Latent variable models: Applications in education

Most theories in the social sciences involve relationships among constructs which are not directly observable. Behavioral measures exist of all constructs, such as intelligence, creativity, and other cognitive traits, aggressiveness, sociability, and other personality and affective characteristics; but these observed measures are usually assumed to be imperfect indicators of the (presumed) underlying construct. The imperfections exist because of errors of measurement and because the observed behavior may be influenced by other underlying constructs in addition to the one of primary interest. Statistical methods, called latent variable models, have been developed to provide rigorous tests of theories involving unobserved variables. This paper describes the major types of latent variable models, shows how they can be applied in educational research, and gives representative examples of their use from the literature.     

Latent growth curves within developmental structural equation models

This report uses structural equation modeling to combine traditional ideas from repeated-measures ANOVA with some traditional ideas from longitudinal factor analysis. A longitudinal model that includes correlations, variances, and means is described as a latent growth curve model (LGM). When merged with repeated-measures data, this technique permits the estimation of parameters representing both individual and group dynamics. The statistical basis of this model allows hypothesis testing of various developmental ideas, including models of alternative dynamic functions and models of the sources of individual differences in these functions. Aspects of these latent growth models are illustrated with a set of longitudinal WISC data from young children and by using the LISREL V computer program.     

Latent trait modelling of rater accuracy in formative peer assessment of English-Chinese consecutive interpreting

Despite the increasing popularity of peer assessment in tertiary-level interpreter education, very little research has been conducted to examine the quality of peer ratings on language interpretation. While previous research on the quality of peer ratings, particularly rating accuracy, mainly relies on correlation and analysis of variance, latent trait modelling emerges as a useful approach to investigate rating accuracy in rater-mediated performance assessment. The present study demonstrates the use of multifaceted Rasch partial credit modelling to explore the accuracy of peer ratings on English-Chinese consecutive interpretation. The analysis shows that there was a relatively wide spread of rater accuracy estimates and that statistically significant differences were found between peer raters regarding rating accuracy. Additionally, it was easier for peer raters to assess some students accurately than others, to peer-assess target language quality accurately than the other rating domains, and to provide accurate ratings to English-to-Chinese interpretation than the other direction. Through these findings, latent trait modelling demonstrates its capability to produce individual-level indices, measure rater accuracy directly, and accommodate sparse data rating designs. It is therefore hoped that substantive inquiries into peer assessment of language interpretation could utilise latent trait modelling to move this line of research forward.     

How valid are scholars' departmental rating models for assessing the quality of graduate programs?

The validity of the scholars' departmental rating (SDR) model for determining the quality of an institution's graduate program has been the subject of intense controversy for over a half-century. This study, using the aggregated data from each of four classical rankings of graduate programs in United States universities, found that the rankings of institutions in separate studies correlate significantly with each other and that the results from the SDR model correlate significantly with the objective measures of academic honors, basic research, and research and development awards. The author concludes that the SDR model is valid for the purposes intended.     

Peer assessment accounting for student agreement

Peer assessment has been gaining significant ground as a means of fostering an environment of accountability and responsibility for group projects in higher education. A popular peer assessment method assigns individual grades via a linear relationship to peer assessment scores. Using this method, a group member who receives his or her group’s average peer assessment score is assigned the instructor‐given group grade; the group member who receives a total peer assessment score of zero is assigned an individual grade of zero. Unfortunately, applying this method often requires time‐consuming exploratory data analysis because of the potential for the method to yield a high spread of grades, including grades over 100%. The present study proposes a modification, which accounts for the degree of student agreement. When the modified procedure results in a change from the group grade, the direction of change is always the same, but with smaller magnitude, requiring less subsequent data analysis and instructor time demands. Easy‐to‐modify SAS code for applying the method is presented in the Appendix.     

The Latent Variable-Autoregressive Latent Trajectory Model: A General Framework for Longitudinal Data Analysis

In recent years, longitudinal data have become increasingly relevant in many applications, heightening interest in selecting the best longitudinal model to analyze them. Too often, traditional practice rather than substantive theory guides the specific model selected. This opens the possibility that alternative models might better correspond to the data. In this paper, we present a general longitudinal model that we call the Latent Variable-Autoregressive Latent Trajectory (LV-ALT) model that includes most other longitudinal models with continuous outcomes as special cases. It is capable of specializing to most models dictated by theory or prior research while having the capacity to compare them to alternative ones. If there is little guidance on the best model, the LV-ALT provides a way to determine the appropriate empirical match to the data. We present the model, discuss its identification and estimation, and illustrate how the LV-ALT reveals new things about a widely used empirical example.     

