A heuristic method for the comparison of related structures

By extending a technique for testing the difference between two dependent correlations developed by Wolfe, a strategy is proposed in a more general matrix context for evaluating a variety of data analysis schemes that are supposed to clarify the structure underlying a set of proximity measures. In the applications considered, a data analysis scheme is assumed to reconstruct in matrix form the given data set (represented as a proximity matrix) based on some specific model or procedure. Thus, an evaluation of the adequacy of reconstruction can be developed by comparing matrices, one containing the original proximities and the second containing the reconstructed values. Possible applications in multidimensional scaling, clustering, and related contexts are emphasized using four broad categories: (a) Given two different reconstructions based on a single data set, does either represent the data significantly better than the other? (b) Given two reconstructions based on a single data set using two different procedures (or possibly, two distinct data sets and a common method), is either reconstruction significantly closer to a particular theoretical structure that is assumed to underlie the data (where the latter is also represented in matrix form)? (c) Given two theoretical structures and one reconstruction based on a single data set, does either represent the reconstruction better than the other? (d) Given a single reconstruction based on one data set, is the information present in the data accounted for satisfactorily by the reconstruction? In all cases, these tasks can be approached by a nonparametric procedure that assesses the similarity in pattern between two appropriately defined matrices. The latter are obtained from the original data, the reconstructions, and/or the theoretical structures. Finally, two numerical examples are given to illustrate the more general discussion.     

Boundary Identification in Experiential Groups as a Tool for Practice,Research, and Training

Psychological boundaries are an integral part of group processes. A novel evaluation method presented in this article seeks to reveal chronological boundary changes. Through the application of this method, the triangular relationships among the group process, the content, and the frame of reference are identified. A unique feature of this computer-assisted (Atlas.ti) analysis is that boundary shifts are tracked and quantified, allowing for specific qualitative exploration. The innovative use of qualitative thematic content analysis shown here, combined with the quantification of elements of the group process, can possibly provide group leaders with a framework for the conceptualization and identification of boundary movement in the group.     

Group differences in size estimation

Fifty-two subjects differing in sex, age, education and domicile (rural or urban) were given the problem of judging the height of an upright board in a natural setting. A preliminary analysis was made on the basis of the simple initial ratio method, both for the original data in feet and for original data converted to log units. Because the effects of interaction of the several variables made the results of this method inconclusive, the analysis of variance technique, as described by Yates (11) for data where the classes are not equally represented, was applied. This technique showed that, while together the four factors markedly affected judgment, sex had no significant individual effect, age had the biggest individual effect but possibly a spurious one, education and domicile had suspiciously large individual effects, and the effect of the four factors may be regarded as simply additive. The relation of the findings to those of previous investigators is discussed. The authors regard as an important result of the analysis the guidance it offers in the design of further experiments, since it demonstrates the value of equal representation for all classes into which data are to be segregated.Responsible for the experiment and general interpretation.Responsible for the statistical analysis.     

异同判断中“快同效应”的大脑机制：一项ERP研究

采用高密度的事件相关电位（ERPs）技术,记录分析了大学生被试在执行异同判断任务[包括不同颜色刺激对（DC）,不同形状刺激对（DS）和相同刺激对（Same）]时的脑内时程动态变化。行为结果表明,“同”反应的确显著快于“异”反应,表现出明显的快同效应。ERP结果显示：在280-320 ms内,DS和DC条件均比Same条件诱发一个更负的N2成分。偶极子溯源分析表明,DC和DS条件下,N2可能起源于大脑的前扣带皮层（ACC）,可能与“异”反应早期不一致信息（颜色或形状）的认知监控和调节有关;反之Same条件下,N2成分可能起源于楔前叶,主要反映了“同”反应早期知觉识别中整体特征比较加工的过程（同一性指示器）。另外,在450 ms左右, DC和DS比Same条件均诱发了一个更负的P3成分,可能反映了对刺激局部特征的比较和识别（慢速比较器）,并与选择性注意和资源分配等高级认知活动有关;并且,Same条件下P3成分的潜伏期更短,与行为结果一致。以上研究结果表明,异同判断中“同”反应和“异”反应可能有着不同的比较通道和大脑机制,支持双过程模型理论;同时表明,慢速比较器和同一性指示器可能是序列加工的。     

