Estimation for structural equation models with missing data

A direct method in handling incomplete data in general covariance structural models is investigated. Asymptotic statistical properties of the generalized least squares method are developed. It is shown that this approach has very close relationships with the maximum likelihood approach. Iterative procedures for obtaining the generalized least squares estimates, the maximum likelihood estimates, as well as their standard error estimates are derived. Computer programs for the confirmatory factor analysis model are implemented. A longitudinal type data set is used as an example to illustrate the results.This research was supported in part by Research Grant DAD1070 from the U.S. Public Health Service. The author is indebted to anonymous reviewers for some very valuable suggestions. Computer funding is provided by the Computer Services Centre, The Chinese University of Hong Kong.     

Penalized optimal scaling for ordinal variables with an application to international classification of functioning core sets

Ordinal data occur frequently in the social sciences. When applying principal component analysis (PCA), however, those data are often treated as numeric, implying linear relationships between the variables at hand; alternatively, non-linear PCA is applied where the obtained quantifications are sometimes hard to interpret. Non-linear PCA for categorical data, also called optimal scoring/scaling, constructs new variables by assigning numerical values to categories such that the proportion of variance in those new variables that is explained by a predefined number of principal components (PCs) is maximized. We propose a penalized version of non-linear PCA for ordinal variables that is a smoothed intermediate between standard PCA on category labels and non-linear PCA as used so far. The new approach is by no means limited to monotonic effects and offers both better interpretability of the non-linear transformation of the category labels and better performance on validation data than unpenalized non-linear PCA and/or standard linear PCA. In particular, an application of penalized optimal scaling to ordinal data as given with the International Classification of Functioning, Disability and Health (ICF) is provided.     

Isotonic ordinal probabilistic models (ISOP)

The concept of an ordinal instrumental probabilistic comparison is introduced. It relies on an ordinal scale given a priori and on the concept of stochastic dominance. It is used to define a weakly independently ordered system, or isotonic ordinal probabilistic (ISOP) model, which allows the construction of separate sample-free ordinal scales on a set of subjects and a set of items. The ISOP-model is a common nonparametric theoretical structure for unidimensional models for quantitative, ordinal and dichotomous variables.Fundamental theorems on dichotomous and polytomous weakly independently ordered systems are derived. It is shown that the raw score system has the same formal properties as the latent system, and therefore the latter can be tested at the observed empirical level.I wish to thank 3 reviewers and 2 editors who contributed a lot to the readability and precision of the article.     

Multiple-answer multiple-choice test items: Responding and scoring through bayes and minimax strategies

A multiple-answer multiple-choice test item has a certain number of alternatives,any number of which might be keyed. The examinee is also allowed to mark any number of alternatives. This increased flexibility over the one keyed alternative case is useful in practice but raises questions about appropriate scoring rules. In this article a certain class of item scoring rules called thebinary class is considered. The concepts ofstandard scoring rules and equivalence among these scoring rules are introduced in the misinformation model for which the traditional knowledge model is a special case. The examinee's strategy with respect to a scoring rule is examined. The critical role of a quantity called the scoring ratio is emphasized. In the case of examinee uncertainty about the number of correct alternatives on an item, a Bayes and a minimax strategy for the examinee are developed. Also an appropriate response for the examiner to the minimax strategy is outlined.Research partially supported under Grants N00014-67-A-0314-0022 from the Office of Naval Research and GS-32514 and MPS 75-07539 from the National Science Foundation.     

Measuring rationality independent of social desirability

The development of a test to measure Elli's concept of rationality is described. In the first study discussed, a 58-item test is developed to measure rationality, and the reliability and convergent validity of the test is described. In a second study, the discriminant validity of the test is examined. An attempt is also made to reduce social-desirability content in the test by eliminating items most highly correlated with a Social Desirability Scale. The final 44-item test is found to be high in both reliability and validity. The factor structure of the test is also examined.     

An empirically derived scoring system for intermale aggression in mice

Scoring systems used to assess intermale aggression have been characterized by arbitrary scales and wide variability in the behaviors selected for measurement. The use of such different systems severely limits the ability of investigators to make meaningful comparisons among studies and indicates that there is a need for a common, statistically derived evaluative system for intermale aggression. We measured the frequency and duration of five major components of agonistic behavior exhibited by intact males toward olfactory bulbectomized stimulus males and then analyzed the data using a number of univariate and multivariate procedures. The results were used to generate two statistically based scoring systems, one a short-form index and the other a composite index for more detailed studies of aggression. It is hoped that these statistically derived systems will be adopted by other investigators to increase methodological congruence in the field.     

A note on the equivalence of the graded response model and the sequential model

This paper concerns items that consist of several item steps to be responded to sequentially. The item scoreX is defined as the number of correct responses until the first failure. Samejima's graded response model states that each steph=1,...,m is characterized by a parameterb _h , and, for a subject with ability, Pr(Xh; )=F(–b _h ). Tutz's general sequential model associates with each step a parameterdh, and it states that Pr(Xh;)= _r ^=1h G(–d _r ). Tutz's (1991, 1997) conjectures that the models are equivalent if and only ifF(x)=G(x) is an extreme value distribution. This paper presents a proof for this conjecture.     

Constrained maximum likelihood estimation of two-level covariance structure model via EM type algorithms

In this paper, the constrained maximum likelihood estimation of a two-level covariance structure model with unbalanced designs is considered. The two-level model is reformulated as a single-level model by treating the group level latent random vectors as hypothetical missing-data. Then, the popular EM algorithm is extended to obtain the constrained maximum likelihood estimates. For general nonlinear constraints, the multiplier method is used at theM-step to find the constrained minimum of the conditional expectation. An accelerated EM gradient procedure is derived to handle linear constraints. The empirical performance of the proposed EM type algorithms is illustrated by some artifical and real examples.This research was supported by a Hong Kong UCG Earmarked Grant, CUHK 4026/97H. We are greatly indebted to D.E. Morisky and J.A. Stein for the use of their AIDS data in our example. We also thank the Editor, two anonymous reviewers, W.Y. Poon and H.T. Zhu for constructive suggestions and comments in improving the paper. The assistance of Michael K.H. Leung and Esther L.S. Tam is gratefully acknowledged.     

Automated Integrative Complexity: Current Challenges and Future Directions

Automating integrative complexity is fraught with many challenges. To address these challenges, we discuss the tension between a specificity approach and a more flexible multiple‐pass approach, the multifaceted nature of the complexity construct, the gold standard for complexity measurement, the difficulty of human scoring and its consequences for automation, and some ways forward for creating the best complexity measurements. In so doing, we present new data demonstrating (1) initial evidence for the validity of a new automated system for measuring two different forms of complexity (elaborative and dialectical), (2) the danger of constructing measurements in a purely ad hoc fashion that ignores prospective testing, (3) human‐to‐computer correspondence is in part a function of human‐to‐human correspondence, (4) human‐to‐computer correspondence increases systematically as one uses tests with larger units of analysis, and (5) the lack of correspondence of different systems (both human and automated) may occur in part because they were designed for different units of analysis.     

多级评分模型下的题库结构对CAT的影响分析

在多级评分模型下,项目的难度参数或步骤参数有多个,在对多级评分模型进行选题时,通常对项目的多个难度参数用一个综合的指标来概括.当对每个项目的难度参数进行有效的综合后,综合后的难度参数分布发生了改变,这时如果增加适量的平均难度较难或较易的项目进入题库,测验的精度和项目的曝光率都有一定的改善.