A Comparison of Three-Step Approaches for Auxiliary Variables in Latent Class and Latent Profile Analysis

In this article, 3-step methods to include predictors and distal outcomes in commonly used mixture models are evaluated. Two Monte Carlo simulation studies were conducted to compare the pseudo class (PC), Vermunt’s (2010), and the Lanza, Tan, and Bray (LTB) 3-step approaches with respect to bias of parameter estimates in latent class analysis (LCA) and latent profile analysis (LPA) models with auxiliary variables. For coefficients of predictors of class membership, results indicated that Vermunt’s method yielded more accurate estimates for LCA and LPA compared to the PC method. With distal outcomes of latent classes and latent profiles, the LTB method produced the lowest relative bias of coefficient estimates and Type I error rates close to nominal levels.     

Specifying Piecewise Latent Trajectory Models for Longitudinal Data

Piecewise latent trajectory models for longitudinal data are useful in a wide variety of situations, such as when a simple model is needed to describe nonlinear change, or when the purpose of the analysis is to evaluate hypotheses about change occurring during a particular period of time within a model for a longer overall time frame, such as change that occurs following onset of a treatment or some other event. However, the specification of various forms of piecewise models has not been fully explicated for the structural equation modeling (SEM) framework. This article describes piecewise models as a straightforward extension of the basic SEM model for linear growth, which makes them relatively easy both to specify and to interpret. After presenting models for 2 linear slopes (or pieces) in detail, the article discusses extensions that include additional linear slopes (i.e., a 3-piece model) or a quadratic factor (i.e., a hybrid linear-quadratic model).     

MIMIC Latent Class Analysis Model for Alcoholic Diagnosis

The multiple indicators multiple causes (MIMIC) latent class analysis (LCA) model is an excellent classification method when researchers cannot find a "gold standard" to classify participants. The MIMIC-LCA model includes features of a typical LCA model and also introduces a new relation between the latent class and covariates. In other words, a logistic regression type of analysis between participants' categorical latent status and their background information is added. Detailed statistical setups of the MIMIC-LCA model and algorithmic procedures are derived. The model features, parameter estimations, and model selections for MIMIC-LCA models are also presented. Specifically, the MIMIC-LCA model is estimated by a generalized expectation-maximization algorithm under the maximum likelihood frameworks. A substantive application of the MIMIC-LCA model in diagnosing alcoholics and, in particular, examining potential risk factors for alcoholism is demonstrated.     

An Alternative Approach for Nonlinear Latent Variable Models

In the last decades there has been an increasing interest in nonlinear latent variable models. Since the seminal paper of Kenny and Judd, several methods have been proposed for dealing with these kinds of models. This article introduces an alternative approach. The methodology involves fitting some third-order moments in addition to the means and covariances. This article discusses how the model equations can be formulated and how several standard tests, like the model fit and Lagrange multiplier tests, can be performed. The new method compares favorably with the maximum likelihood method in several studies and can provide evidence of interaction that earlier approaches might ignore.     

用于保险信息系统的跨平台安全应用协议

阐述了一个用于保险信息系统的安全应用协议,实现Unix和Windows操作系统间的信息交互,完成保险业务流程。同时,应用用户认证和数据加密传输技术,保证了数据安全。     

A review of reliability procedures for measuring observer agreement

The present article reviews the procedures that have been developed for measuring the reliability of human observers' judgments when making direct observations of behavior. Measures such as the percentage of agreement, Cohen's kappa, and phi have been used to measure observer agreement; however, these coefficients have serious limitations. In addition to specifying the deficiencies that exist with these excessively used reliability measures, the present article discusses recently developed univariate and multivariate agreement measures that are based on quasi-equiprobability and quasi-independence models and estimates. Improvements in precision are provided by such models and estimates since they (1) yield a probability based coefficient of agreement with a directly interpretable meaning, (2) correct for the proportion of “chance” agreement, and (3) allow the partitioning of the agreement and disagreement estimates within the models.     

学习契约:远程学习效果评价的书面协议

过程性评价是远程学习评价的重要部分.作为过程性评价方式的典型代表,学习契约正越来越受到教学评价理论和实践的关注.为了充分理解和有效操作远程学习中学习契约这一评价方法,本文在整合国内外相关资料的基础上,论述了学习契约的定义与类型,分析了学习契约在远程学习中的特征与优势、基本原则和设计方法,并且提供了四个设计模板.     

