A general model for the analysis of multilevel data

A general model is developed for the analysis of multivariate multilevel data structures. Special cases of the model include repeated measures designs, multiple matrix samples, multilevel latent variable models, multiple time series, and variance and covariance component models.We would like to acknowledge the helpful comments of Ruth Silver. We also wish to thank the referees for helping to clarify the paper. This work was partly carried out with research funds provided by the Economic and Social Research Council (U.K.).     

Canonical analysis of two convex polyhedral cones and applications

Canonical analysis of two convex polyhedral cones consists in looking for two vectors (one in each cone) whose square cosine is a maximum. This paper presents new results about the properties of the optimal solution to this problem, and also discusses in detail the convergence of an alternating least squares algorithm. The set of scalings of an ordinal variable is a convex polyhedral cone, which thus plays an important role in optimal scaling methods for the analysis of ordinal data. Monotone analysis of variance, and correspondence analysis subject to an ordinal constraint on one of the factors are both canonical analyses of a convex polyhedral cone and a subspace. Optimal multiple regression of a dependent ordinal variable on a set of independent ordinal variables is a canonical analysis of two convex polyhedral cones as long as the signs of the regression coefficients are given. We discuss these three situations and illustrate them by examples.     

Hierarchical classes: Model and data analysis

A discrete, categorical model and a corresponding data-analysis method are presented for two-way two-mode (objects × attributes) data arrays with 0, 1 entries. The model contains the following two basic components: a set-theoretical formulation of the relations among objects and attributes; a Boolean decomposition of the matrix. The set-theoretical formulation defines a subset of the possible decompositions as consistent with it. A general method for graphically representing the set-theoretical decomposition is described. The data-analysis algorithm, dubbed HICLAS, aims at recovering the underlying structure in a data matrix by minimizing the discrepancies between the data and the recovered structure. HICLAS is evaluated with a simulation study and two empirical applications.This research was supported in part by a grant from the Belgian NSF (NFWO) to Paul De Boeck and in part by NSF Grant BNS-83-01027 to Seymour Rosenberg. We thank Iven Van Mechelen for clarifying several aspects of the Boolean algebraic formulation of the model and Phipps Arabie for his comments on an earlier draft.     

Rhetoric and “doing philosophy”

By drawing new distinctions labelled appeal and response to replace traditional rhetorical modes of written discourse, the essay sketches a new perspective about what philosophers are doing rhetorically in doing philosophy. To think of philosophers as simply engaged in argument is an oversimplification and a distortion of what philosophers do. Crucial to doing philosophy are four activities: (1) definition and redefinition of problems and issues that form both the focus of the canonical historical literature of philosophy and what goes on in contemporary philosophy as a discipline, (2) the development and use of formal languages and technical vocabularies to abbreviate and label complexity and to disambiguate and precise distinctions necessary to deal with problems and issues, (3) the development and exploration of argumentative appeals for acceptance or refutation of answers to questions raised by the philosophical problematic, and (4) the development and exploration of explanatory responses to questions raised by the problematic. In so far as these four activities are driven and sanctioned by the current, self-defining philosophical problematic, contemporary philosophy as a body of knowledge is historical, cumulative, and marked by progress, and the doing of philosophy is fundamentally the making of written appeals and responses about its problematic.     

Choice with delayed and probabilistic reinforcers: effects of variability, time between trials, and conditioned reinforcers.

In a discrete-trials procedure with pigeons, a response on a green key led to a 4-s delay (during which green houselights were lit) and then a reinforcer might or might not be delivered. A response on a red key led to a delay of adjustable duration (during which red houselights were lit) and then a certain reinforcer. The delay was adjusted so as to estimate an indifference point--a duration for which the two alternatives were equally preferred. Once the green key was chosen, a subject had to continue to respond on the green key until a reinforcer was delivered. Each response on the green key, plus the 4-s delay that followed every response, was called one "link" of the green-key schedule. Subjects showed much greater preference for the green key when the number of links before reinforcement was variable (averaging four) than when it was fixed (always exactly four). These findings are consistent with the view that probabilistic reinforcers are analogous to reinforcers delivered after variable delays. When successive links were separated by 4-s or 8-s "interlink intervals" with white houselights, preference for the probabilistic alternative decreased somewhat for 2 subjects but was unaffected for the other 2 subjects. When the interlink intervals had the same green houselights that were present during the 4-s delays, preference for the green key decreased substantially for all subjects. These results provided mixed support for the view that preference for a probabilistic reinforcer is inversely related to the duration of conditioned reinforcers that precede the delivery of food.     

