Item Analysis by the Hierarchical Generalized Linear Model

The hierarchical generalized linear model (HGLM) is presented as an explicit, two-level formulation of a multilevel item response model. In this paper, it is shown that the HGLM is equivalent to the Rasch model and that, characteristic of the HGLM, person ability can be expressed in the form of random effects rather than parameters. The two-level item analysis model is presented as a latent regression model with person-characteristic variables. Furthermore, it is shown that the two-level HGLM model can be extended to a three-level latent regression model that permits investigation of the variation of students' performance across groups, such as is found in classrooms and schools, and of the interactive effect of person-and group-characteristic variables.     

Centering,Scale Indeterminacy,and Differential Item Functioning Detection in Hierarchical Generalized Linear and Generalized Linear Mixed Models

In this article, we discuss and illustrate two centering and anchoring options available in differential item functioning (DIF) detection studies based on the hierarchical generalized linear and generalized linear mixed modeling frameworks. We compared and contrasted the assumptions of the two options, and examined the properties of their DIF estimates with a simulation study. For reference purposes, the results were compared to those obtained from using the Mantel-Haenszel procedure as well. Finally, we discuss some implications regarding the choice of model parameterizations for DIF detection using these frameworks.     

Hierarchical Generalized Linear Models for the Analysis of Judge Ratings

It is known that the Rasch model is a special two-level hierarchical generalized linear model (HGLM). This article demonstrates that the many-faceted Rasch model (MFRM) is also a special case of the two-level HGLM, with a random intercept representing examinee ability on a test, and fixed effects for the test items, judges, and possibly other facets. This perspective suggests useful modeling extensions of the MFRM. For example, in the HGLM framework it is possible to model random effects for items and judges in order to assess their stability across examinees. The MFRM can also be extended so that item difficulty and judge severity are modeled as functions of examinee characteristics (covariates), for the purposes of detecting differential item functioning and differential rater functioning. Practical illustrations of the HGLM are presented through the analysis of simulated and real judge-mediated data sets involving ordinal responses.     

带干扰的双广义泊松风险模型

经典的风险模型是假定保险公司按单位时间常数速率收取保险费,盈余过程{R(t),t0}中的S(t)=N(t)∑Yi为一复合泊松过程.本文将保费收入过程及索赔过程同时进行推广,即将保费到达过程及索赔计数过程均推广为一广义齐次P0isson过程,同时在模型中加入了随机干扰项.应用鞅论的方法,针对此模型给出了Lundberg不等式和破产概率公式.     

A Standardized Generalized Dimensionality Discrepancy Measure and a Standardized Model‐Based Covariance for Dimensionality Assessment for Multidimensional Models

The standardized generalized dimensionality discrepancy measure and the standardized model‐based covariance are introduced as tools to critique dimensionality assumptions in multidimensional item response models. These tools are grounded in a covariance theory perspective and associated connections between dimensionality and local independence. Relative to their precursors, they allow for dimensionality assessment in a more readily interpretable metric of correlations. A simulation study demonstrates the utility of the discrepancy measures’ application at multiple levels of dimensionality analysis, and compares them to factor analytic and item response theoretic approaches. An example illustrates their use in practice.     

带干扰的广义双泊松双险种风险模型

经典风险模型描述的是一单险种的风险过程.讨论了带干扰的双险种风险模型,将保费到达过程推广为一Poisson过程.运用鞅方法,得出了破产概率满足Lundberg不等式,并给出了生存概率的Feller表示.     

多层线性模型的原理及应用

本文对多层线性模型 (HierarchicalLinearModels ,HLM)的理论缘起、应用范围以及其应用原理进行了阐述 ,在指出经典统计技术处理多层数据结构上的局限的同时 ,表明了多层线性模型在这方面的优越性。本文最后对多层线性模型的效果及局限性进行了简要分析。     

Item Function Characteristics and Dimensionality for Alternative Response Formats in Mathematics

