A general structural equation model with dichotomous,ordered categorical,and continuous latent variable indicators

A structural equation model is proposed with a generalized measurement part, allowing for dichotomous and ordered categorical variables (indicators) in addition to continuous ones. A computationally feasible three-stage estimator is proposed for any combination of observed variable types. This approach provides large-sample chi-square tests of fit and standard errors of estimates for situations not previously covered. Two multiple-indicator modeling examples are given. One is a simultaneous analysis of two groups with a structural equation model underlying skewed Likert variables. The second is a longitudinal model with a structural model for multivariate probit regressions.This research was supported by Grant No. 81-IJ-CX-0015 from the National Institute of Justice, by Grant No. DA 01070 from the U.S. Public Health Service, and by Grant No. SES-8312583 from the National Science Foundation. I thank Julie Honig for drawing the figures. Requests for reprints should be sent to Bengt Muthén, Graduate School of Education, University of California, Los Angeles, California 90024.     

Political Extremism and a Generalized Propensity to Discriminate Among Values

Research exploring the psychological differences between people supporting extreme versus moderate ideologies is growing. However, this research has rarely examined the domain of values. Here, we explore this domain by assessing the possibility that political extremists discriminate more among values compared to moderates, namely, that extremists exhibit strong commitment toward some values at the expense of other values, whereas moderates would acknowledge a multiplicity of values as equally important. First, we propose a model positing that a value discriminability parameter captures a general tendency to discriminate among values. Second, we test empirically the prediction that, compared to moderates, political extremists exhibit a higher discriminability parameter. This prediction is supported by four studies (including one based on the European Social Survey where representative samples from 29 European countries are examined) where participants reported their ideological orientation and rated the importance of basic human values (we focused on basic values because these transcend the political domain, thus highlighting general effects). Specifically, in all studies we observed a positive correlation between political extremism and residual variability in ratings, a hallmark of a higher discriminability parameter. These findings highlight the value domain as critical to understanding differences between political extremists and moderates.     

BELIEF VS. COMMITMENT, VALIDITY VS. VALUE: A RESPONSE TO WARD GOODENOUGH

Abstract. This paper is on Ward Goodenough's recent article (27: 3), suggesting that his points can be clarified by reiterating the distinction between the realms of meaning and relevance. Religion's "truth" is in the form of its ualue; the "proof" which it requires is uindication; and the resulting "faith" must be understood as commitment.     

The substitutability of reinforcers

Substitutability is a construct borrowed from microeconomics that describes a continuum of possible interactions among the reinforcers in a given situation. Highly substitutable reinforcers, which occupy one end of the continuum, are readily traded for each other due to their functional similarity. Complementary reinforcers, at the other end of the continuum, tend to be consumed jointly in fairly rigid proportion, and therefore cannot be traded for one another except to achieve that proportion. At the center of the continuum are reinforcers that are independent with respect to each other; consumption of one has no influence on consumption of another. Psychological research and analyses in terms of substitutability employ standard operant conditioning paradigms in which humans and nonhumans choose between alternative reinforcers. The range of reinforcer interactions found in these studies is more readily accommodated and predicted when behavior-analytic models of choice consider issues of substitutability. New insights are gained into such areas as eating and drinking, electrical brain stimulation, temporal separation of choice alternatives, behavior therapy, drug use, and addictions. Moreover, the generalized matching law (Baum, 1974) gains greater explanatory power and comprehensiveness when measures of substitutability are included.     

Generalized Rough Sets (Preclusivity Fuzzy-Intuitionistic (BZ) Lattices)

The standard Pawlak approach to rough set theory, as an approximation space consisting of a universe U and an equivalence (indiscernibility) relation R U x U, can be equivalently described by the induced preclusivity ("discernibility") relation U x U \ R, which is irreflexive and symmetric.We generalize the notion of approximation space as a pair consisting of a universe U and a discernibility or preclusivity (irreflexive and symmetric) relation, not necessarily induced from an equivalence relation. In this case the "elementary" sets are not mutually disjoint, but all the theory of generalized rough sets can be developed in analogy with the standard Pawlak approach. On the power set of the universe, the algebraic structure of the quasi fuzzy-intuitionistic "classical" (BZ) lattice is introduced and the sets of all "closed" and of all "open" definable sets with the associated complete (in general nondistributive) ortholattice structures are singled out.The rough approximation of any fixed subset of the universe is the pair consisting of the best "open" approximation from the bottom and the best "closed" approximation from the top. The properties of this generalized rough approximation mapping are studied in the context of quasi-BZ lattice structures of "closed-open" ordered pairs (the "algebraic logic" of generalized rough set theory), comparing the results with the standard Pawlak approach. A particular weak form of rough representation is also studied.     

