Integrating covariates into circumplex structures: an extension procedure for Browne’s circular stochastic process model

Circumplex structures are elements of various psychological domains. Most work focuses on assessing the circular ordering of circumplex indicators and their relationships with covariates. In this article, an extension procedure for Browne’s circumplex model is presented. Our approach models the relationships among circumplex indicators and the relationships of covariates with a latent circumplex simultaneously without affecting the circumplex indicators’ positions on the circumplex. The approach builds upon Browne’s Fourier series parameterization of a correlation function, which is used to model the latent circumplex correlation structure. It extends the shape of the correlation function to the profile of each covariate’s correlations with the circumplex. The model is specified in the framework of structural equation modeling, thereby making it possible to test various hypotheses. Procedures are presented for deriving interval estimates for the parameters that relate the covariates to the circumplex. The model is compared to other approaches for assessing the relationships of a circumplex with covariates. The results of the exemplary applications and a simulation study were in favor of the suggested model. The approach is furthermore illustrated with a real-data example, focusing on the relationships between the interpersonal circumplex and the rivalry and admiration aspects of narcissism.     

Analysis of structural equation model with ignorable missing continuous and polytomous data

The main purpose of this article is to develop a Bayesian approach for structural equation models with ignorable missing continuous and polytomous data. Joint Bayesian estimates of thresholds, structural parameters and latent factor scores are obtained simultaneously. The idea of data augmentation is used to solve the computational difficulties involved. In the posterior analysis, in addition to the real missing data, latent variables and latent continuous measurements underlying the polytomous data are treated as hypothetical missing data. An algorithm that embeds the Metropolis-Hastings algorithm within the Gibbs sampler is implemented to produce the Bayesian estimates. A goodness-of-fit statistic for testing the posited model is presented. It is shown that the proposed approach is not sensitive to prior distributions and can handle situations with a large number of missing patterns whose underlying sample sizes may be small. Computational efficiency of the proposed procedure is illustrated by simulation studies and a real example.The work described in this paper was fully supported by a grant from the Research Grants Council of the HKSAR (Project No. CUHK 4088/99H). The authors are greatly indebted to the Editor and anonymous reviewers for valuable comments in improving the paper; and also to D. E. Morisky and J.A. Stein for the use of their AIDS data set.     

论虚概念

把外延理解为“具有概念所反映的特有属性的客观事物(或类)”,导致“虚概念没有外延”或“有外延但是空类”此类有问题的结论,应该理解为由概念(思维)中的对象组成;而把虚概念理解为“所指称的对象不存在于客观世界的概念”,又导致把理想模型等科学概念当成虚概念,实际上,对象有虚实,属性也有虚实。实对象、实属性,是无异议的实概念;虚对象、实属性,也是实概念,如思维科学中的概念;实对象、虚属性,是虚概念,如“地心说”中的概念;虚对象、虚属性,是公认的虚概念,如鬼魂。可见,无论对象虚实,只要所指称的对象的主要特征所反映的属性是非客观的概念就是虚概念。     

The Pleasures of Anticipation: Enriching Intuitionistic Logic

We explore a relation we call anticipation between formulas, where A anticipates B (according to some logic) just in case B is a consequence (according to that logic, presumed to support some distinguished implicational connective ) of the formula AB. We are especially interested in the case in which the logic is intuitionistic (propositional) logic and are much concerned with an extension of that logic with a new connective, written as a, governed by rules which guarantee that for any formula B, aB is the (logically) strongest formula anticipating B. The investigation of this new logic, which we call ILa, will confront us on several occasions with some of the finer points in the theory of rules and with issues in the philosophy of logic arising from the proposed explication of the existence of a connective (with prescribed logical behaviour) in terms of the conservative extension of a favoured logic by the addition of such a connective. Other points of interest include the provision of a Kripke semantics with respect to which ILa is demonstrably sound, deployed to establish certain unprovability results as well as to forge connections with C. Rauszer's logic of dual intuitionistic negation and dual intuitionistic implication, and the isolation of two relations (between formulas), head-implication and head-linkage, which, though trivial in the setting of classical logic, are of considerable significance in the intuitionistic context.     

A Generalization of the Łukasiewicz Algebras

We introduce the variety _n ^m , m 1 and n 2, of m-generalized ukasiewicz algebras of order n and characterize its subdirectly irreducible algebras. The variety _n ^m is semisimple, locally finite and has equationally definable principal congruences. Furthermore, the variety _n ^m contains the variety of ukasiewicz algebras of order n.     

