A modified beta binomial model with applications to multiple choice and taste tests

A modified beta binomial model is presented for use in analyzing ramdom guessing multiple choice tests and certain forms of taste tests. Detection probabilities for each item are distributed beta across the population subjects. Properties for the observable distribution of correct responses are derived. Two concepts of true score estimates are presented. One, analogous to Duncan's empirical Bayes posterior mean score, is appropriate for assessing the subject's performance on that particular test. The second is more suitable for predicting outcomes on similar tests.This research was made possible by a grant from the Center for Food Policy Research, Graduate School of Business, Columbia University.     

随机截距潜在转变分析(RI-LTA)——个案自我转变与个案间差异的分离

传统的潜在转变分析属于单水平分析, 但其同样也可以看作二水平分析。Muthén和Asparouhov就以二水平分析的视角在单水平分析框架内提出了随机截距潜在转变分析(RI-LTA), 其中跨时间点产生的自我转变可以看作在水平1进行分析, 跨时间点不变的个案间差异可以看作在水平2进行分析, 使个案的自我转变和个案间的初始差异分离, 避免了高估保留在初始类别的概率。某研究型大学2016级本科生的追踪调查数据被用于演示使用随机截距潜在转变分析的过程。该方法的最大优势是通过引入随机截距避免了高估保留在本类别的转变概率。未来研究可以运用蒙特卡洛模拟研究探究随机截距潜在转变分析模型的适用性, 也可以用多水平分析的思路为灵感, 探究多水平随机截距潜在转变分析在统计软件中的实现。     

Estimation of a Latent Variable Regression Growth Curve Model for Individuals Cross-Classified by Clusters

The cross-classified multiple membership latent variable regression (CCMM-LVR) model is a recent extension to the three-level latent variable regression (HM3-LVR) model which can be utilized for longitudinal data that contains individuals who changed clusters over time (for instance, student mobility across schools). The HM3-LVR model can include the initial status on growth effect as varying across those clusters and allows testing of more flexible hypotheses about the influence of initial status on growth and of factors that might impact that relationship, but only in the presence of pure clustering of participants within higher-level units. This Monte Carlo study was conducted to evaluate model estimation under a variety of conditions and to measure the impact of ignoring cross-classified data when estimating the incorrectly specified HM3-LVR model in a scenario in which true values for parameters are known. Furthermore, results from a real-data analysis were used to inform the design of the simulation. Overall, it would be recommended for researchers to utilize the CCMM-LVR model over the HM3-LVR model when individuals are cross-classified, and to use a bare minimum of more than 100 clustering units in order to avoid overestimation of the level-3 variance component estimates.     

Dynamic probability of reinforcement for cooperation: Random game termination in the centipede game

Experimental games have previously been used to study principles of human interaction. Many such games are characterized by iterated or repeated designs that model dynamic relationships, including reciprocal cooperation. To enable the study of infinite game repetitions and to avoid endgame effects of lower cooperation toward the final game round, investigators have introduced random termination rules. This study extends previous research that has focused narrowly on repeated Prisoner's Dilemma games by conducting a controlled experiment of two‐player, random termination Centipede games involving probabilistic reinforcement and characterized by the longest decision sequences reported in the empirical literature to date (24 decision nodes). Specifically, we assessed mean exit points and cooperation rates, and compared the effects of four different termination rules: no random game termination, random game termination with constant termination probability, random game termination with increasing termination probability, and random game termination with decreasing termination probability. We found that although mean exit points were lower for games with shorter expected game lengths, the subjects' cooperativeness was significantly reduced only in the most extreme condition with decreasing computer termination probability and an expected game length of two decision nodes.     

热手谬误和赌徒谬误心理机制研究述评

在知觉随机序列时,人们倾向于把序列中实际上各自独立的相邻结果看作是存在正相关或负相关的,而出现热手谬误或赌徒谬误,又称为随机序列中的正负近因效应。有关这两谬误最早的心理机制的探索中,Kahneman 和Tversky采用局部代表性启发法对此进行了解释。但是这种解释也存在诸多不足,因此近期的一些模型（因果模型、Urn模型、记忆模型、适应模型和两阶段格式塔模型）分别从不同角度对两种谬误提出了新的解释。最后文章指出研究方法、神经机制、个体差异以及生活中的应用是该领域研究的几个未来发展方向     