Contrast and reallocation of extraneous reinforcers as a function of component duration and baseline rate of reinforcement

Four pigeons responded on multiple schedules arranged on a “main” key in a two-key experimental chamber. A constant schedule component was alternated with another component that was varied over conditions. On an extra response key, conjoint schedules of reinforcement that operated in both components were arranged concurrently with the multiple schedule on the main key. On the main key, changes in reinforcement rate in the varied component were inversely related to changes in response rates in the constant component (behavioral contrast). On the extra key, some reinforcers were reallocated between components, depending on the schedules in effect on the main key in the varied component. In the varied component, the obtained rates of reinforcement on the extra key were inversely related to main-key reinforcement rate. In the constant component, extra-key reinforcer rates were positively related to main-key reinforcer rates obtained in the varied component, and were not a function of response rates on the extra key. In two comparisons, the rate at which components alternated and the value of the main-key schedule in the constant component were varied. Consistent with earlier work, long components reduced the extent of contrast. Reductions in contrast as a function of component duration were accompanied by similar reductions in the extent of reinforcer reallocation on the extra key. In the second comparison, lowering the rate of reinforcement in the constant component increased the rate at which extra-key reinforcers were obtained, reduced the extent of reinforcer reallocation, and reduced contrast. Overall, the results are consistent with the suggestion that some contrast effects are due to the changes in extraneous reinforcement during the constant component, and that manipulations of component duration, and manipulations of the rate of reinforcement in the constant component, affect contrast because they influence the extent of extraneous reinforcer real-location.     

教师评分用语词义赋值特征的分析

本研究运用模糊统计试验方法对教师的六组定性的评分用语词 (符号 )进行了经验赋值。参加赋值的是 2 66名小学教师。结果表明 ,六组评分用语词 (符号 )都是模糊概念 ,其中每种评分方式中处于最高等级的词 (符号 )的模糊度最小 ,处于中间等级的词 (符号 )的模糊度居中 ,处于最低等级的词 (符号 )的模糊度最大。词 (符号 )义的模糊度与评价的把握度呈现负相关 ,即词 (符号 )义越具体 ,模糊度越小 ,赋值的把握度就越大 ;反之 ,词义越含混 ,模糊度越大 ,赋值的把握度就越小。教师对各种评分用语词 (符号 )的赋值受百分制的“及格—不及格”的划分的影响 ,受评分方式中等级数目的影响 ,即增加评分等级会减少评分用语词 (符号 )的模糊度 ,增加赋值的把握度 ,还受评分用语词 (符号 )本身数量特征的影响。在各种评分方式中 ,评语词 (符号 )在心理量表上的距离是不等的。本研究的结果对教育评价的实践具有一定的参考价值。     

Decompositions and biplots in three-way correspondence analysis

In this paper correspondence analysis for three-way contingency tables is presented using three-way generalisations of the singular value decomposition. It is shown that in combination with Lancaster's (1951) additive decomposition of interactions in three-way tables, a detailed analysis is possible of the deviations from independence. Finally, biplots are shown to produce powerful graphical representations of the results from three-way correspondence analyses. An example from child development is used to illustrate the theoretical developments.     

On the discriminability of stimulus duration.

The performance of pigeons trained to detect differences in the duration of stimuli was analysed using a matching model of signal detection. Two white stimuli, S1 and S2, differing in duration, were arranged with equal probability on the center key of a three-key chamber. S1 was systematically varied from 5 seconds to 25 seconds while S2 remained constant at 30 seconds. On completion of the center-key stimulus, a peck on the center key turned on the two red side keys. A left-key response was "correct" when S1 had been in effect on the center key and a right-key response was "correct" on S2 trials. A correct response produced a 3-second magazine light accompanied intermittently by food. Incorrect responses produced 3-second blackouts. Detection performance was measured under two procedures. In the first, the obtained reinforcement ratio was uncontrolled by allowing the number of food reinforcements obtained for correct left- and right-key responses to vary as the stimuli were changed. In the second procedure, the presentation of food reinforcement was controlled by holding the obtained reinforcement ratio constant. Discriminability changed as a function of stimulus differences under both procedures. No such trend was found in response bias.