The effects of type of instruction,animacy cues,and dimensionality of objects on the shape bias in 3‐ to 6‐year‐old children

Robust evidence exists for the shape bias, or children's tendency to extend novel names and categorize objects more readily on the basis of shape than on other object features. However, issues remain about the conditions that affect the shape bias and its importance as a linguistic device. In this research, we examined how type of instruction (common noun naming, proper noun naming, same kind, and goes with), animacy of objects (animate, inanimate), and dimensionality of objects (two‐dimensional, three‐dimensional) affect the shape bias in 3‐ to 6‐year‐old children. Overall, all children showed strong use of the shape bias with categorization (same kind, goes with) instructions, the former in line with the shape‐as‐cue theory. Additionally, the shape bias was quite robust in the inanimate condition, regardless of type of instruction or dimensionality of objects. However, in the animate condition, a proper noun naming instruction coupled with an animate object cue reduced the shape bias across both two‐ and three‐dimensional objects. Implications of these findings are presented.

Highlights

• This study assessed the “shape bias,” a linguistic strategy young children routinely use when confronted with the task of extending a novel name from one object to another.
• Novel name extension and categorization tasks were used in this study.
• Shape bias was affected by the type of instructions, animacy of objects, and dimensionality of objects.

     

层级一致性指标的多级评分拓展

在认知诊断评估实践中,属性层级合理性的验证非常重要,而现有指标仅停留在0-1计分测验,无法适应考试形式和评分方式多样化的实践需求。研究将0-1计分层级一致性指标（MHCI）拓展至多级计分的层级一致性指标（GHCI）,模拟和实证研究结果表明：（1）GHCI具有和MHCI相同的本质含义,考虑了父项目和子项目得分的多种可能性,从而将MHCI纳入GHCI体系;（2）在多级或混合计分情境,MHCI会有信息损失,容易发生低估,且易受转换比例的影响;（3）GHCI在模拟和实践情境均具较好的适宜性,拟合截断值的设置可依属性层级而定。     

Does inversion affect boundary extension for briefly-presented views?

Inverting scenes interferes with visual perception and memory on many tasks. Might scene inversion eliminate boundary extension (BE) for briefly-presented photographs? In Experiment 1, an upright or inverted photograph (133, 258, or 383?ms) was followed by a 258 ms masked interval and a test photograph showing the identical view. Test photographs were rated as “same”, “closer”, or “farther away” (5-point scale). BE was just as great for inverted as upright views at the 133 and 383 ms durations, but surprisingly was greater for inverted views at the 258 ms duration. In Experiment 2, 258-ms views yielded greater BE when the study photographs were always tested in the opposite orientation, indicating that the difference in BE was related to encoding. Results suggest that scene construction beyond the view boundaries occurs rapidly and is not impeded by scene inversion, but that changes in the relative quality of visual details available for upright and inverted views may sometimes yield increased BE for inverted scenes.     

A note on monotonicity of item response functions for ordered polytomous item response theory models

A monotone relationship between a true score (τ) and a latent trait level (θ) has been a key assumption for many psychometric applications. The monotonicity property in dichotomous response models is evident as a result of a transformation via a test characteristic curve. Monotonicity in polytomous models, in contrast, is not immediately obvious because item response functions are determined by a set of response category curves, which are conceivably non-monotonic in θ. The purpose of the present note is to demonstrate strict monotonicity in ordered polytomous item response models. Five models that are widely used in operational assessments are considered for proof: the generalized partial credit model (Muraki, 1992, Applied Psychological Measurement, 16, 159), the nominal model (Bock, 1972, Psychometrika, 37, 29), the partial credit model (Masters, 1982, Psychometrika, 47, 147), the rating scale model (Andrich, 1978, Psychometrika, 43, 561), and the graded response model (Samejima, 1972, A general model for free-response data (Psychometric Monograph no. 18). Psychometric Society, Richmond). The study asserts that the item response functions in these models strictly increase in θ and thus there exists strict monotonicity between τ and θ under certain specified conditions. This conclusion validates the practice of customarily using τ in place of θ in applied settings and provides theoretical grounds for one-to-one transformations between the two scales.     

On measurement properties of continuation ratio models

Three classes of polytomous IRT models are distinguished. These classes are the adjacent category models, the cumulative probability models, and the continuation ratio models. So far, the latter class has received relatively little attention. The class of continuation ratio models includes logistic models, such as the sequential model (Tutz, 1990), and nonlogistic models, such as the acceleration model (Samejima, 1995) and the nonparametric sequential model (Hemker, 1996). Four measurement properties are discussed. These are monotone likelihood ratio of the total score, stochastic ordering of the latent trait by the total score, stochastic ordering of the total score by the latent trait, and invariant item ordering. These properties have been investigated previously for the adjacent category models and the cumulative probability models, and for the continuation ratio models this is done here. It is shown that stochastic ordering of the total score by the latent trait is implied by all continuation ratio models, while monotone likelihood ratio of the total score and stochastic ordering on the latent trait by the total score are not implied by any of the continuation ratio models. Only the sequential rating scale model implies the property of invariant item ordering. Also, we present a Venn-diagram showing the relationships between all known polytomous IRT models from all three classes.