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.     

A non-linear utility theory with multiple objectives

The aim of this paper is to make optimum several objectives at the same time which would enable a measurement of utility for several possible alternatives. The problem is solved if a strong or weak dominance exists between the alternatives, otherwise a set of incomparable alternatives would be present. Therefore, indifference curve analysis offers the outcome but as these indifference loci are difficult to determine only the characteristics of this analysis are maintained viz. decreasing marginal utility, non-linearity and even non-convexity. Indifference and reference point theory with the Minkowski min–max-metric only respond to these characteristics. Also the problem of generating alternatives during the process is taken into consideration. © 1998 John Wiley & Sons, Ltd.     

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.     

同性恋形成机制探析

尽管人们对同性恋越来越宽容,但它仍是一种反常规现象.让现有同性恋者放弃同恋行为来减少同性恋难度很大,也不人道.在同性恋形成机制的问题上,有生理机制说和社会心理机制说.本文倾向于社会心理机制说.尝试从同性恋的社会心理机制上把同性恋分为两个形成亚型,并说明了每个亚型形成的具体过程.     

概率性输入,噪音“与”门(PINA)模型

当前认知诊断测验的主要目的是对被试进行合理分类,进而采用类别变量去描述被试对某技能或知识(即认知属性)的掌握情况,但该粗糙的分类方法不能精细地区分不同被试之间的差异。对此,采用掌握概率这一连续变量去描述被试对某认知属性的掌握情况是一种值得尝试的做法。本文首先基于高阶潜在特质(简称"潜质")模型给出了认知属性掌握概率的量化定义,之后与多成分潜质模型相结合提出了概率性输入,噪音"与"门(PINA)模型;其次,采用MCMC算法实现了对PINA的参数估计,结果表明参数估计程序对各参数的估计返真性均较好;最后,以ECPE数据为例来说明PINA在实际测验分析中具有可行性。     

Attribute Dismissal and Valence Effects in Preferential Decision Processing

The processing of attribute information during preference‐based decision making is affected by both the valence of that information and its importance to the decision. Although these two factors have typically been examined separately, we propose that their effects on elaboration and encoding are often codependent. Results of four experiments demonstrate that the traditional negativity effect, whereby negative attribute information is processed more extensively than positive attribute information, obtains only for the subset of attributes perceived to be most important. Among other attributes, the negativity effect is reduced or even reversed (a positivity effect). Our findings suggest important qualifications to prevailing notions of selective information processing. Copyright © 2017 John Wiley & Sons, Ltd.     

多级计分测验中基于残差统计量的被试拟合研究

本文提出一种多级计分项目下的个人拟合统计量R, 考察它在检测6种常见的异常作答模式(作弊、猜测、随机、粗心、创新作答、混合异常)下的表现, 并与标准化对数似然统计量l_zp进行比较。结果表明：(1) 在异常作答覆盖率较低并且异常作答类型为作弊和猜测时, R的检测率显著高于l_zp; (2) 随着测验长度和被试异常程度的增加, 两种统计量的检测率都会上升; (3) 在一些条件下, R与l_zp检测效果接近。实证数据分析进一步展示了R统计量的使用方法和过程, 结果也表明R统计量具有较好的应用前景。     

A sequential cognitive diagnosis model for polytomous responses

This paper proposes a general polytomous cognitive diagnosis model for a special type of graded responses, where item categories are attained in a sequential manner, and associated with some attributes explicitly. To relate categories to attributes, a category‐level Q‐matrix is used. When the attribute and category association is specified a priori, the proposed model has the flexibility to allow different cognitive processes (e.g., conjunctive, disjunctive) to be modelled at different categories within a single item. This model can be extended for items where categories cannot be explicitly linked to attributes, and for items with unordered categories. The feasibility of the proposed model is examined using simulated data. The proposed model is illustrated using the data from the Trends in International Mathematics and Science Study 2007 assessment.     

谱聚类算法在不同属性层级结构诊断评估中的应用

聚类分析已成功用于认知诊断评估(CDA)中,使用广泛的聚类分析方法为K-means算法,有研究已证明K-means在CDA中具有较好的聚类效果。而谱聚类算法通常比K-means分类效果更佳,本研究将谱聚类算法引进CDA,探讨了属性层级结构、属性个数、样本量和失误率对该方法的影响。研究发现：（1）谱聚类算法要比K-means提供更好的聚类结果,尤其在实验条件较苛刻时,谱聚类算法更加稳健;（2）线型结构聚类效果最好,收敛型和发散型相近,独立型结构表现较差;（3）属性个数和失误率增加后,聚类效果会下降;（4）样本量增加后,聚类效果有所提升,但K-means方法有时会有反向结果出现。