The Creativity Matrix: Spotlights and Blind Spots in Our Understanding of the Phenomenon

In this paper, we organize past and present theories and models of creativity by using a new conceptual framework—the creativity matrix—with the aim of highlighting the dimensions of creativity we know a lot about and those we tend to either ignore or find difficult to study. This matrix is formed by bringing together a developmental model of creativity (the 4 C's) and a structural one (the 5 A's). We start by briefly describing these two conceptual frameworks, and then, we proceed to exploring the matrix itself by describing how the 5 A's are dynamically organized at each “level” of the 4 C's. Importantly, our overview of the matrix is informed by existing models and concepts that address one of more of the C's and the A's. This gives us a unique opportunity to take stock of what has been studied so far and, toward the end, consider new avenues for the development of theory and research agendas within creativity studies.     

Typical delay determines waiting time on periodic-food schedules: Static and dynamic tests

Pigeons and other animals soon learn to wait (pause) after food delivery on periodic-food schedules before resuming the food-rewarded response. Under most conditions the steady-state duration of the average waiting time, t, is a linear function of the typical interfood interval. We describe three experiments designed to explore the limits of this process. In all experiments, t was associated with one key color and the subsequent food delay, T, with another. In the first experiment, we compared the relation between t (waiting time) and T (food delay) under two conditions: when T was held constant, and when T was an inverse function of t. The pigeons could maximize the rate of food delivery under the first condition by setting t to a consistently short value; optimal behavior under the second condition required a linear relation with unit slope between t and T. Despite this difference in optimal policy, the pigeons in both cases showed the same linear relation, with slope less than one, between t and T. This result was confirmed in a second parametric experiment that added a third condition, in which T + t was held constant. Linear waiting appears to be an obligatory rule for pigeons. In a third experiment we arranged for a multiplicative relation between t and T (positive feedback), and produced either very short or very long waiting times as predicted by a quasi-dynamic model in which waiting time is strongly determined by the just-preceding food delay.     

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.).     

Test theory without an answer key

A general model is presented for homogeneous, dichotomous items when the answer key is not known a priori. The model is structurally related to the two-class latent structure model with the roles of respondents and items interchanged. For very small sets of respondents, iterative maximum likelihood estimates of the parameters can be obtained by existing methods. For other situations, new estimation methods are developed and assessed with Monte Carlo data. The answer key can be accurately reconstructed with relatively small sets of respondents. The model is useful when a researcher wants to study objectively the knowledge possessed by members of a culturally coherent group that the researcher is not a member of.This research was supported by NSF Grant No. SES-8320173 to the authors. We gratefully acknowledge comments and suggestions from John Boyd, Tarow Indow, and Kathy Maher as well as the editor and several anonymous referees.     

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.     

Stimulus effects on concurrent performance in transition

Six experimentally naive pigeons were exposed to concurrent variable-interval variable-interval schedules in a three-key procedure in which food reinforcement followed pecks on the side keys and pecks on the center key served as changeover responses. In Phase 1, 3 birds were exposed to 20 combinations of five variable-interval values, with each variable-interval value consistently associated with a different color on the side keys. Another 3 pigeons were exposed to the same 20 conditions, but with a more standard procedure that used a nondifferential discriminative stimulus on the two side keys throughout all conditions. In Phase 2, the differential and nondifferential stimulus conditions were reversed for each pigeon. Each condition lasted for one 5-hr session and one subsequent 1-hr session. In the last 14 conditions of each phase, the presence of differential discriminative stimuli decreased the time necessary for differential responding to develop and increased the sensitivity of behavior to reinforcement distribution in the 1st hr of training; during the last hours of training in each condition, however, the effects of the differential discriminative stimuli could not be distinguished from the effects of reinforcement distribution per se. These results show the importance of studying transitions in behavior as well as final performance. They may also be relevant to discrepancies in the results of previous experiments that have used nonhuman and human subjects.     

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.     

Constructing the exact significance level for a person fit statistic

This paper uses an extension of the network algorithm originally introduced by Mehta and Patel to construct exact tail probabilities for testing the general hypothesis that item responses are distributed according to the Rasch model. By assuming that item difficulties are known, the algorithm is applicable to the statistical tests either given the maximum likelihood ability estimate or conditioned on the total score. A simulation study indicates that the network algorithm is an efficient tool for computing the significance level of a person fit statistic based on test lengths of 30 items or less.     

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.     

4-5年级学生的空间表征与几何能力的相关性研究

本研究是“学生空间能力和几何能力关系”研究的一部分,以小学4、5年级学生为被试(共117人),以空问表征能力测验和几何能力测验为测验工具,初步探讨了学生空间表征与几何能力的关系。对数据结果的分析表明:①就总成绩而言,五年级学生的空间表在成绩明显高于四年级学生的成绩,但并不是空间表征的所有方面都存在着显著的年级差异;②就空间测验的总成绩而言,无论是四、五年级分别考察还是总起来考察,空间成绩与几何成绩之间的相关显著,但就各个分项而言,并不是空间测验的各项都与几何测验成绩有显著相关;学生的几何成绩在一定程度上可通过回归方程:Y_i=0.5736X_i+0.7635加以预测。