多水平随机中介效应估计及其比较

本文在综述各类多水平中介模型的基础上, 聚焦于自变量、中介变量、因变量都来自多水平结构中较低水平的多水平随机中介效应模型, 通过蒙特卡洛模拟研究比较该模型与简化的多水平固定中介效应模型、传统中介效应模型的差别, 并考察了目前用于多水平随机中介效应的三种参数估计方法：限制性极大似然、极大似然、最小方差二次无偏估计在不同情况下对随机中介效应估计的优劣。研究结果显示：当数据符合多水平随机中介效应模型时, 使用简化模型将错误估计中介效应及其标准误, 得到不正确的统计检验结果; 使用多水平随机中介效应模型能够实现对中介效应的正确估计和检验, 其中限制性极大似然或极大似然估计方法优于最小方差二次无偏估计方法。     

Random error reduction in analytic hierarchies: a comparison of holistic and decompositional decision strategies

The principle of ‘divide and conquer’ (DAC) suggests that complex decision problems should be decomposed into smaller, more manageable parts, and that these parts should be logically aggregated to derive an overall value for each alternative. Decompositional procedures have been contrasted with holistic evaluations that require decision makers to simultaneously consider all the relevant attributes of the alternatives under consideration (Fischer, 1977 ). One area where decompositional procedures have a clear advantage over holistic procedures is in the reduction of random error (Ravinder, 1992 ; Ravinder and Kleinmuntz, 1991 ; Kleinmuntz, 1990 ). Adopting the framework originally developed by Ravinder and colleagues, this paper details the results of a study of the random error variances associated with another popular multi‐criteria decision‐making technique, the Analytic Hierarchy Process (AHP); (Saaty, 1977 , 1980 ), as well as the random error variances of a holistic version of the Analytic Hierarchy Process (Jensen, 1983 ). In addition, data concerning various psychometric properties (e.g. the convergent validity and temporal stability) and values of AHP inconsistency are reported for both the decompositional and holistic evaluations. The results of the study show that the Ravinder and Kleinmuntz ( 1991 ) error‐propagation framework extends to the AHP and decompositional AHP judgments are more consistent than their holistic counterparts. Copyright © 2001 John Wiley & Sons, Ltd.     

The Probability of Small Schedule Values and Preference for Random-Interval Schedules

Preference for working on variable schedules and temporal discrimination were simultaneously examined in two experiments using a discrete-trial, concurrent-chains arrangement with fixed interval (FI) and random interval (RI) terminal links. The random schedule was generated by first sampling a probability distribution after the programmed delay to reinforcement on the FI schedule had elapsed, and thus the RI never produced a component schedule value shorter than the FI and maintained a rate of reinforcement half that of the FI. Despite these features, the FI was not strongly preferred. The probability of obtaining the smallest programmed delay to reinforcement on the RI schedule was manipulated in Experiment 1, and the interaction of this probability and initial link length was examined in Experiment 2. As the probability of obtaining small values in the RI increased, preference for the schedule increased while the discriminated time of reinforcer availability in the terminal link decreased. Both of these effects were attenuated by lengthening the initial links. The results support the view that in addition to the delay to reinforcement, the probability of obtaining a short delay is an important choice-affecting variable that likely contributes to the robust preferences for variable, as opposed to fixed, schedules of reinforcement.     

LGM模型中缺失数据处理方法的比较:ML方法与Diggle-Kenward选择模型

追踪研究中缺失数据十分常见。本文通过Monte Carlo模拟研究,考察基于不同前提假设的Diggle-Kenward选择模型和ML方法对增长参数估计精度的差异,并考虑样本量、缺失比例、目标变量分布形态以及不同缺失机制的影响。结果表明:(1)缺失机制对基于MAR的ML方法有较大的影响,在MNAR缺失机制下,基于MAR的ML方法对LGM模型中截距均值和斜率均值的估计不具有稳健性。(2)DiggleKenward选择模型更容易受到目标变量分布偏态程度的影响,样本量与偏态程度存在交互作用,样本量较大时,偏态程度的影响会减弱。而ML方法仅在MNAR机制下轻微受到偏态程度的影响。     

Stronger effects of self-generated than cue-induced expectations when verifying predictions in data graphs

Expectations can come in different forms when analyzing and presenting data. Prior studies have documented stronger effects (behavioral and electrophysiological) of self-generated predictions as compared to cues. While participants presumably cannot help but use their own predictions, they might sometimes ignore cues (of low validity). In two experiments we compared the impact of cues (verbal and visual) and self-generated predictions on the performance of participants checking their current prediction against a presented data graph (linear upward or downward trend). Different from prior studies, the setup allowed for within-experiment comparison of different cue formats and ensured that cues could not be ignored. Nevertheless we found that self-generated predictions had a stronger impact than cues. Verbal cues had a stronger effect than visual cues without verbalization. Responses to graphs with a linear upward trend were faster and were influenced more strongly by predictions, than the response to graphs with a downward trend.