Rater strategies for reaching agreement on pupil text quality

Novice members of a Norwegian national rater panel tasked with assessing Year 8 pupils’ written texts were studied during three successive preparation sessions (2011–2012). The purpose was to investigate how the raters successfully make use of different decision-making strategies in an assessment situation where pre-set criteria and standards give a rather strict framework. The data sources were the raters’ pair assessment dialogues. The analysis shows that the raters use a ‘shared standards strategy’, but when reaching agreement on text quality they also seem to make very good use of assessment strategies related to their work as writing teachers. Moreover, asymmetries in knowledge and participation among raters contribute to creating an image of writing assessment as a challenging hermeneutic practice. It is suggested that future rater preparation would gain from being attentive to the internalised assessment practices teachers bring to the fore when working as raters.     

Leaders: Latent danger for democracy even in education

The Art of Technical Writing: A Manual for Scientists, Engineers, and Students. Eugene Ehrlich and Daniel Murphy. New York: Thomas Y. Crowell Company, Apollo Edition, 1969. 182 pp. $1.95 paper.

A Primer on Food, Agriculture, and Public Policy. Earl O. Heady. New York: Random House, Inc., 1967. 169 pp. $4.95.

Professional Education for Ministry. Edward E. Thornton. Nashville: Abingdon Press, 1970. 301 pp. $7.50.

Psychology and the Superior Athlete, Bryant J. Cratty and Miroslav Vanek. New York: The Macmillan Company, 1970. 212 pp. $6.95 cloth.

The Slow Learner, edited by Joseph S. Roucek. New York: Philosophical Library, Inc., 1969. vi &; 373 pp. $10.00.

Storytelling and Creative Drama. Dewey W. Chambers. Dubuque, Iowa: William C. Brown, Publishers 1970. 92 pp.

Turmoil and Transition: Higher Education and Student Politics in India. Philip G. Altbach, editor. New York: Basic Books, Inc., Publishers, 1968. 277 pp. $7.50 cloth.     

Latent Differential Equation Models for Binary and Ordinal Data

This study evaluates latent differential equation models on binary and ordinal data. Binary and ordinal data are widely used in psychology research and many statistical models have been developed, such as the probit model and the logit model. We combine the latent differential equation model with the probit model through a threshold approach, and then compare the threshold model with a naive model, which blindly treats binary and ordinal data as continuous. Simulation results suggest that the naive model leads to bias on binary data and on ordinal data with fewer than 5 levels, whereas the threshold model is unbiased and efficient for binary and ordinal data. Two example analyses on empirical binary data and ordinal data show that the threshold model also has better external validity. The R code for the threshold model is provided.     

A Bayesian Approach for Estimating Multilevel Latent Contextual Models

In many applications of multilevel modeling, group-level (L2) variables for assessing group-level effects are generated by aggregating variables from a lower level (L1). However, the observed group mean might not be a reliable measure of the unobserved true group mean. In this article, we propose a Bayesian approach for estimating a multilevel latent contextual model that corrects for measurement error and sampling error (i.e., sampling only a small number of L1 units from a L2 unit) when estimating group-level effects of aggregated L1 variables. Two simulation studies were conducted to compare the Bayesian approach with the maximum likelihood approach implemented in Mplus. The Bayesian approach showed fewer estimation problems (e.g., inadmissible solutions) and more accurate estimates of the group-level effect than the maximum likelihood approach under problematic conditions (i.e., small number of groups, predictor variable with a small intraclass correlation). An application from educational psychology is used to illustrate the different estimation approaches.     

Latent Class Analysis for Multiple Discrete Latent Variables: A Study on the Association Between Violent Behavior and Drug-Using Behaviors

This article proposes a new type of latent class analysis, joint latent class analysis (JLCA), which provides a set of principles for the systematic identification of the subsets of joint patterns for multiple discrete latent variables. Inferences about the parameters are obtained by a hybrid method of expectation-maximization and Newton–Raphson algorithms. We apply JLCA in an investigation of adolescent violent behavior and drug-using behaviors. The data are from 4,957 male high-school students who participated in the Youth Risk Behavior Surveillance System in 2015. The JLCA approach identifies the different joint patterns of 4 latent variables: violent behavior, alcohol consumption, tobacco cigarette smoking, and other drug use. The JLCA uncovers 4 common violent behaviors and 3 representative behavioral patterns for each of 3 other latent variables. In addition, the JLCA supports 3 common joint classes, representing the most probable simultaneous patterns for being violent and being a drug user among adolescent males.     

Interrater agreement for discriminant classifications for the adjustment scales for children and adolescents

Investigation of interrater agreement for the Adjustment Scales for Children and Adolescents (ASCA) discriminant classifications is reported. Two teaching professionals or paraprofessionals working in the same classroom for a minimum of 1 hour per day provided independent ratings of the same child using the ASCA. A total of 119 students ranging in age from 7 to 18 years were independently rated on the ASCA. Results indicated significant and moderate to substantial interrater agreement for the discriminant classifications. © 2002 Wiley Periodicals, Inc.