Maximum likelihood estimation of the joint covariance matrix for sections of tests given to distinct samples with application to test equating

Consider an old testX consisting ofs sections and two new testsY andZ similar toX consisting ofp andq sections respectively. All subjects are given testX plus two variable sections from either testY orZ. Different pairings of variable sections are given to each subsample of subjects. We present a method of estimating the covariance matrix of the combined test (X ₁, ...,X _s ,Y ₁, ...,Y _p ,Z ₁, ...,Z _q ) and describe an application of these estimation techniques to linear, observed-score, test equating.The author is indebted to Paul W. Holland and Donald B. Rubin for their encouragement and many helpful comments and suggestions that contributed significantly to the development of this paper.This research was supported by the Program Statistics Research Project of the ETS Research Statistics Group.     

Parental divorce as a factor in children''s perception of human relationships: An analysis of human movement responses in the Rorschach test

The subjects were 108 Swedish children between 10 and 12 years old, who constituted a divorce and a non-divorce group of 27 girls and 27 boys each. Rorschach Tests were administered individually and human movement responses were analysed. Non-divorce children perceived more cooperative and fewer hostile interactions than the divorce children. Responses containing figures engaged in hostile interaction were most common among divorce girls, whereas the divorce boys had difficulties in perceiving any interaction whatsoever. The different effect of parental divorce on the ability of girls and boys to develop satisfactory social relationships is discussed.     

The second offspring of General Process Learning Theory: Overt behavior as the ambassador of the mind

Wasserman suggested in a recent book review that the study of intervening cognitive processes represents a current focus of interest in animal learning and that this has led to a revitalization of comparative psychology. An examination of the volume reviewed suggests that he may have overstated the case. Most of the authors to whom he refers expressed dissatisfaction with traditional stimulus-response associationism but few argued for the extreme (information processing) sort of cognitive approach described by Wasserman.     

Covariance structure analysis in several populations

This paper is concerned with the study of covariance structural models in several populations. Estimation theory of the parameters that are subject to general functional restraints is developed based on the generalized least squares approach. Asymptotic properties of the constrained estimator are studied; and asymptotic chi-square tests are presented to evaluate appropriate model comparisons. The method of multipliers and the standard reparametrization technique are discussed in obtaining the estimates. The methodology is demonstrated by a set of real data.Computer facilities were provided by the Computer Services Center, The Chinese University of Hong Kong. The authors are indebted to several anonymous reviewers for suggestions for improvement of this paper.     

On Herrnstein's equation and related forms

In 1970, Herrnstein proposed a simple equation to describe the relation between response and reinforcement rates on interval schedules. Its empirical basis is firm, but its theoretical foundation is still uncertain. Two approaches to the derivation of Herrnstein's equation are discussed. It can be derived as the equilibrium solution to a process model equivalent to familiar linear-operator learning models. Modifications of this approach yield competing power-function formulations. The equation can also be derived from the assumption that response strength is proportional to reinforcement rate, given that there is a ceiling on response rate. The proportional relation can, in turn, be derived from a threshold assumption equivalent to Shimp's “momentary maximizing”. This derivation implies that the two parameters of Herrnstein's equation should be correlated, and may explain its special utility in application to internal schedules.     

Two simple classes of mastery scores based on the beta-binomial model

Two simple classes of mastery scores which are suitable for hand calculations are presented for beta-binomial test score distributions combined with linear and cubic referral success. The models provide a simple way to explore the consequences of selecting an arbitrary mastery score. Such assessment would be useful whenever the test user is not willing to posta priori a loss ratio, but wishes to look at the various consequences before aiming at a particular score.     

Fitting cross-classification table data to models when observations are subject to classification error

Individuals are classified in a cross-classification table where two behavioral observations on each individual determine the classification. The problem is to test certain structural models assumed to underlie the cross-classified observations. A minimum chi-square test procedure is proposed.     

Stopping rules for multi-category computerized classification testing

Computerized classification testing (CCT) aims to classify persons into one of two or more possible categories to make decisions such as mastery/non-mastery or meet most/meet all/exceed. A defining feature of CCT is its stopping criterion: the test terminates when there is enough confidence to make a decision. There is abundant research on CCT with a single cut-off, and two common stopping criteria are the sequential probability ratio test (SPRT) statistic and the generalized likelihood ratio statistic (GLR). However, there is a relative scarcity of research extending the SPRT to the multi-hypothesis case for when there is more than one cut-off. In this paper, we propose a new multi-category GLR (mGLR) statistic as well as a stochastically curtailed version of the CCT with three or more categories. A simulation study was conducted to show that the mGLR statistic outperformed the existing stopping rules by generating shorter average test length without sacrificing classification accuracy. Results also revealed that the stochastically curtailed mGLR successfully increased test efficiency in certain testing conditions.     

Using a Fork as a Hairbrush: Investigating Dual Routes to Release from Functional Fixedness

Functional fixedness involves difficulty with conceptualizing creative object uses. When it obstructs problem‐solving, individuals must reframe their approach. We examined how different training techniques—chunk decomposition (i.e., considering an object’s basic parts and physical properties) and constraint relaxation (i.e., considering an object’s different functions)—might rely upon different routes to creative reframing. Additionally, we investigated how different forms of cognitive load interact with these dual routes. Participants learned one of three techniques. Chunk decomposition participants created object breakdown diagrams; constraint relaxation participants created object functions lists; and free association (control) participants wrote a word that they associated with each of several concrete nouns. After training, participants attempted to solve five functional fixedness problems. E1 investigated how increasing germane cognitive load via either direct or indirect prompting affected training transfer. Experiment 2 investigated how reducing extraneous cognitive load by providing no transfer instructions and using an eye‐closure strategy. Across both experiments, results supported differences in accuracy and response latency by training. However, chunk decomposition and constraint relaxation did not follow the same pattern, suggesting different mechanisms of the effect. We discuss possible applications to increase innovation in real‐world domains such as education, business, and engineering.