Constrained least squares estimators of oblique common factors

An expression is given for weighted least squares estimators of oblique common factors, constrained to have the same covariance matrix as the factors they estimate. It is shown that if as in exploratory factor analysis, the common factors are obtained by oblique transformation from the Lawley-Rao basis, the constrained estimators are given by the same transformation. Finally a proof of uniqueness is given.The research reported in this paper was partly supported by Natural Sciences and Engineering Research Council Grant No. A6346.     

A comparison between the development of the appearance-reality distinction in the People's Republic of China and the United States

A study of the appearance-reality distinction in American 3- to 5-year-olds was replicated with Chinese 3- to 5-year-olds. The error patterns, age changes, and absolute levels of performance were similar in the two samples. It was speculated that the acquisition of this distinction may be a universal, possibly age-linked development that is probably fueled by experiences with appearance-reality discrepancies that are available in all cultures.     

Feedback interventions and driving speed: A parametric and comparative analysis

Five experiments were conducted to assess the effects of several variables on the efficacy of feedback in reducing driving speed. Experiment 1 systematically varied the criterion used to define speeding, and results showed that the use of a lenient criterion (20 km/hr over the speed limit), which allowed for the posting of high percentages of drivers not speeding, was more effective in reducing speeding than the use of a stringent criterion (10 km/hr over the speed limit). In Experiment 2 an analysis revealed that posting feedback reduced speeding on a limited access highway and the effects persisted to some degree up to 6 km. Experiments 3 and 4 compared the effectiveness of an unmanned parked police vehicle (Experiment 3) and a police air patrol speeding program (Experiment 4) with the feedback sign and determined whether the presence of either of these enforcement variables could potentiate the efficacy of the sign. The results of both experiments demonstrated that although the two enforcement programs initially produced larger effects than the feedback sign, the magnitude of their effect attenuated over time. Experiment 5 compared the effectiveness of a traditional enforcement program with a warning program which included handing out a flier providing feedback on the number and types of accidents occuring on the road during the past year. This experiment demonstrated that the warning program produced a marked reduction in speeding and the traditional enforcement program did not. Furthermore, the warning program and a feedback sign together produced an even greater reduction in speeding than either alone.     

CONSERVATION IN COMMUNITY SCHOOL CHILDREN FROM THE MADANG,SOUTHERN HIGHLANDS,AND NORTH SOLOMONS PROVINCES OF PAPUA NEW GUINEA

Three hundred and eight primary level boys and girls from the Madang, North Solomons, and Southern Highlands Provinces of Papua New Guinea were tested for conservation of number, length, quantity, and area. School grade, and age were related to performance in some cases, though sex had little effect. There were significant differences between the language-culture groups tested on three of the four conservation tasks. Since there was little consistency of performance over the four tasks, it was suggested that explanations of the variations of cognitive performance found within Papua New Guinea, and between Papua New Guinean groups and others may need to give attention to specific characteristics of each group's environment.     

A generalization of comparative probability on finite sets

Let ? be a binary relation on a finite algebra $\text{A}$ of events A, B,…, where A ? B is interpreted as “A is more probable than B.” Conventional subjective probability is concerned with the existence of a probability measure P on $\text{A}$ that agrees with ? in the sense that A ? B ? P(A) > P(B). Because evidence suggests that some people's comparative probability judgments do not admit an agreeing probability measure, this paper explores a more flexible scheme for representing ? numerically. The new representation has A ? B ? p(A, B) > 0, where p is a monotonic and normalized skew-symmetric function on $\text{A}$ × $\text{A}$ that replaces P's additivity by a conditional additivity property. Conditional additivity says that $\text{p(A ? B, C) + p(?, C) = p(A, C) + p(B, C)}$ whenever A and B are disjoint. The paper examines consequences of this representation, presents examples of ? that it accommodates but which violate the conventional representation, formulates axioms for ? on $\text{A}$ that are necessary and sufficient for the representation, and discusses specializations in which p in separable in its arguments.     

Discrete dynamic choice: An extension of the choice models of thurstone and luce

The present paper deals with the extension of two well-known static discrete choice theories to the dynamic situation in which individuals make choices at several points in (continuous) time. A dynamic version of Luce's Axiom, “independence from irrelevant alternatives”, is proposed and some of its implications are derived. In the static case Yellott (J. Math. Psych. 1977, 15, 109–146) and others have demonstrated that an independent random utility model generated from the extreme value distribution exp(?e^?ax?b) becomes equivalent to Luce's Axiom. Yellott also introduced an axiom called “invariance under uniform expansions of the choice set”, and he proved that within the class of random utility models with independent identically distributed utilities (apart from a location shift) this axiom is equivalent to Luce's Axiom. These results are extended to the dynamic situation and it is shown that if the utility processes are expressed by so-called extremal processes the corresponding choice model is Markovian. A nonstationary generalization is proposed which is a substantial interest in applications where the parameters of the choice process are influenced by previous choice experience or by time-varying exogenous variables. In particular, it is demonstrated that the nonstationary model is Markovian if and only if the joint choice probabilities at two points in time have a particular form. Thus, the paper provides a rationale for applying a specific class of Markov models as the point of departure when modelling mobility processes that involve individual discrete decisions over time.     

Some deterministic models of concept identification

It is shown that deterministic models can compete effectively with stochastic models in summarizing concept identification behavior. Three groups of deterministic models are examined. Examination of individual learners' trial by trial behavior in a concept experiment shows: (1) One person exhibited behavior consistent with a Hypothesis Permutation (HP) model despite being a nonlearner who showed no evidence of improvement over a period of 24 trials. However, when all 50 persons studied in each of two treatment groups were examined, only 22 members of one group and 10 of the other showed no inconsistencies with deterministic local consistency assumptions. (2) Certain deterministic computer programs could find at least one satisfactory order for predicting all responses by 18 of the 22 consistent solvers and 6 of the 10 consistent solvers, respectively, in the two groups just mentioned. For these 24 persons, then, a less restrictive deterministic model is adequate than for the others. (3) Those 38 original members of the first treatment group who met a stringent learning criterion were compared with respect to predictions generated by stochastic and mathematized deterministic models. One deterministic model (RSS-U 9-state) is in some respects the best of the models examined, but this success is a partial reflection of estimating eight parameters from the data.     

An axiomatization of the ratio/difference representation

If ≥_r and ≥_d are two quaternary relations on an arbitrary set A, a ratio/difference representation for ≥_r and ≥_d is defined to be a function f that represents ≥_r as an ordering of numerical ratios and ≥_d as an ordering of numerical differences. Krantz, Luce, Suppes and Tversky (1971, Foundations of Measurement. New York, Academic Press) proposed an axiomatization of the ratio/difference representation, but their axiomatization contains an error. After describing a counterexample to their axiomatization, Theorem 1 of the present article shows that it actually implies a weaker result: if ≥_r and ≥_d are two quaternary retations satisfying the axiomatization proposed by Krantz et al. (1971), and if ≥_r′ and ≥_d′ are the relations that are inverse to ≥_r and ≥_d, respectively, then either there exists a ratio/difference representation for ≥_r and ≥_d, or there exists a ratio/difference representation for ≥_r′ and ≥_d′, but not both. Theorem 2 identifies a new condition which, when added to the axioms of Krantz et al. (1971), yields the existence of a ratio/difference representation for relations ≥_r and ≥_d.