Constructing informative model priors using hierarchical methods

Despite their negative reputation, informative priors are very useful in inference. Priors that express psychologically meaningful intuitions damp out random fluctuations in the data due to sampling variability, without sacrificing flexibility. This article focuses on how an intuitively satisfying informative prior distribution can be constructed. In particular, it demonstrates how the hierarchical introduction of a parameterized generative account of the set of models under consideration naturally imposes a non-uniform prior distribution over the models, encoding existing intuitions about the models. The hierarchical approach for constructing informative model priors is made concrete using a worked example, the Varying Abstraction Model (VAM), a family of categorization models including and expanding the exemplar and prototype models. It is shown how psychological intuitions about the relative plausibilities of the models in the VAM can be formally captured in an informative prior distribution over these models, by specifying a theoretically informed process for generating the models in the VAM. The smoothing effect of the informative prior in estimation is demonstrated by considering ten previously published data sets from the category learning literature.     

An introduction to Bayesian model selection for evaluating informative hypotheses

Most researchers have specific expectations concerning their research questions. These may be derived from theory, empirical evidence, or both. Yet despite these expectations, most investigators still use null hypothesis testing to evaluate their data, that is, when analysing their data they ignore the expectations they have. In the present article, Bayesian model selection is presented as a means to evaluate the expectations researchers have, that is, to evaluate so called informative hypotheses. Although the methodology to do this has been described in previous articles, these are rather technical and havemainly been published in statistical journals. The main objective of thepresent article is to provide a basic introduction to the evaluation of informative hypotheses using Bayesian model selection. Moreover, what is new in comparison to previous publications on this topic is that we provide guidelines on how to interpret the results. Bayesian evaluation of informative hypotheses is illustrated using an example concerning psychosocial functioning and the interplay between personality and support from family.     

The effectiveness of a proactive coping intervention targeting self-management in diabetes patients

Objective: The study’s aim was to investigate psychological, behavioral and medical long-term outcomes of an existing self-management intervention targeting the development of proactive coping skills (e.g. goal setting and identifying barriers) in type 2 diabetes patients. The study aimed to replicate prior research showing the intervention’s effectiveness, and to extend it by (a) adding booster sessions and (b) prolonging the period of follow-up measurement to capture long-term effects.

Design/outcome measures: A total of 141 type 2 diabetes patients were included in the intervention. The intervention employed a 5-step approach to target proactive coping skills. Psychological (e.g. proactive coping and self-efficacy) and behavioural variables (e.g. self-care, diet and physical activity) were assessed at baseline (T1), after the initial phase of the intervention (T2), after the booster phase (T3) and at follow-up (T4), comprising a total period of 15 months. Medical variables were assessed at T1 and T4.

Results: Employing piecewise Latent Growth Curve Modelling, results showed that participants improved on all psychological and behavioural variables during the initial phase and maintained these improvements over 12 months. The booster phase yielded no further improvements. Mixed findings were obtained on medical outcomes.

Conclusion: The original intervention is effective, but the added value of the booster sessions is uncertain.     

Four bootstrap confidence intervals for the binomial-error model

Confidence intervals for the mean function of the true proportion score ( _x ), where andx respectively denote the true proportion and observed test scores, can be approximated by the Efron, Bayesian, and parametric empirical Bayes (PEB) bootstrap procedures. The similarity of results yielded by all the bootstrap methods suggests the following: the unidentifiability problem of the prior distributiong() can be bypassed with respect to the construction of confidence intervals for the mean function, and a beta distribution forg() is a reasonable assumption for the test scores in compliance with a negative hypergeometric distribution. The PEB bootstrap, which reflects the construction of Morris intervals, is introduced for computing predictive confidence bands for x. It is noted that the effect of test reliability on the precision of interval estimates varies with the two types of confidence statements concerned.The Authors are indebted to the Editor and anonymous reviewers for constructive suggestions and comments. The authors wish to thank Min-Te Chao and Cheng-Der Fuh for some useful suggestions at earlier stages of writing this paper.     