The purpose of this study was to investigate the technical properties of stem-equivalent mathematics items differing only with respect to response format. Using socio- economic factors to define the strata, a proportional stratified random sample of 1,366 Connecticut sixth-grade students were administered one of three forms. Classical item analysis, dimensionality assessment, item response theory goodness-of-fit, and an item bias analysis were conducted. Analysis of variance and confirmatory factor analysis were used to examine the functioning of the items presented in the three different formats. It was found that, after equating forms, the constructed-response formats were somewhat more difficult than the multiple-choice format. However, there was no significant difference across formats with respect to item discrimination. A differential item functioning (DIF) analysis was conducted using both the Mantel-Haenszel procedure and the comparison of the item characteristic curves. The DIF analysis indicated that the presence of bias was not greatly affected by item format; that is, items biased in one format tended to be biased in a similar manner when presented in a different format, and unbiased items tended to remain so regardless of format.     

The Student Risk Screening Scale: Exploring Dimensionality and Differential Item Functioning

This research attempted to discover the degree to which performance on assessments that have no direct consequences for individual students can be attributed to students' motivational states in addition to their underlying achievement in the domains measured. If such findings were reliable, it would allow us to correct underestimates of domain performance due to lack of motivation. Such corrections would be extremely interesting in explaining differential subgroup performance in state or national assessments that have institutional but not individual consequences. Recent information on international assessments (e.g., the Third International Mathematics and Science Study [TIMSS]) indicates that 12th-grade students in the United States are doing poorly on such assessments compared with their peers in other countries. These poor results are usually attributed to cognitive factors such as students' opportunities to learn, etc. However, a partial explanation may be motivational. Because the low-stakes tests were administered in these 12th-graders' final year in high school, this timing may have negatively affected motivation, and thus performance. Using TIMSS released math items, we provided $10.00 per item correct so as to increase a motivational effect and thus increase performance. However, the monetary incentive was not effective in improving performance.     

A Longitudinal Hierarchical Linear Model for Estimating School Effects and Their Stability

This paper presents a general longitudinal model for estimating school effects and their stability. Previous research on the stability of school performance over successive years has produced inconsistent findings. We argue that the findings have been inconsistent for at least two reasons: researchers have estimated different types of school effects, and they have not distinguished between instability due to true changes in school performance and instability due to measurement and sampling error. We describe two different types of school effects, each relevant to a different policy audience, and we present a longitudinal model that is capable of separating true changes in school effects from sampling and measurement error. The model also provides a means for estimating the effects of school policies and practices while controlling statistically for the effects of factors exogenous to the schooling system. This paper provides an example of the approach based on data describing two cohorts of students from one Education Authority in Scotland. It concludes with a discussion of the limitations of the model and implications for those collecting indicators of school performance for planning and evaluation purposes.     

用非参数项目反应理论模型研究大规模 教育考试维度的问题

大规模教育考试的维度与考试分数的意义解释、考生在考试中的行为表现解释密切相关。利用非参数项目反应理论模型选择试题组成单维量表,可以达到研究考试维度的目的。选择单维量表试题时,下界c值的确定,是个值得探讨的问题。用非参数项目反应理论模型对英语考试的三个量表维度研究发现,从每一个量表中只能选择出一个单维量表,而不是与每一部分测量的微技能数相应的多个单维量表;每一单维量表测量的均为该部分不同微技能的组合。这个特征表明这些单维量表均为基本单维量表,非严格单维量表。无论c值为0.3,还是0.2,选择出的基本单维量表均满足弱单调性要求,整个单维量表的区分功能不会有明显差异。     

Assessing Dimensionality of a Set of Item Responses-Comparison of Different Approaches

This study compares the performance of three methodologies for assessing unidi-mensionality: DIMTEST, Holland and Rosenbaum's approach, and nonlinear factor analysis. Each method is examined and compared with other methods on simulated and real data sets. Seven data sets, all with 2,000 examinees, were generated: three unidimensional and four two-dimensional data sets. Two levels of correlation between abilities were considered:ρ= 3 and ρ= . 7. Eight different real data sets were used: Four of them were expected to be unidimensional, and the other four were expected to be two-dimensional. Findings suggest that all three methods correctly confirmed unidimensionality but differed in their ability to detect lack of unidimensionality. DIMTEST showed excellent power in detecting lack of unidimensionality; Holland and Rosenbaum's and nonlinear factor analysis approaches showed good power, provided the correlation between abilities was low.     