The true‐change model with individual method effects: Reliability issues

The true intra‐individual change model is generalized by defining individual method effects. This allows the analysis of non‐congeneric test–retest variables assumed to measure a common, possibly (temporally) transient, attribute. Temporal change in the attribute between different times of measurement is modelled by the true‐change variable. Individual causal method effects, due to heterogeneity of the measurement methods, account for the imperfect correlation of the true‐score variables at each time of measurement. The reliability of the composite scores, at each time of measurement, and the reliability of the difference composite score may be estimated with appropriate coefficients derived from the model. Measurements of daily life tension in adult females serve to illustrate how the model can be used empirically.     

Inferring the structure of latent class

Present optimization techniques in latent class analysis apply the expectation maximization algorithm or the Newton-Raphson algorithm for optimizing the parameter values of a prespecified model. These techniques can be used to find maximum likelihood estimates of the parameters, given the specified structure of the model, which is defined by the number of classes and, possibly, fixation and equality constraints. The model structure is usually chosen on theoretical grounds. A large variety of structurally different latent class models can be compared using goodness-of-fit indices of the chi-square family, Akaike’s information criterion, the Bayesian information criterion, and various other statistics. However, finding the optimal structure for a given goodness-of-fit index often requires a lengthy search in which all kinds of model structures are tested. Moreover, solutions may depend on the choice of initial values for the parameters. This article presents a new method by which one can simultaneously infer the model structure from the data and optimize the parameter values. The method consists of a genetic algorithm in which any goodness-of-fit index can be used as a fitness criterion. In a number of test cases in which data sets from the literature were used, it is shown that this method provides models that fit equally well as or better than the models suggested in the original articles.     

Postmodeling Sensitivity Analysis to Detect the Effect of Missing Data Mechanisms

Incomplete or missing data is a common problem in almost all areas of empirical research. It is well known that simple and ad hoc methods such as complete case analysis or mean imputation can lead to biased and/or inefficient estimates. The method of maximum likelihood works well; however, when the missing data mechanism is not one of missing completely at random (MCAR) or missing at random (MAR), it too can result in incorrect inference. Statistical tests for MCAR have been proposed, but these are restricted to a certain class of problems. The idea of sensitivity analysis as a means to detect the missing data mechanism has been proposed in the statistics literature in conjunction with selection models where conjointly the data and missing data mechanism are modeled. Our approach is different here in that we do not model the missing data mechanism but use the data at hand to examine the sensitivity of a given model to the missing data mechanism. Our methodology is meant to raise a flag for researchers when the assumptions of MCAR (or MAR) do not hold. To our knowledge, no specific proposal for sensitivity analysis has been set forth in the area of structural equation models (SEM). This article gives a specific method for performing postmodeling sensitivity analysis using a statistical test and graphs. A simulation study is performed to assess the methodology in the context of structural equation models. This study shows success of the method, especially when the sample size is 300 or more and the percentage of missing data is 20% or more. The method is also used to study a set of real data measuring physical and social self-concepts in 463 Nigerian adolescents using a factor analysis model.     

Dynamic estimation in the extended marginal Rasch model with an application to mathematical computer-adaptive practice

We introduce a general response model that allows for several simple restrictions, resulting in other models such as the extended Rasch model. For the extended Rasch model, a dynamic Bayesian estimation procedure is provided, which is able to deal with data sets that change over time, and possibly include many missing values. To ensure comparability over time, a data augmentation method is used, which provides an augmented person-by-item data matrix and reproduces the sufficient statistics of the complete data matrix. Hence, longitudinal comparisons can be easily made based on simple summaries, such as proportion correct, sum score, etc. As an illustration of the method, an example is provided using data from a computer-adaptive practice mathematical environment.     

