Constrained Maximum Likelihood Estimation for Two-level Mean and Covariance Structure Models

Maximum likelihood is commonly used for estimation of model parameters in analysis of two-level structural equation models. Constraints on model parameters could be encountered in some situations such as equal factor loadings for different factors. Linear constraints are the most common ones and they are relatively easy to handle in maximum likelihood analysis. Nonlinear constraints could be encountered in complicated applications. In this paper we develop an EM-type algorithm for estimating model parameters with both linear and nonlinear constraints. The empirical performance of the algorithm is demonstrated by a Monte Carlo study. Application of the algorithm for linear constraints is illustrated by setting up a two-level mean and covariance structure model for a real two-level data set and running an EQS program.     

基于累加两水平统计模型的年降雨量预测

为了有效地对不同地域的年降雨量进行预测,本文通过建立一个累加两水平统计模型,通过对数据间关系难以确定且非平稳的原始降雨量时间序列进行累加处理,给出模型的参数估计,然后通过模型给出预测值,同时将本文所提出的预测方法与其他常用方法进行比较,结果显示,该方法有较强的实用性。     

Multiple Imputation Strategies for Multiple Group Structural Equation Models

Although structural equation modeling software packages use maximum likelihood estimation by default, there are situations where one might prefer to use multiple imputation to handle missing data rather than maximum likelihood estimation (e.g., when incorporating auxiliary variables). The selection of variables is one of the nuances associated with implementing multiple imputation, because the imputer must take special care to preserve any associations or special features of the data that will be modeled in the subsequent analysis. For example, this article deals with multiple group models that are commonly used to examine moderation effects in psychology and the behavioral sciences. Special care must be exercised when using multiple imputation with multiple group models, as failing to preserve the interactive effects during the imputation phase can produce biased parameter estimates in the subsequent analysis phase, even when the data are missing completely at random or missing at random. This study investigates two imputation strategies that have been proposed in the literature, product term imputation and separate group imputation. A series of simulation studies shows that separate group imputation adequately preserves the multiple group data structure and produces accurate parameter estimates.     

Cross-Level Invariance in Multilevel Factor Models

When modeling latent variables at multiple levels, it is important to consider the meaning of the latent variables at the different levels. If a higher-level common factor represents the aggregated version of a lower-level factor, the associated factor loadings will be equal across levels. However, many researchers do not consider cross-level invariance constraints in their research. Not applying these constraints when in fact they are appropriate leads to overparameterized models, and associated convergence and estimation problems. This simulation study used a two-level mediation model on common factors to show that when factor loadings are equal in the population, not applying cross-level invariance constraints leads to more estimation problems and smaller true positive rates. Some directions for future research on cross-level invariance in MLSEM are discussed.     

New Empirical Evidence for the Design of Group Randomized Trials in Education

Abstract

This article provides practical guidance for researchers who are designing studies that randomize groups to measure the impacts of educational interventions. The article (a) provides new empirical information about the values of parameters that influence the precision of impact estimates (intraclass correlations and R ² values) and includes outcomes other than standardized test scores and data with a three-level structure rather than a two-level structure, and (b) discusses the error (both generalizability and estimation error) that exists in estimates of key design parameters and the implications this error has for design decisions. Data for the paper come primarily from two studies: the Chicago Literacy Initiative: Making Better Early Readers Study (CLIMBERS) and the School Breakfast Pilot Project (SBPP). The analysis sample from CLIMBERS comprised 430 four-year-old children from 47 preschool classrooms in 23 Chicago public schools. The analysis sample from the SBPP study comprised 1,151 third graders from 233 classrooms in 111 schools from 6 school districts. Student achievement data from the Reading First Impact Study is also used to supplement the discussion.     

The Consequences of Ignoring Multilevel Data Structures in Nonhierarchical Covariance Modeling

This study examined the effects of ignoring multilevel data structures in nonhierarchical covariance modeling using a Monte Carlo simulation. Multilevel sample data were generated with respect to 3 design factors: (a) intraclass correlation, (b) group and member configuration, and (c) the models that underlie the between-group and within-group variance components associated with multilevel data. Covariance models that ignored the multilevel structure were then fit to the data. Results indicated that when variables exhibit minimal levels of intraclass correlation, the chi-square model/data fit statistic, the parameter estimators, and the standard error estimators are relatively unbiased. However, as the level of intraclass correlation increases, the chi-square statistic, the parameters, and their standard errors all exhibit estimation problems. The specific group/member configurations as well as the underlying between-group and within-group model structures further exacerbate the estimation problems encountered in the nonhierarchical analysis of multilevel data.     

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.     

