Varieties of Linear Calculi

A uniform calculus for linear logic is presented. The calculus has the form of a natural deduction system in sequent calculus style with general introduction and elimination rules. General elimination rules are motivated through an inversion principle, the dual form of which gives the general introduction rules. By restricting all the rules to their single-succedent versions, a uniform calculus for intuitionistic linear logic is obtained. The calculus encompasses both natural deduction and sequent calculus that are obtained as special instances from the uniform calculus. Other instances give all the invertibilities and partial invertibilities for the sequent calculus rules of linear logic. The calculus is normalizing and satisfies the subformula property for normal derivations.     

Equivalent linear logistic test models

This paper is about the Linear Logistic Test Model (LLTM). We demonstrate that there are infinitely many equivalent ways to specify a model. An implication is that there may well be many ways to change the specification of a given LLTM and achieve the same improvement in model fit. To illustrate this phenomenon, we analyze a real data set using a Lagrange multiplier test for the specification of the model. This Lagrange multiplier test is similar to the modification index used in structural equation modeling.     

Testing the significance of the successive components in redundancy analysis

In this paper we study the interrelationships between two sets of data measured on the same subjects via redundancy analysis. We consider redundancy analysis from an inferential point of view. Under the hypothesis of multinormality, tests of significance are obtained for each successive redundancy component so that only the significant factors are retained for prediction purposes. An example illustrates the method. The authors would like to thank the Editor and the referees for their helpful comments. This research has been partly financed by NSERC (Canada).     

Typology and psychological effects of adolescents' interpersonal relationships in Taiwan

The present research explored Taiwanese adolescent students' interpersonal relationships and examined whether teachers' evaluations of these students' health and academic performances varied with the students' interpersonal relationship patterns. Data ( n  = 2310) were based on a panel study conducted by the Taiwan Youth Project in 2001 (eighth grade) and 2002 (ninth grade). Latent class models and hierarchical linear models were used to analyse the data. Adolescent students' interpersonal relationships were categorized as Multiple Contacts, Parents- and Peers-Close, Peers-Close, and Few Contacts. The research results showed that not only adolescents' self-reports of self-esteem and depressed mood but also teachers' evaluations of adolescents' health and academic performances varied with adolescents' interpersonal relationship patterns. An influence of teachers' character and work environment on their evaluations of students was found. Teachers who had more years of teaching and higher job satisfaction rated their students as having better health, and teachers who felt greater respect from their students reported that their students had better academic performance. The connection between adolescents' psychological well-being and the roles of parents, peers and teachers is also discussed.     

全息项目因素分析在心理学研究中的应用

文章首先指出了经典线性因素分析的种种局限;然后介绍了一种基于“被试—项目矩阵”而非仅仅协方差矩阵或相关矩阵的全息项目因素分析,该方法能克服经典线性因素分析的种种局限,在心理学研究中尤其是人格研究中有着其他因素分析方法不可替代的作用。     

Lambda Calculus and Intuitionistic Linear Logic

The introduction of Linear Logic extends the Curry-Howard Isomorphism to intensional aspects of the typed functional programming. In particular, every formula of Linear Logic tells whether the term it is a type for, can be either erased/duplicated or not, during a computation. So, Linear Logic can be seen as a model of a computational environment with an explicit control about the management of resources.This paper introduces a typed functional language ! and a categorical model for it.The terms of ! encode a version of natural deduction for Intuitionistic Linear Logic such that linear and non linear assumptions are managed multiplicatively and additively, respectively. Correspondingly, the terms of ! are built out of two disjoint sets of variables. Moreover, the -abstractions of ! bind variables and patterns. The use of two different kinds of variables and the patterns allow a very compact definition of the one-step operational semantics of !, unlike all other extensions of Curry-Howard Isomorphism to Intuitionistic Linear Logic. The language ! is Church-Rosser and enjoys both Strong Normalizability and Subject Reduction.The categorical model induces operational equivalences like, for example, a set of extensional equivalences.The paper presents also an untyped version of ! and a type assignment for it, using formulas of Linear Logic as types. The type assignment inherits from ! all the good computational properties and enjoys also the Principal-Type Property.     

Assessment and prediction in an ecological system: Application of the general linear model to the response-class concept

This study investigated the extent to which observed frequencies of covarying responses could be utilized in the prediction of classroom behavior. Five behavior categories were observed daily over a 12-week period in the regular classroom settings of four fifth-grade and two fourth-grade male students. For each subject, stepwise regression analyses were conducted to determine which behaviors accounted for the largest proportions of variance in a single response category. The proportions of variance explained in the behavior categories of the subjects ranged from 8.9 to 75.4%. Further, response categories serving as predictor variables, as well as the number of predictor variables entered into the equations, differed across subjects. These results are discussed in terms of their implications for behavioral assessment and treatment application.     

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.     

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.