Assessment of Differential Item Functioning Under Cognitive Diagnosis Models: The DINA Model Example

The assessment of differential item functioning (DIF) is routinely conducted to ensure test fairness and validity. Although many DIF assessment methods have been developed in the context of classical test theory and item response theory, they are not applicable for cognitive diagnosis models (CDMs), as the underlying latent attributes of CDMs are multidimensional and binary. This study proposes a very general DIF assessment method in the CDM framework which is applicable for various CDMs, more than two groups of examinees, and multiple grouping variables that are categorical, continuous, observed, or latent. The parameters can be estimated with Markov chain Monte Carlo algorithms implemented in the freeware WinBUGS. Simulation results demonstrated a good parameter recovery and advantages in DIF assessment for the new method over the Wald method.     

非齐次等式约束线性回归模型回归系数的广义条件岭估计

时非齐次等式约束线性回归模型回归系数提出广义条件岭估计.证明了在一定的条件下,在均方误差矩阵、均方误差及广义均方误差意义下,广义条件岭估计都优于约束最小二乘估计和狭义条件岭估计.     

Looking Beyond the Overall Scores of NAEP Assessments: Applications of Generalized Linear Mixed Modeling for Exploring Value-Added Item Difficulty Effects

The central idea of differential item functioning (DIF) is to examine differences between two groups at the item level while controlling for overall proficiency. This approach is useful for examining hypotheses at a finer-grain level than are permitted by a total test score. The methodology proposed in this paper is also aimed at estimating differences at the item rather than the overall score level, yet with the innovation where item-level differences for many groups simultaneously are the focus. This is a straightforward generalization of DIF as variance rather than one or several group differences; conceptually, this can be referred to as item difficulty variation (IDV). When instruction is of interest, and "groups" is a unit at which instruction is determined or delivered, then IDV signals value-added effects that can be influenced by either demographic or instructional variables.     

广义特征向量的广义线性相关性

研究复数域上亏损矩阵的广义特征向量。根据广义特征子空间链,提出广义特征向量组的广义线性相关与广义线性无关的概念,用以刻画若当链的计算复杂性。     

多层线性模型在心理和教育纵向研究中的运用

多层线性模型是分析具有层次结构数据的一种新型统计分析技术,与传统统计方法相比,多层线性模型具有模型假设与实际更吻合、结果解释更合理等特点.近年来,这一方法的应用逐渐在社会科学的研究中得到广泛应用.多层线性模型在分析具有层次结构的研究数据时具有精确估计、对测量时间间隔时间低等优点.同时在使用过程中也要满足合理选择时间变量、至少3次以上的追踪数据等要求.     

Use of Restricted Item Response Models for Examining Item Difficulty Ordering and Slope Uniformity

This article demonstrates the utility of restricted item response models for examining item difficulty ordering and slope uniformity for an item set that reflects varying cognitive processes. Twelve sets of paired algebra word problems were developed to systematically reflect various types of cognitive processes required for successful performance. This resulted in a total of 24 items. They reflected distance-rate–time (DRT), interest, and area problems. Hypotheses concerning difficulty ordering and slope uniformity for the items were tested by constraining item difficulty and discrimination parameters in hierarchical item response models. The first set of model comparisons tested the equality of the discrimination and difficulty parameters for each set of paired items. The second set of model comparisons examined slope uniformity within the complex DRT problems. The third set of model comparisons examined whether the familiarity of the story context affected item difficulty for two types of complex DRT problems. The last set of model comparisons tested the hypothesized difficulty ordering of the items.     

约束线性回归模型回归系数的广义条件岭估计

对齐次等式约束线性回归模型回归系数的岭估计进行推广,得出广义条件岭估计．证明了在一定的条件下,在均方误差矩阵、均方误差及广义均方误差意义下广义条件岭估计都优于约束最小二乘估计,并且证明了广义条件岭估计是回归系数的可容许估计．