On the misuse of manifest variables in the detection of measurement bias

Measurement invariance (lack of bias) of a manifest variableY with respect to a latent variableW is defined as invariance of the conditional distribution ofY givenW over selected subpopulations. Invariance is commonly assessed by studying subpopulation differences in the conditional distribution ofY given a manifest variableZ, chosen to substitute forW. A unified treatment of conditions that may allow the detection of measurement bias using statistical procedures involving only observed or manifest variables is presented. Theorems are provided that give conditions for measurement invariance, and for invariance of the conditional distribution ofY givenZ. Additional theorems and examples explore the Bayes sufficiency ofZ, stochastic ordering inW, local independence ofY andZ, exponential families, and the reliability ofZ. It is shown that when Bayes sufficiency ofZ fails, the two forms of invariance will often not be equivalent in practice. Bayes sufficiency holds under Rasch model assumptions, and in long tests under certain conditions. It is concluded that bias detection procedures that rely strictly on observed variables are not in general diagnostic of measurement bias, or the lack of bias.Preparation of this article was supported in part by PSC-CUNY grant #661282 to Roger E. Millsap.     

Easy bayes estimation for rasch-type models

A Bayes estimation procedure is introduced that allows the nature and strength of prior beliefs to be easily specified and modal posterior estimates to be obtained as easily as maximum likelihood estimates. The procedure is based on constructing posterior distributions that are formally identical to likelihoods, but are based on sampled data as well as artificial data reflecting prior information. Improvements in performance of modal Bayes procedures relative to maximum likelihood estimation are illustrated for Rasch-type models. Improvements range from modest to dramatic, depending on the model and the number of items being considered.This research was supported by ORN Contact #00014-86-K0087. We wish to thank Sheng-Hui Chu and Dzung-Ji Lii for providing intelligent and energetic programming support for this article. We also thank one of the reviewers for pointing out several interesting and useful perspectives.     

A Gibbs sampler for the multidimensional four-parameter logistic item response model via a data augmentation scheme

The four-parameter logistic (4PL) item response model, which includes an upper asymptote for the correct response probability, has drawn increasing interest due to its suitability for many practical scenarios. This paper proposes a new Gibbs sampling algorithm for estimation of the multidimensional 4PL model based on an efficient data augmentation scheme (DAGS). With the introduction of three continuous latent variables, the full conditional distributions are tractable, allowing easy implementation of a Gibbs sampler. Simulation studies are conducted to evaluate the proposed method and several popular alternatives. An empirical data set was analysed using the 4PL model to show its improved performance over the three-parameter and two-parameter logistic models. The proposed estimation scheme is easily accessible to practitioners through the open-source IRTlogit package.     

Bayesian benefits with JASP

We illustrate the Bayesian approach to data analysis using the newly developed statistical software program JASP. With JASP, researchers are able to take advantage of the benefits that the Bayesian framework has to offer in terms of parameter estimation and hypothesis testing. The Bayesian advantages are discussed using real data on the relation between Quality of Life and Executive Functioning in children with Autism Spectrum Disorder.     

Adaptive scaling of reward in episodic memory: a replication study

Reward is thought to enhance episodic memory formation via dopaminergic consolidation. Bunzeck, Dayan, Dolan, and Duzel [(2010). A common mechanism for adaptive scaling of reward and novelty. Human Brain Mapping, 31, 1380–1394] provided functional magnetic resonance imaging (fMRI) and behavioural evidence that reward and episodic memory systems are sensitive to the contextual value of a reward—whether it is relatively higher or lower—as opposed to absolute value or prediction error. We carried out a direct replication of their behavioural study and did not replicate their finding that memory performance associated with reward follows this pattern of adaptive scaling. An effect of reward outcome was in the opposite direction to that in the original study, with lower reward outcomes leading to better memory than higher outcomes. There was a marginal effect of reward context, suggesting that expected value affected memory performance. We discuss the robustness of the reward memory relationship to variations in reward context, and whether other reward-related factors have a more reliable influence on episodic memory.     

基于时空变化的步态识别算法研究

本文提出了一种八椭圆人体模型,并在此基础上提出了基于变化信息的步态识别算法。对每个视频序列,采用基于贝叶斯规则的检测算法检测出目标人体区域;将目标人体区域按比例划分为八个区域并分别用椭圆拟合,建立人体椭圆模型;用人体姿势的时空变化——相邻帧间的模型参数的差值作为特征,用归一化后的Mahalanobis距离和Euclidean距离分别进行相似性度量,NN和KNN技术用于最终的分类。实验结果表明,该算法拥有较高的识别率和较低的计算代价。