Estimation of the Coefficient of Variation with Minimum Risk: A Sequential Method for Minimizing Sampling Error and Study Cost

The coefficient of variation is an effect size measure with many potential uses in psychology and related disciplines. We propose a general theory for a sequential estimation of the population coefficient of variation that considers both the sampling error and the study cost, importantly without specific distributional assumptions. Fixed sample size planning methods, commonly used in psychology and related fields, cannot simultaneously minimize both the sampling error and the study cost. The sequential procedure we develop is the first sequential sampling procedure developed for estimating the coefficient of variation. We first present a method of planning a pilot sample size after the research goals are specified by the researcher. Then, after collecting a sample size as large as the estimated pilot sample size, a check is performed to assess whether the conditions necessary to stop the data collection have been satisfied. If not an additional observation is collected and the check is performed again. This process continues, sequentially, until a stopping rule involving a risk function is satisfied. Our method ensures that the sampling error and the study costs are considered simultaneously so that the cost is not higher than necessary for the tolerable sampling error. We also demonstrate a variety of properties of the distribution of the final sample size for five different distributions under a variety of conditions with a Monte Carlo simulation study. In addition, we provide freely available functions via the MBESS package in R to implement the methods discussed.     

Robust mean and covariance structure analysis through iteratively reweighted least squares

Robust schemes in regression are adapted to mean and covariance structure analysis, providing an iteratively reweighted least squares approach to robust structural equation modeling. Each case is properly weighted according to its distance, based on first and second order moments, from the structural model. A simple weighting function is adopted because of its flexibility with changing dimensions. The weight matrix is obtained from an adaptive way of using residuals. Test statistic and standard error estimators are given, based on iteratively reweighted least squares. The method reduces to a standard distribution-free methodology if all cases are equally weighted. Examples demonstrate the value of the robust procedure.The authors acknowledge the constructive comments of three referees and the Editor that lead to an improved version of the paper. This work was supported by National Institute on Drug Abuse Grants DA01070 and DA00017 and by the University of North Texas Faculty Research Grant Program.     

Information matrix estimation procedures for cognitive diagnostic models

Two new methods to estimate the asymptotic covariance matrix for marginal maximum likelihood estimation of cognitive diagnosis models (CDMs), the inverse of the observed information matrix and the sandwich-type estimator, are introduced. Unlike several previous covariance matrix estimators, the new methods take into account both the item and structural parameters. The relationships between the observed information matrix, the empirical cross-product information matrix, the sandwich-type covariance matrix and the two approaches proposed by de la Torre (2009, J. Educ. Behav. Stat., 34, 115) are discussed. Simulation results show that, for a correctly specified CDM and Q-matrix or with a slightly misspecified probability model, the observed information matrix and the sandwich-type covariance matrix exhibit good performance with respect to providing consistent standard errors of item parameter estimates. However, with substantial model misspecification only the sandwich-type covariance matrix exhibits robust performance.     

Flexible representations in visual working memory and interactions with long‐term learning: Commentary on the special issue

This special issue of the British Journal of Psychology brings together cutting edge research on a range of topics in visual working memory (VWM). In this commentary, we attempt to summarize common themes in current VWM research exemplified in this issue. The articles include several reviews of important topics as well as empirical papers covering three main themes. The first concerns the nature of mental representations of memoranda in the commonly used delayed estimation task, where both fine‐grained and broad categorical details appear to be represented, and their susceptibility to interference. The second concerns interactions between VWM representations, both those that produce individuation of representations and those that create an overarching ensemble structure. Finally, the third main topic concerns the use of VWM during visual search and in the learning of repeated configurations in search displays. The work presented here, and other work in the field, points to a rich interplay between representations in VWM but also between VWM and information in long‐term memory. Opportunities for further investigation are highlighted throughout.     

The influence of number line estimation precision and numeracy on risky financial decision making

This study examined whether different aspects of mathematical proficiency influence one's ability to make adaptive financial decisions. “Numeracy” refers to the ability to process numerical and probabilistic information and is commonly reported as an important factor which contributes to financial decision‐making ability. The precision of mental number representation (MNR), measured with the number line estimation (NLE) task has been reported to be another critical factor. This study aimed to examine the contribution of these mathematical proficiencies while controlling for the influence of fluid intelligence, math anxiety and personality factors. In our decision‐making task, participants chose between two options offering probabilistic monetary gain or loss. Sensitivity to expected value was measured as an index for the ability to discriminate between optimal versus suboptimal options. Partial correlation and hierarchical regression analyses revealed that NLE precision better explained EV sensitivity compared to numeracy, after controlling for all covariates. These results suggest that individuals with more precise MNR are capable of making more rational financial decisions. We also propose that the measurement of “numeracy,” which is commonly used interchangeably with general mathematical proficiency, should include more diverse aspects of mathematical cognition including basic understanding of number magnitude.     

Muscle Synergies for Turning During Human Walking

Muscle synergy describes reduced set of functional muscle co-activation patterns. We aimed to identify muscle synergies of turning compared with straight walking. Twelve healthy adults (men: 7, women: 5) performed straight walking (SW), left turning (LT), and right turning (RT) at self-selected speeds. By using non-negative matrix factorization (NMF), we extracted muscle synergies from sixteen electromyography (EMG) signals on the right side and assigned similar muscle synergies among SW, LT, and RT into the same cluster by combining k-means clustering and intraclass correlation coefficient (ICC) analysis. We obtained task-specific clusters of muscle synergies extracted from SW, LT, or RT condition and identified the clusters that share synergies among the conditions. The central nervous system produces specific synergies involving turning behaviors and fundamental synergies for walking.     

