Truth in Applicative Theories

We give a survey on truth theories for applicative theories. It comprises Frege structures, universes for Frege structures, and a theory of supervaluation. We present the proof-theoretic results for these theories and show their syntactical expressive power. In particular, we present as a novelty a syntactical interpretation of ID₁ in a applicative truth theory based on supervaluation.     

Standard errors of fit indices using residuals in structural equation modeling

The asymptotic standard errors of the correlation residuals and Bentler's standardized residuals in covariance structures are derived based on the asymptotic covariance matrix of raw covariance residuals. Using these results, approximations of the asymptotic standard errors of the root mean square residuals for unstandardized or standardized residuals are derived by the delta method. Further, in mean structures, approximations of the asymptotic standard errors of residuals, standardized residuals and their summary statistics are derived in a similar manner. Simulations are carried out, which show that the asymptotic standard errors of the various types of residuals and the root mean square residuals in covariance, correlation and mean structures are close to actual ones.The author is indebted to the reviewers for their comments and suggestions which have led to an improvement of this work.     

Models for ordinal hierarchical classes analysis

This paper proposes an ordinal generalization of the hierarchical classes model originally proposed by De Boeck and Rosenberg (1998). Any hierarchical classes model implies a decomposition of a two-way two-mode binary arrayM into two component matrices, called bundle matrices, which represent the association relation and the set-theoretical relations among the elements of both modes inM. Whereas the original model restricts the bundle matrices to be binary, the ordinal hierarchical classes model assumes that the bundles are ordinal variables with a prespecified number of values. This generalization results in a classification model with classes ordered along ordinal dimensions. The ordinal hierarchical classes model is shown to subsume Coombs and Kao's (1955) model for nonmetric factor analysis. An algorithm is described to fit the model to a given data set and is subsequently evaluated in an extensive simulation study. An application of the model to student housing data is discussed.     

Chunk hierarchies and retrieval structures: Comments on Saariluoma and Laine

The empirical results of Saariluoma and Laine are discussed and their computer simulations are compared with CHREST, a computational model of perception, memory and learning in chess. Mathematical functions such as power functions and logarithmic functions account for Saariluoma and Laine's correlation heuristic and for CHREST very well. However, these functions fit human data well only with game positions, not with random positions. As CHREST, which learns using spatial proximity, accounts for the human data as well as Saariluoma and Laine's correlation heuristic, their conclusion that frequency-based heuristics match the data better than proximity-based heuristics is questioned. The idea of flat chunk organisation and its relation to retrieval structures is discussed. In the conclusion, emphasis is given to the need for detailed empirical data, including information about chunk structure and types of errors, for discriminating between various learning algorithms.     

教育和心理研究中的多层线性模型

多层线性模型是分析具有层次结构数据的一种新型统计分析技术,与传统统计方法相比,具有模型假设与实际更吻合、结果解释更合理等特点。近年来这一方法的应用逐渐在社会科学的研究中受到重视。文章从多层线性模型的基本假设入手,较系统地介绍了模型参数估计和假设检验的方法,并通过一个具体例子将这一方法与传统回归分析方法相比,进一步说明了多层线性模型在分析具有层次结构数据时的优点。     

Psychological distress: A hierarchical factor model of the Multiple Affect Adjective Check List (MAACL)

Recent investigations of the structure of psychological distress have indicated that hierarchical models can accommodate both unitary and multifaceted conceptions of distress. The present study tested the hierarchical framework suggested by Zuckerman, Lubin, and Rinck (1983) for the Multiple Affect Adjective Check List (MAACL), a commonly used measure of psychological distress. One- and two-factor models were estimated using maximum-likelihood methods. Results indicated that the two-factor solution, with correlated positive and negative affect factors, provided a significantly better fit to the data than did the omnibus one-factor solution. These results provide further support for hierarchical models of distress.     

Sample size and bentler and Bonett's nonnormed fit index

Bentler and Bonett's nonnormed fit index is a widely used measure of goodness of fit for the analysis of covariance structures. This note shows that contrary to what has been claimed the nonnormed fit index is dependent on sample size. Specifically for a constant value of a fitting function, the nonnormed index is inversely related to sample size. A simple alternative fit measure is proposed that removes this dependency. In addition, it is shown that this new measure as well as the old nonnormed fit index can be applied to any fitting function that measures the deviation of the observed covariance matrix from the covariance matrix implied by the parameter estimates for a model.     

Latent variable modeling in heterogeneous populations

Common applications of latent variable analysis fail to recognize that data may be obtained from several populations with different sets of parameter values. This article describes the problem and gives an overview of methodology that can address heterogeneity. Artificial examples of mixtures are given, where if the mixture is not recognized, strongly distorted results occur. MIMIC structural modeling is shown to be a useful method for detecting and describing heterogeneity that cannot be handled in regular multiple-group analysis. Other useful methods instead take a random effects approach, describing heterogeneity in terms of random parameter variation across groups. These random effects models connect with emerging methodology for multilevel structural equation modeling of hierarchical data. Examples are drawn from educational achievement testing, psychopathology, and sociology of education. Estimation is carried out by the LISCOMP program.Presidential address delivered at the Psychometric Society meetings in Los Angeles, USA and Leuven, Belgium, July 1989. The research was supported by Grant No. SES-8821668 from the National Science Foundation and by Grant No. OERI-G-86-003 from the Office for Educational Research and Improvement, Department of Education. I thank Leigh Burstein, Mike Hollis, Linda Muthén, and Albert Satorra for helpful discussions and Tammy Tam, Jin-Wen Yang, Suk-Woo Kim, and Lynn Short for computational assistance. Designs were created by Arlette Collier, Rita Ling and Jennifer Edic-Bryant.     

Why Combine Logics?

Combining logics has become a rapidly expanding entreprise that is inspired mainly by concerns about modularity and the wish to join together tailor made logical tools into more powerful but still manageable ones. A natural question is whether it offers anything new over and above existing standard languages.By analysing a number of applications where combined logics arise, we argue that combined logics are a potentially valuable tool in applied logic, and that endorsements of standard languages often miss the point. Using the history of quantified modal logic as our main example, we also show that the use of combined structures and logics is a recurring theme in the analysis of existing logical systems.     

Linear structural equations with latent variables

An interdependent multivariate linear relations model based on manifest, measured variables as well as unmeasured and unmeasurable latent variables is developed. The latent variables include primary or residual common factors of any order as well as unique factors. The model has a simpler parametric structure than previous models, but it is designed to accommodate a wider range of applications via its structural equations, mean structure, covariance structure, and constraints on parameters. The parameters of the model may be estimated by gradient and quasi-Newton methods, or a Gauss-Newton algorithm that obtains least-squares, generalized least-squares, or maximum likelihood estimates. Large sample standard errors and goodness of fit tests are provided. The approach is illustrated by a test theory model and a longitudinal study of intelligence.This investigation was supported in part by a Research Scientist Development Award (KO2-DA00017) and a research grant (DA01070) from the U. S. Public Health Service.