基于中间件技术的三层网络结构的研究与应用

在电信计费账务系统日趋复杂的情况下,客户机/服务器模式已无法适应电信业务对计费账务系统的要求。应用中间件技术的三层体系结构为实现高效、安全的计费系统提供了新的平台。文章首先讨论了传统二层体系结构的缺陷,介绍了中间件的概念和三层结构的特点,并把中间件技术应用于电信计费账务系统中,解决数据大量用户的接入、系统间服务调用等问题。     

The Relation between Teacher Specialization and Student Reading Achievement

This study investigates the relationship between teacher specialization and the reading achievement of fourth-grade students in Sweden. The empirical base is data from PIRLS 2011. The main method of analysis is a two-level regression. Results revealed a positive relationship between reading achievement and teacher education relevant for subject and grade level while there was no relationship between reading achievement and teaching experience. The relation between reading achievement and teacher specialization remained significant when the influence of parents’ educational levels and students’ early reading abilities were controlled for. A tendency of compensatory effects could be observed, with teacher specialization having a stronger effect in low-performing classrooms. The findings support the conclusion that relevant teacher education is of importance for teacher effectiveness.     

Analysis of Longitudinal Studies With Missing Data Using Covariance Structure Modeling With Full-Information Maximum Likelihood

A didactic discussion of covariance structure modeling in longitudinal studies with missing data is presented. Use of the full-information maximum likelihood method is considered for model fitting, parameter estimation, and hypothesis testing purposes, particularly when interested in patterns of temporal change as well as its covariates and predictors. The approach is illustrated with an application of the popular level-and-shape model to data from a cognitive intervention study of elderly adults.     

Comparison of Mediated Effects: A Correlation Structure Modeling Approach

A correlation structure modeling method for comparison of mediated effects is outlined. The procedure permits point and interval estimation of differences in mediator effects, and is useful with models postulating 1 or more predictor, intervening, or response variables that may also be latent constructs. The approach allows scale-free evaluation of differences in effects of any explanatory upon criterion variables transmitted via studied mediators, and is applied on data from a study of older adults with recent vision loss.     

Multilevel Cognitive Diagnosis Models for Assessing Changes in Latent Attributes

Cognitive diagnosis models (CDMs) have been developed to evaluate the mastery status of individuals with respect to a set of defined attributes or skills that are measured through testing. When individuals are repeatedly administered a cognitive diagnosis test, a new class of multilevel CDMs is required to assess the changes in their attributes and simultaneously estimate the model parameters from the different measurements. In this study, the most general CDM of the generalized deterministic input, noisy “and” gate (G‐DINA) model was extended to a multilevel higher order CDM by embedding a multilevel structure into higher order latent traits. A series of simulations based on diverse factors was conducted to assess the quality of the parameter estimation. The results demonstrate that the model parameters can be recovered fairly well and attribute mastery can be precisely estimated if the sample size is large and the test is sufficiently long. The range of the location parameters had opposing effects on the recovery of the item and person parameters. Ignoring the multilevel structure in the data by fitting a single‐level G‐DINA model decreased the attribute classification accuracy and the precision of latent trait estimation. The number of measurement occasions had a substantial impact on latent trait estimation. Satisfactory model and person parameter recoveries could be achieved even when assumptions of the measurement invariance of the model parameters over time were violated. A longitudinal basic ability assessment is outlined to demonstrate the application of the new models.     

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.     

Impact of Diagnosticity on the Adequacy of Models for Cognitive Diagnosis under a Linear Attribute Structure: A Simulation Study

Compared to unidimensional item response models (IRMs), cognitive diagnostic models (CDMs) based on latent classes represent examinees' knowledge and item requirements using discrete structures. This study systematically examines the viability of retrofitting CDMs to IRM‐based data with a linear attribute structure. The study utilizes a procedure to make the IRM and CDM frameworks comparable and investigates how estimation accuracy is affected by test diagnosticity and the match between the true and fitted models. The study shows that comparable results can be obtained when highly diagnostic IRM data are retrofitted with CDM, and vice versa, retrofitting CDMs to IRM‐based data in some conditions can result in considerable examinee misclassification, and model fit indices provide limited indication of the accuracy of item parameter estimation and attribute classification.     

Detecting Multidimensional DIF in Polytomous Items with IRT Methods and Estimation Approaches

The purpose of this study was to investigate multidimensional DIF with a simple and nonsimple structure in the context of multidimensional Graded Response Model (MGRM). This study examined and compared the performance of the IRT-LR and Wald test using MML-EM and MHRM estimation approaches with different test factors and test structures in simulation studies and applying real data sets. When the test structure included two dimensions, the IRT-LR (MML-EM) generally performed better than the Wald test and provided higher power rates. If the test included three dimensions, the methods provided similar performance in DIF detection. In contrast to these results, when the number of dimensions in the test was four, MML-EM estimation completely lost precision in estimating the nonuniform DIF, even with large sample sizes. The Wald with MHRM estimation approaches outperformed the Wald test (MML-EM) and IRT-LR (MML-EM). The Wald test had higher power rate and acceptable type I error rates for nonuniform DIF with the MHRM estimation approach.The small and/or unbalanced sample sizes, small DIF magnitudes, unequal ability distributions between groups, number of dimensions, estimation methods and test structure were evaluated as important test factors for detecting multidimensional DIF.     