Time-series analysis in operant research

A time-series method is presented, nontechnically, for analysis of data generated in individual-subject operant studies, and is recommended as a supplement to visual analysis of behavior change in reversal or multiple-baseline experiments. The method can be used to identify three kinds of statistically significant behavior change: (a) changes in score levels from one experimental phase to another, (b) reliable upward or downward trends in scores, and (c) changes in trends between phases. The detection of, and reliance on, serial dependency (autocorrelation among temporally adjacent scores) in individual-subject behavioral scores is emphasized. Examples of published data from the operant literature are used to illustrate the time-series method.     

Estimation of Controlled Direct Effects in Longitudinal Mediation Analyses with Latent Variables in Randomized Studies

Abstract

In a randomized study with longitudinal data on a mediator and outcome, estimating the direct effect of treatment on the outcome at a particular time requires adjusting for confounding of the association between the outcome and all preceding instances of the mediator. When the confounders are themselves affected by treatment, standard regression adjustment is prone to severe bias. In contrast, G-estimation requires less stringent assumptions than path analysis using SEM to unbiasedly estimate the direct effect even in linear settings. In this article, we propose a G-estimation method to estimate the controlled direct effect of treatment on the outcome, by adapting existing G-estimation methods for time-varying treatments without mediators. The proposed method can accommodate continuous and noncontinuous mediators, and requires no models for the confounders. Unbiased estimation only requires correctly specifying a mean model for either the mediator or the outcome. The method is further extended to settings where the mediator or outcome, or both, are latent, and generalizes existing methods for single measurement occasions of the mediator and outcome to longitudinal data on the mediator and outcome. The methods are utilized to assess the effects of an intervention on physical activity that is possibly mediated by motivation to exercise in a randomized study.     

A computer program for Spearman-K?rber and probit analysis of psychometric function data.

PMETRIC is a computer program for the analysis of observed psychometric functions. It can estimate the parameters of these functions, using either probit analysis (a parametric technique) or the Spearman-K?rber method (a nonparametric one). For probit analysis, either a maximum likelihood or a minimum chi 2 criterion may be used for parameter estimation. In addition, standard errors of parameter estimates can be estimated via bootstrapping. The program can be used to analyze data obtained from either yes-no or m-alternative forced-choice tasks. To facilitate the use of PMETRIC in simulation work, an associated program, PMETGEN, is provided for the generation of simulated psychometric function data. Use of PMETRIC is illustrated with data from a duration discrimination task.     

The use of configural frequency analysis for explorative data analysis

Configural frequency analysis (CFA) is a widely used method of explorative data analysis. It tries to detect patterns in the data that occur significantly more or significantly less often than expected by chance. Patterns which occur more often than expected by chance are called CFA types, while those which occur less often than expected by chance are called CFA antitypes. The patterns detected are used to generate knowledge about the mechanisms underlying the data. We investigate the ability of CFA to detect adequate types and antitypes in a number of simulation studies. The basic idea of these studies is to predefine sets of types and antitypes and a mechanism which uses them to create a simulated data set. This simulated data set is then analysed with CFA and the detected types and antitypes are compared to the predefined ones. The predefined types and antitypes together with the method to generate the data are called a data generation model. The results of the simulation studies show that CFA can be used in quite different research contexts to detect structural dependencies in observed data. In addition, we can learn from these simulation studies how much data is necessary to enable CFA to reconstruct the predefined types and antitypes with sufficient accuracy. For one of the data generation models investigated, implicitly underlying knowledge space theory, it was shown that zero‐order CFA can be used to reconstruct the predefined types (which can be interpreted in this context as knowledge states) with sufficient accuracy. Theoretical considerations show that first‐order CFA cannot be used for this data generation model. Thus, it is wrong to consider first‐order CFA, as is done in many publications, as the standard or even only method of CFA.     

