Using item-specific instructional information in achievement modeling

The problem of detecting instructional sensitivity (item basis) in test items is considered. An illustration is given which shows that for tests with many biased items, traditional item bias detection schemes give a very poor assessment of bias. A new method is proposed instead. This method extends item response theory (IRT) by including item-specific auxiliary measurement information related to opportunity-to-learn. Item-specific variation in measurement relations across students with varying opportunity-to-learn is allowed for.This paper was presented at the 1987 AERA meeting in Washington, DC. This research was supported by grant OERI-G-86-003 from the Office of Educational Research and Improvement, Department of Education. The author thanks Michael Hollis and Chih-fen Kao for valuable research assistance, and appreciates valuable comments made by an anonymous reviewer.     

Factor structure in groups selected on observed scores

A new method is proposed for estimating factor means and factor covariances in a group of individuals selected on their observed scores. The selection variable is, for example, the total score on an admissions test. Given a factor model for the test items based on the group of test takers, we may be interested in the factor structure for those in the top quartile. The differences in factor means and covariances between this selected group and the full group gives useful information both on successful test performance and on test validity. The new method draws on the classic Pearson-Lawley selection formulas. It avoids the fallacy of factor analysis on the selected group, which would lead to incorrect estimates. The new method is applied to a simple factor structure model for the GMAT test. Although the majority of the GMAT items test verbal skills, it is found that a quantitative factor shows the greatest change in moving from average to top quartile test takers.     

On structural equation modeling with data that are not missing completely at random

A general latent variable model is given which includes the specification of a missing data mechanism. This framework allows for an elucidating discussion of existing general multivariate theory bearing on maximum likelihood estimation with missing data. Here, missing completely at random is not a prerequisite for unbiased estimation in large samples, as when using the traditional listwise or pairwise present data approaches. The theory is connected with old and new results in the area of selection and factorial invariance. It is pointed out that in many applications, maximum likelihood estimation with missing data may be carried out by existing structural equation modeling software, such as LISREL and LISCOMP. Several sets of artifical data are generated within the general model framework. The proposed estimator is compared to the two traditional ones and found superior.The research of the first author was supported by grant No. SES-8312583 from the National Science Foundation and by a Spencer Foundation grant. We wish to thank Chuen-Rong Chan for drawing the path diagram.     

A general structural equation model with dichotomous,ordered categorical,and continuous latent variable indicators

A structural equation model is proposed with a generalized measurement part, allowing for dichotomous and ordered categorical variables (indicators) in addition to continuous ones. A computationally feasible three-stage estimator is proposed for any combination of observed variable types. This approach provides large-sample chi-square tests of fit and standard errors of estimates for situations not previously covered. Two multiple-indicator modeling examples are given. One is a simultaneous analysis of two groups with a structural equation model underlying skewed Likert variables. The second is a longitudinal model with a structural model for multivariate probit regressions.This research was supported by Grant No. 81-IJ-CX-0015 from the National Institute of Justice, by Grant No. DA 01070 from the U.S. Public Health Service, and by Grant No. SES-8312583 from the National Science Foundation. I thank Julie Honig for drawing the figures. Requests for reprints should be sent to Bengt Muthén, Graduate School of Education, University of California, Los Angeles, California 90024.     

The Christology of Veli-Matti Kärkkäinen re-visited from the perspective of Scandinavian Creation Theology

This article is a response to Veli-Matti Kärkkäinen's Christology from the perspective of Scandinavian creation theology. Starting from the identification of a common post-liberal horizon, together with similar challenges from anti-liberal theology, the author enters into a critical examination of Kärkkäinen's systematic theology elaborating on the possible contributions from Gustaf Wingren. First, the significance of creation as horizon of understanding for Christology is discussed. Second, the relationship between anthropology and Christology is investigated, with a special focus on theological resources to transcend the dichotomies and the zero-sum game that places God and humans in opposition as competitors.     

Clinical manifestations and stages of Rett syndrome

The presentation and clinical diagnosis of Rett syndrome at various ages and stages are reviewed. In addition to the classical form, variability in phenotype between different atypical Rett forms is given. Obligatory, supportive, and differential diagnostic criteria are summarized. Long-term follow-up findings in ageing Rett women are addressed.     

Bayesian structural equation modeling: A more flexible representation of substantive theory

This article proposes a new approach to factor analysis and structural equation modeling using Bayesian analysis. The new approach replaces parameter specifications of exact zeros with approximate zeros based on informative, small-variance priors. It is argued that this produces an analysis that better reflects substantive theories. The proposed Bayesian approach is particularly beneficial in applications where parameters are added to a conventional model such that a nonidentified model is obtained if maximum-likelihood estimation is applied. This approach is useful for measurement aspects of latent variable modeling, such as with confirmatory factor analysis, and the measurement part of structural equation modeling. Two application areas are studied, cross-loadings and residual correlations in confirmatory factor analysis. An example using a full structural equation model is also presented, showing an efficient way to find model misspecification. The approach encompasses 3 elements: model testing using posterior predictive checking, model estimation, and model modification. Monte Carlo simulations and real data are analyzed using Mplus. The real-data analyses use data from Holzinger and Swineford's (1939) classic mental abilities study, Big Five personality factor data from a British survey, and science achievement data from the National Educational Longitudinal Study of 1988. (PsycINFO Database Record (c) 2012 APA, all rights reserved).     

Rejoinder to MacCallum, Edwards, and Cai (2012) and Rindskopf (2012): Mastering a new method

This rejoinder discusses the general comments on how to use Bayesian structural equation modeling (BSEM) wisely and how to get more people better trained in using Bayesian methods. Responses to specific comments cover how to handle sign switching, nonconvergence and nonidentification, and prior choices in latent variable models. Two new applications are included. The first one revisits the Kaplan (2009) science model by considering priors on primary parameters. The second one applies BSEM to the bifactor model that was hypothesized in the original Holzinger and Swineford (1939) study. (PsycINFO Database Record (c) 2012 APA, all rights reserved).