Computational behavior dynamics: an alternative description of Nevin (1969).

A computational processing behavior-dynamic model was instantiated in the form of a computer program that "behaved" on the task developed by Nevin (1969). In this classic discrete-trials experiment, the relative frequency of choosing a response alternative matched the relative frequency of reinforcement for that alternative, the local structure of responding was opposite that predicted by momentary maximizing (i.e., the probability of a changeover decreased with run length), and absolute and relative response rates varied independently. The behavior-dynamic model developed here qualitatively reproduced these three results (but not in quantitative and specific detail) and also generated some interesting, as-yet-untested predictions about performance in Nevin's task. The model was discussed as an example of a stochastic behavior-dynamic alternative to algebraic behavior theory.     

Fixed-ratio pausing: Joint effects of past reinforcer magnitude and stimuli correlated with upcoming magnitude

Pigeons responded on fixed-ratio schedules ending in small or large reinforcers (grain presentations of different duration) interspersed within each session. In mixed-schedule conditions, the response key was lit with a single color throughout the session, and pausing was directly related to the past reinforcer (longer pauses after large reinforcers than after small ones). In multiple-schedule conditions, different colors accompanied the ratios ending in small and large reinforcers, and pausing was affected by the upcoming reinforcer as well as the past one. Pauses were shorter before large reinforcers than before small ones, but they continued to be longer after large reinforcers than after small ones. The influence of the past reinforcer was modulated by the magnitude of the upcoming reinforcer; in the presence of the stimulus before the small reinforcer, the effect of the past reinforcer was enhanced relative to its effect in the stimulus before the large reinforcer. These results show that pausing between ratios is jointly determined by two competing factors: past conditions of reinforcement and stimuli correlated with upcoming conditions.     

Examining differential item functioning due to item difficulty and alternative attractiveness

A method for analyzing test item responses is proposed to examine differential item functioning (DIF) in multiple-choice items through a combination of the usual notion of DIF, for correct/incorrect responses and information about DIF contained in each of the alternatives. The proposed method uses incomplete latent class models to examine whether DIF is caused by the attractiveness of the alternatives, difficulty of the item, or both. DIF with respect to either known or unknown subgroups can be tested by a likelihood ratio test that is asymptotically distributed as a chi-square random variable.     

影响频度记忆的几个因素

本研究通过两个实验探讨了刺激呈现频度、刺激的形式及其性质、加工深度、操作难度、意向性诸因素对频度记忆的影响,结果表明频度编码并不是一个独立、自动的加工系统,对其它识记过程有影响的因素同时也能改变被试的频度估计水平;意向的作用主要体现在当识记任务有一定难度且又缺乏有效的回忆线索时,能够在有限的范围内提高频度估计的水平;记忆痕迹的深度和广度对于频度信息的提取来说是两个彼此关联的线索。此外,本文还就频度记忆领域几个主要理论观点作了简要评述。     

量词肯定句和否定句的理解

本研究试图探索人们对舍有“所有”、“每一个”、“有一些”等量词的肯定句、否定句和双重否定句的理解。要求成人被试尽快判断呈现在计算机屏幕上的句子和哪一幅图画的内容相符。结果表明,影响反应时的因素为(1)句子的表层结构和它的底层意义的一致程度;(2)句子的意义和从图画中得出的命题的一致程度;(3)句子中使用的量词。结果还表明,否定句的判断时间不一定全都比肯定句的长。