Structural equation models with continuous and polytomous variables

A two-stage procedure is developed for analyzing structural equation models with continuous and polytomous variables. At the first stage, the maximum likelihood estimates of the thresholds, polychoric covariances and variances, and polyserial covariances are simultaneously obtained with the help of an appropriate transformation that significantly simplifies the computation. An asymptotic covariance matrix of the estiates is also computed. At the second stage, the parameters in the structural covariance model are obtained via the generalized least squares approach. Basic statistical properties of the estimates are derived and some illustrative examples and a small simulation study are reported.This research was supported in part by a research grant DA01070 from the U. S. Public Health Service. We are indebted to several referees and the editor for very valuable comments and suggestions for improvement of this paper. The computing assistance of King-Hong Leung and Man-Lai Tang is also gratefully acknowledged.     

A general approach to categorical data analysis with missing data,using generalized linear models with composite links

A general approach for analyzing categorical data when there are missing data is described and illustrated. The method is based on generalized linear models with composite links. The approach can be used (among other applications) to fill in contingency tables with supplementary margins, fit loglinear models when data are missing, fit latent class models (without or with missing data on observed variables), fit models with fused cells (including many models from genetics), and to fill in tables or fit models to data when variables are more finely categorized for some cases than others. Both Newton-like and EM methods are easy to implement for parameter estimation.The author thanks the editor, the reviewers, Laurie Hopp Rindskopf, and Clifford Clogg for comments and suggestions that substantially improved the paper.     

句子加工和语义记忆结构的实验研究

本文报告的实验,以句子验证范式为基础,采用常规试验和信号试验相混合的程序,对汉语句子加工的有关问题作了考察,实验结果表明,句子理解的时间,依赖于人对句中所含概念之间语义关系的认知度;人对句子的理解是一个部分信息逐渐积累的过程。根据实验材料,作者对语义记忆的结构问题作了讨论。     

Parameterizing inequality constraints on unique variances in linear structural models

Current computer programs for analyzing linear structural models will apparently handle only two types of constraints: fixed parameters, and equality of parameters. An important constraint not handled is inequality; this is particularly crucial for preventing negative variance estimates. In this paper, a method is described for imposing several kinds of inequality constraints in models, without the necessity for having computer programs which explicitly allow such constraints. The examples discussed include the prevention of Heywood cases, extension to inequalities of parameters to be greater than a specified value, and imposing ordered inequalities. Work on this project was aided by the City University of New York—Professional Staff Congress Research Award Program Grant Number 13631.     

Ordinal data,ordered scale points,and order statistics

This paper concerns ordinal responses. An ordered Dirichlet distribution describes prior and posterior beliefs about the cumulative probabilities of response categories. Associating the response categories with intervals of a latent random variable then induces a distribution on the order statistics of that variable. The psychometrician can use the asymptotic theory of order statistics to learn how distributional assumptions about the latent variable effect inference. An example relates the skewness of a latent variable to the proportional odds and proportional hazards models of McCullagh [1980].     

Stimuli, reinforcers, and behavior: an integration

We propose that a fundamental unit of behavior is the concurrent discriminated operant, and we discuss in detail a quantitative model of the concurrent three-term contingency that is based on the notion that an animal's behavior is controlled to differing extents by both stimulus—behavior and behavior—reinforcer relations. We show how this model can describe performance in a variety of experimental procedures: conditional discrimination and matching to sample, both with and without reinforcement for responses that are traditionally identified as errors; conditional discrimination with more than two stimuli and choice alternatives; delayed matching to sample and delayed reinforcement in matching to sample; second-order and complex conditional discrimination; and multiple and concurrent schedules. Although the model is incomplete in its coverage, and may be incorrect, we believe that this conceptual approach will bear fruit in the development of behavior theory.     

The whirligig of time: Some thoughts on Staddon and Higa.

Staddon and Higa's theory of timing finds analogy with physics' concern with the relativity of time and irreversible processes. Their model raises general issues about the nature and function of models and, specifically, the extent to which it has captured the stimulus events in temporal control.     

Generating items during testing: Psychometric issues and models

On-line item generation is becoming increasingly feasible for many cognitive tests. Item generation seemingly conflicts with the well established principle of measuring persons from items with known psychometric properties. This paper examines psychometric principles and models required for measurement from on-line item generation. Three psychometric issues are elaborated for item generation. First, design principles to generate items are considered. A cognitive design system approach is elaborated and then illustrated with an application to a test of abstract reasoning. Second, psychometric models for calibrating generating principles, rather than specific items, are required. Existing item response theory (IRT) models are reviewed and a new IRT model that includes the impact on item discrimination, as well as difficulty, is developed. Third, the impact of item parameter uncertainty on person estimates is considered. Results from both fixed content and adaptive testing are presented.This article is based on the Presidential Address Susan E. Embretson gave on June 26, 1999 at the 1999 Annual Meeting of the Psychometric Society held at the University of Kansas in Lawrence, Kansas. —Editor     

Mixtures of conditional mean- and covariance-structure models

Models and parameters of finite mixtures of multivariate normal densities conditional on regressor variables are specified and estimated. We consider mixtures of multivariate normals where the expected value for each component depends on possibly nonnormal regressor variables. The expected values and covariance matrices of the mixture components are parameterized using conditional mean- and covariance-structures. We discuss the construction of the likelihood function, estimation of the mixture model with regressors using three different EM algorithms, estimation of the asymptotic covariance matrix of parameters and testing for the number of mixture components. In addition to simulation studies, data on food preferences are analyzed.The authors are grateful to Donald B. Rubin and Michael E. Sobel for critical reading of a first draft of this paper and to three anonymous reviewers ofPsychometrika for their helpful comments and suggestions. The research of the first and the third author was supported by a grant from the Deutsche Forschungsgemeinschaft.