Concise formulas for the standard errors of component loading estimates

Concise formulas for the asymptotic standard errors of component loading estimates were derived. The formulas cover the cases of principal component analysis for unstandardized and standardized variables with orthogonal and oblique rotations. The formulas can be used under any distributions for observed variables as long as the asymptotic covariance matrix for sample covariances/correlations is available. The estimated standard errors in numerical examples were shown to be equivalent to those by the methods using information matrices.The author is indebted to anonymous reviewers for the corrections and suggestions on this study, which have led to improvements of earlier versions of this article.     

A Multitrait–Multisource Confirmatory Factor Analytic Approach to the Construct Validity of ADHD and ODD Rating Scales with Malaysian Children

Confirmatory factor analysis (CFA) was used to model a multitrait by multisource matrix to determine the convergent and discriminant validity of measures of attention-deficit hyperactivity disorder (ADHD)-inattention (IN), ADHD-hyperactivity/impulsivity (HI), and oppositional defiant disorder (ODD) in 917 Malaysian elementary school children. The three trait factors were ADHD-IN, ADHD-HI, and ODD. The two source factors were parents and teachers. Similar to earlier studies with Australian and Brazilian children, the parent and teacher measures failed to show convergent and discriminant validity with Malaysian children. The study outlines the implications of such strong source effects in ADHD-IN, ADHD-HI, and ODD measures for the use of such parent and teacher scales to study the symptom dimensions.     

Equivalents of Mingle and Positive Paradox

Relevant logic is a proper subset of classical logic. It does not include among its theorems any ofpositive paradox A (B A)mingle A (A A)linear order (A B) (B A)unrelated extremes (A ) (B B¯)This article shows that those four formulas have different effects when added to relevant logic, and then lists many formulas that have the same effect as positive paradox or mingle.     

A factor simplicity index

We propose an index for assessing the degree of factor simplicity in the context of principal components and exploratory factor analysis. The new index, which is called Loading Simplicity, is based on the idea that the communality of each variable should be related to few components, or factors, so that the loadings in each variable are either zero or as far from zero as possible. This index does not depend on the scale of the factors, and its maximum and minimum are only related to the degree of simplicity in the loading matrix. The aim of the index is to enable the degree of simplicity in loading matrices to be compared.The author would like to thank the review team for their insights and recommendations. This work was supported by a grant SEC2001-3821-C05-C02 from the Spanish Ministry of Science and Technology.     

Categorical Abstract Algebraic Logic Metalogical Properties

Metalogical properties that have traditionally been studied in the deductive system context (see, e.g., [21]) and transferred later to the institution context [33], are here formulated in the -institution context. Preservation under deductive equivalence of -institutions is investigated. If a property is known to hold in all algebraic -institutions and is preserved under deductive equivalence, then it follows that it holds in all algebraizable -institutions in the sense of [36].     

Standard errors for procrustes solutions

The asymptotic standard errors for the procrustes solutions are derived for orthogonal rotation, direct oblique rotation and indirect oblique rotation. The standard errors for the first two rotations are obtained using the augmented information matrices. For the indirect oblique solution, the standard errors of rotated parameters are derived from the information matrix of unrotated loadings using the chain rule for information matrices. For all three types of rotation, the standard errors of rotated parameters are presented for unstandardized and standardized manifest variables. Numerical examples show the similarity of theoretical and simulated values.     

Two-Stage maximum likelihood estimation in the misspecified restricted latent class model

The maximum likelihood classification rule is a standard method to classify examinee attribute profiles in cognitive diagnosis models (CDMs). Its asymptotic behaviour is well understood when the model is assumed to be correct, but has not been explored in the case of misspecified latent class models. This paper investigates the asymptotic behaviour of a two-stage maximum likelihood classifier under a misspecified CDM. The analysis is conducted in a general restricted latent class model framework addressing all types of CDMs. Sufficient conditions are proposed under which a consistent classification can be obtained by using a misspecified model. Discussions are also provided on the inconsistency of classification under certain model misspecification scenarios. Simulation studies and a real data application are conducted to illustrate these results. Our findings can provide some guidelines as to when a misspecified simple model or a general model can be used to provide a good classification result.     

Matrix training of preliteracy skills with preschoolers with autism

Matrix training is a generative approach to instruction in which words are arranged in a matrix so that some multiword phrases are taught and others emerge without direct teaching. We taught 4 preschoolers with autism to follow instructions to perform action-picture combinations (e.g., circle the pepper, underline the deer). Each matrix contained 6 actions on 1 axis and 6 pictures on the other axis. We used most-to-least prompting to train the instructions along the diagonal of each matrix and probed the untrained combinations. For 2 participants, untrained responding emerged after the minimum amount of training. The other 2 participants required further training before untrained combinations emerged. At the end of the study, 3 of the 4 participants performed the trained actions with previously known pictures, letters, and numbers. This study demonstrated that matrix training is an efficient approach to teaching language and literacy skills to children with autism.     

Estimation and visualization of confusability matrices from adaptive measurement data

We present a simple but effective method based on Luce’s choice axiom [Luce, R.D. (1959). Individual choice behavior: A theoretical analysis. New York: John Wiley & Sons] for consistent estimation of the pairwise confusabilities of items in a multiple-choice recognition task with arbitrarily chosen choice-sets. The method combines the exact (non-asymptotic) Bayesian way of assessing uncertainty with the unbiasedness emphasized in the classical frequentist approach.We apply the method to data collected using an adaptive computer game designed for prevention of reading disability. A player’s estimated confusability of phonemes (or more accurately, phoneme-grapheme connections) and larger units of language is visualized in an easily understood way with color cues and explicit indication of the accuracy of the estimates. Visualization of learning-related changes in the player’s performance is considered.The empirical validity of the choice axiom is evaluated using the game data itself. The axiom appears to hold reasonably well although a small systematic violation is observable for the smallest choice-set sizes.     

一种多级评分的广义认知诊断模型

认知诊断是近些年教育测量研究中的热点,大多数的认知诊断模型仅适用于0～1评分的情况.本文提出一种有多个潜变量多个滑动参数的多级评分认知诊断模型——GP-D1NA,只要由评分标准和知识状态能确定理想反应模式,就可以利用此方法进行认知诊断分析.在该方法中,我们给出项目滑动矩阵的概念,将被试的观测得分均看成由某个理想得分的滑动,并采用EM算法估计滑动矩阵.在模拟研究中,采用每掌握一个属性得1分的评分标准,结果表明线性型、收敛型、发散型、无结构型和独立型五种属性层级结构均有较高的判准率.