conditions) the logistic threshold model is a submodel of the extended BTL model. Moreover, representation and uniqueness theorems are proven that provide some evidence that the extended BTL model is a useful and widely applicable generalization of the ordinary BTL model. Finally, the logistic shape of the psychometric function is derived from axioms about binary choice probabilities. This characterization of the logistic threshold model can replace goodness of fit tests for the logistic probability distribution.     

Preference for distribution by equal outcome in 5- and 6-year-old children

This study investigated preferences for types of fairness applied in resource distribution. We consider two types of equal distribution: according to the equal-allocation principle (new resources are distributed evenly without considering currently possessed resources) or the equal-outcome principle (equal outcome amounts result after distribution because current resources are considered). Children aged 5–6 and adults participated. The participant initially had two sets of two marbles (participant condition) or each of two puppets initially had two marbles (puppet condition). Then one puppet distributed new marbles between itself and the participant by equal-outcome. Next, the other puppet distributed new marbles by equal-allocation. The results showed that the majority of children and adults selected the distribution by equal-outcome for both conditions. This suggests that people prefer distribution by equal-outcome to distribution by equal-allocation. However, some children aged 5–6 thought that distribution by equal-allocation was better only when they already had resources.     

Robust Bayesian growth curve modelling using conditional medians

Growth curve models have been widely used to analyse longitudinal data in social and behavioural sciences. Although growth curve models with normality assumptions are relatively easy to estimate, practical data are rarely normal. Failing to account for non-normal data may lead to unreliable model estimation and misleading statistical inference. In this work, we propose a robust approach for growth curve modelling using conditional medians that are less sensitive to outlying observations. Bayesian methods are applied for model estimation and inference. Based on the existing work on Bayesian quantile regression using asymmetric Laplace distributions, we use asymmetric Laplace distributions to convert the problem of estimating a median growth curve model into a problem of obtaining the maximum likelihood estimator for a transformed model. Monte Carlo simulation studies have been conducted to evaluate the numerical performance of the proposed approach with data containing outliers or leverage observations. The results show that the proposed approach yields more accurate and efficient parameter estimates than traditional growth curve modelling. We illustrate the application of our robust approach using conditional medians based on a real data set from the Virginia Cognitive Aging Project.