不完全数据下响应变量的精度估计

讨论了在不完全数据下的响应变量的估计精度,当不可忽略缺失下,样本的响应有缺失数据时,其联合分布是不可识别的.现证明了估计的精度与工具变量的相关性,当工具变量独立于目标变量时,目标变量估计的方差趋于无穷大.     

Two-level Bregman method for MRI reconstruction with graph regularized sparse coding

In this paper, a two-level Bregman method is presented with graph regularized sparse coding for highly undersampled magnetic resonance image reconstruction. The graph regularized sparse coding is incorporated with the two-level Bregman iterative procedure which enforces the sampled data constraints in the outer level and updates dictionary and sparse representation in the inner level. Graph regularized sparse coding and simple dictionary updating applied in the inner minimization make the proposed algorithm converge with a relatively small number of iterations. Experimental results demonstrate that the proposed algorithm can consistently reconstruct both simulated MR images and real MR data efficiently, and outperforms the current state-of-the-art approaches in terms of visual comparisons and quantitative measures.     

Situations Where It Is Appropriate to Use Frequency Estimation Equipercentile Equating

In operational equating situations, frequency estimation equipercentile equating is considered only when the old and new groups have similar abilities. The frequency estimation assumptions are investigated in this study under various situations from both the levels of theoretical interest and practical use. It shows that frequency estimation equating can be used under circumstances when it is not normally used. To link theoretical results with practice, statistical methods are proposed for checking frequency estimation assumptions based on available data: observed‐score distributions and item difficulty distributions of the forms. In addition to the conventional use of frequency estimation equating when the group abilities are similar, three situations are identified when the group abilities are dissimilar: (a) when the two forms and the observed conditional score distributions are similar the two forms and the observed conditional score distributions are similar (in this situation, the frequency estimation equating assumptions are likely to hold, and frequency estimation equating is appropriate); (b) when forms are similar but the observed conditional score distributions are not (in this situation, frequency estimation equating is not appropriate); and (c) when forms are not similar but the observed conditional score distributions are (frequency estimation equating is not appropriate). Statistical analysis procedures for comparing distributions are provided. Data from a large‐scale test are used to illustrate the use of frequency estimation equating when the group difference in ability is large.     

Bayesian Estimation of the True Score Multitrait–Multimethod Model With a Split-Ballot Design

This article examines whether Bayesian estimation with minimally informed prior distributions can alleviate the estimation problems often encountered with fitting the true score multitrait–multimethod structural equation model with split-ballot data. In particular, the true score multitrait–multimethod structural equation model encounters an empirical underidentification when (a) latent variable correlations are homogenous, and (b) fitted to data from a 2-group split-ballot design; an understudied case of empirical underidentification due to a planned missingness (i.e., split-ballot) design. A Monte Carlo simulation and 3 empirical examples showed that Bayesian estimation performs better than maximum likelihood (ML) estimation. Therefore, we suggest using Bayesian estimation with minimally informative prior distributions when estimating the true score multitrait–multimethod structural equation model with split-ballot data. Furthermore, given the increase in planned missingness designs in psychological research, we also suggest using Bayesian estimation as a potential alternative to ML estimation for analyses using data from planned missingness designs.     

农村学校布局调整对学生成绩的影响——基于两水平增值模型的分析

文章使用＂西发项目＂广西壮族自治区的面板数据考察农村小学布局调整对学生成绩的影响,对比两水平增值模型和OLS估计结果发现,学校布局调整整体上对小学生成绩具有负向影响,对语文成绩的影响尤为显著。学校办学条件、生均寄宿面积、学校满意度对学生成绩有正向影响,寄宿生的成绩略低于非寄宿生,家校距离、家庭经济负担、学校配套设施不健全、学校心理疏导缺失等因素对学生成绩产生负向影响,这种负向影响已经超出了学校办学条件等因素对学生成绩的正向影响。在实证研究的基础上,文章提出布局调整过程中,在改善办学条件的同时,应当做好硬件配套设施和软件环境的建设,保障相关财政投入,加强监督,以实现提高教育质量的目标。

Abstract：

This paper use the panel data of BEWAP to study the effect of layout adjustment of schools on student achievement in primary school of rural area in Guangxi Zhuang autonomous region.By the comparisons of two-level value-added model and OLS estimation results,the research shows that the layout adjustment policy generally has a negative effect on primary school students＇ achievement,especially on the language achievement.Specifically,the factors of school condition,dormitory area per-student and degree of school satisfaction have positive impacts on student achievement,the achievement of resident student slightly lower than non-resident student.The factors of farther home-school distance,more financial burden of families,inadequate supporting facilities of schools and the absence of psychological or other assistance have negative impacts on students＇ achievement,which are higher than the policy＇s positive effects.Based on the empirical study,this research suggests that the government should construct better hardware establishment and software condition while the improvement of school condition in the process of layout adjustment,ensure relevant financial input and enhance supervision so as to realize the goal of improving education quality.