Optimal spatial filtering for brain oscillatory activity using the Relevance Vector Machine

Over the past decade, various techniques have been proposed for localization of cerebral sources of oscillatory activity on the basis of magnetoencephalography (MEG) or electroencephalography recordings. Beamformers in the frequency domain, in particular, have proved useful in this endeavor. However, the localization accuracy and efficacy of such spatial filters can be markedly limited by bias from correlation between cerebral sources and short duration of source activity, both essential issues in the localization of brain data. Here, we evaluate a method for frequency-domain localization of oscillatory neural activity based on the relevance vector machine (RVM). RVM is a Bayesian algorithm for learning sparse models from possibly overcomplete data sets. The performance of our frequency-domain RVM method (fdRVM) was compared with that of dynamic imaging of coherent sources (DICS), a frequency-domain spatial filter that employs a minimum variance adaptive beamformer (MVAB) approach. The methods were tested both on simulated and real data. Two types of simulated MEG data sets were generated, one with continuous source activity and the other with transiently active sources. The real data sets were from slow finger movements and resting state. Results from simulations show comparable performance for DICS and fdRVM at high signal-to-noise ratios and low correlation. At low SNR or in conditions of high correlation between sources, fdRVM performs markedly better. fdRVM was successful on real data as well, indicating salient focal activations in the sensorimotor area. The resulting high spatial resolution of fdRVM and its sensitivity to low-SNR transient signals could be particularly beneficial when mapping event-related changes of oscillatory activity.     

迫选式人格测验的传统计分与IRT计分模型

迫选测验的传统计分方式会产生自模式数据, 不能进行传统的信效度检验、因素分析和方差分析等。近年来研究者提出了一些基于项目反应理论的计分模型, 如瑟斯顿IRT模型和MUPP模型等, 它们可以规避自模式数据的弊端。瑟斯顿IRT模型方便进行参数估计, 模型定义灵活; 而MUPP模型的拓展性较差, 参数估计的方法有待提高。另一方面, 已有研究者基于MUPP模型开发了一些抗作假的迫选测验, 而瑟斯顿IRT模型距离这种应用还比较远。此外, 两个模型的适用性和有效性都有待更多的实证研究来检验。     

A note on data smoothing for movement analysis: the relevance of a nonlinear method

The goal of this experiment was to test a potentially useful nonlinear method for smoothing noisy position data, which often is encountered in the analysis of data. This algorithm (7RY) uses a nonlinear smoothing function and behaves like a low-pass filter, automatically removing aberrant points; it is used prior to differentiation of time series so that usable acceleration information can be obtained. The experimental procedure comprises position data collection along with direct accelerometric data recording. From the position-time data, (a) 7RY and (b) Butterworth algorithms have been used to compute twice-differentiated acceleration curves. The directly recorded acceleration measurements were then compared with the acceleration computed from the original position data. Although the results indicated an overall good fit between the recorded and the calculated acceleration curves, only the nonlinear method led to reliable acceleration curves when aberrant points were present in the position data.     

适于自然情境脑成像研究的分析方法:被试间相关及其应用

被试间相关分析是一种基于大脑活动的时间模式的数据分析方法。该方法通过计算接收相同刺激时被试间脑区活动的一致性,探讨认知加工与脑区功能的关系。与传统的基于激活水平的数据分析方法相比,该方法不需要设置严格的实验条件,能更好地应用于自然情境下的脑成像研究。文章介绍了被试间相关分析的基本原理和方法,分析了该方法如何识别认知功能脑区及其可靠性,并结合其在自然情境脑成像以及特定研究领域的应用,阐明被试间相关在自然情境脑成像研究中的优势,以及该方法在多个研究领域的广泛应用扩展了认知神经科学研究的深度和广度。     

Conducting and interpreting canonical correlation analysis in personality research: a user-friendly primer

The purpose of this article is to reduce potential statistical barriers and open doors to canonical correlation analysis (CCA) for applied behavioral scientists and personality researchers. CCA was selected for discussion, as it represents the highest level of the general linear model (GLM) and can be rather easily conceptualized as a method closely linked with the more widely understood Pearson r correlation coefficient. An understanding of CCA can lead to a more global appreciation of other univariate and multivariate methods in the GLM. We attempt to demonstrate CCA with basic language, using technical terminology only when necessary for understanding and use of the method. We present an entire example of a CCA analysis using SPSS (Version 11.0) with personality data.