Four Covariance Structure Models for Canonical Correlation Analysis: A COSAN Modeling Approach

The mathematical connection between canonical correlation analysis (CCA) and covariance structure analysis was first discussed through the Multiple Indicators and Multiple Causes (MIMIC) approach. However, the MIMIC approach has several technical and practical challenges. To address these challenges, a comprehensive COSAN modeling approach is proposed. Specifically, we define four COSAN-CCA models to correspond with four possible combinations of the data to be analyzed and the unique parameters to be estimated. In terms of the data, one can analyze either the unstandardized or standardized variables. In terms of the unique parameters, one can estimate either the weights or loadings. Besides the unique parameters of each COSAN-CCA model, all four COSAN-CCA models also estimate the canonical correlations as their common parameters. Taken together, the four COSAN-CCA models provide the correct point estimates and standard error estimates for all commonly used CCA parameters. Two numeric examples are used to compare the standard error estimates obtained from the MIMIC approach and the COSAN modeling approach. Moreover, the standard error estimates from the COSAN modeling approach are validated by a simulation study and the asymptotic theory. Finally, software implementation and future extensions are discussed.     

多维项目反应理论补偿性模型参数估计:基于广义回归神经网络集合

运用广义回归神经网络(GRNN)方法对小样本多维项目反应理论(MIRT)补偿性模型的项目参数进行估计,尝试解决传统参数估计方法样本数量要求较大的问题。MIRT双参数Logistic补偿模型被设置为二级计分的二维模型。首先,模拟二维能力参数、项目参数值与考生作答矩阵。其次,把通过主成分分析得到的前两个因子在每个题目上的载荷作为区分度的初始值以及题目通过率作为难度的初始值,这两个指标的初始值作为神经网络的输入。集成100个神经网络,其输出值的均值作为MIRT的项目参数估计值。最后,设置2×2种(能力相关水平:0.3和0.7; 两种估计方法:GRNN和MCMC方法)实验处理,对GRNN和MCMC估计方法的返真性进行比较。结果表明,小样本的情况下,基于GRNN集成方法的参数估计结果优于MCMC方法。     

Age differences in the neural response to negative feedback

Affective processing is one domain that remains relatively intact in healthy aging. Investigations into the neural responses associated with reward anticipation have revealed that older and younger adults recruit the same midbrain reward regions, but other evidence suggests this recruitment may differ depending on the valence (gain, loss) of the incentive cue. The goal of the current study was to examine functional covariance during gain and loss feedback in younger and healthy older adults. A group of 15 older adults (mean age = 68.5) and 16 younger adults (mean age = 25.4) completed a revised Monetary Incentive Delay task (rMID; Knutson, Westdorp, Kaiser, &; Hommer, 2000) while in the fMRI scanner. The rMID is a reaction time task where successful performance, either gaining a reward or avoiding a loss, is defined by hitting a button during the brief presentation of a visual target. Participants receive gain and loss anticipation cues before each trial and feedback after each trial with four possible outcomes: +$5.00, +0.00, -$5.00, and -Affective processing is one domain that remains relatively intact in healthy aging. Investigations into the neural responses associated with reward anticipation have revealed that older and younger adults recruit the same midbrain reward regions, but other evidence suggests this recruitment may differ depending on the valence (gain, loss) of the incentive cue. The goal of the current study was to examine functional covariance during gain and loss feedback in younger and healthy older adults. A group of 15 older adults (mean age = 68.5) and 16 younger adults (mean age = 25.4) completed a revised Monetary Incentive Delay task (rMID; Knutson, Westdorp, Kaiser, & Hommer, 2000) while in the fMRI scanner. The rMID is a reaction time task where successful performance, either gaining a reward or avoiding a loss, is defined by hitting a button during the brief presentation of a visual target. Participants receive gain and loss anticipation cues before each trial and feedback after each trial with four possible outcomes: +$5.00, +0.00, -$5.00, and -$0.00. Using seed-voxel partial least squares analyses, with seed voxels in the caudate and ventromedial prefrontal cortex, whole-brain functional covariance revealed that younger and older adults engage the same network of regions to support general feedback processing. However, older adults engaged two additional networks to support processing of negative feedback, gain_miss (+0), loss_miss (-$5), and loss_hit (?0), specifically. These findings are in line with theories of a positivity effect in aging and may have implications for reward-stimulus learning and decision making following performance-contingent negative feedback.     

认知诊断模型中项目水平模型比较统计量的健壮性

使用模拟研究方法比较了以往研究中提出的基于观察信息矩阵、三明治矩阵的Wald（分别表示为W_Obs、W_Sw）、似然比（Likelihood Ratio）统计量以及新提出的基于经验交叉相乘信息矩阵的Wald统计量（W_XPD）在模型——数据失拟条件下进行项目水平上模型比较时的表现。结果显示：（1）W_Sw的一类错误控制率有很强的健壮性。（2）W_XPD在Q矩阵错误设定的大多数条件下的表现优于W_Sw。结论：模型—数据拟合良好时可以使用W_Sw进行项目水平上的模型比较,当模型与数据失拟时W_XPD可能是更好的选择。