On the optimality of the simultaneous redundancy transformations

The objective of this paper is to introduce and motivate additional properties and interpretations for the redundancy variables. It is shown that these variables can be derived by application of certain invariance arguments and without reference to the index of redundancy. In addition, an optimality property for the variables is presented which is important whenever one restricts attention in a study to a subset of the redundancy variables. This optimality property pertains to the subset rather than to the individual variables.This paper is based in part on the author's doctoral dissertation, Department of Statistics, Princeton, University. Research was conducted under the supervision of Lawrence S. Mayer.     

Minimum rank and minimum trace of covariance matrices

This paper considers some mathematical aspects of minimum trace factor analysis (MTFA). The uniqueness of an optimal point of MTFA is proved and necessary and sufficient conditions for a point x to be optimal are established. Finally, some results about the connection between MTFA and the classical minimum rank factor analysis will be presented.     

A note on partitioned determinants

A formula for the determinant of a partitioned matrix, possibly with singular submatrices, is derived and applied to some psychometric and numerical problems.     

The use of latent class models for assessing prerequisite relations and transference among traits

This paper presents a strategy for pairwise assessment which may be used to evaluate the nature of both prerequisite and transference relations existing among a set of traits. This strategy is appropriate for use both within a confirmatory context, in which an attempt is made to establish the validity of some specified set of relations among traits, as well as within an exploratory context, in which a search is made for unconjectured prerequisite and transference relations existing between pairs of traits. Both uses of this strategy are based on a variety of latent class models which are representative of various possible relational states existing between pairs of traits. Thus, the nature of trait relations may be investigated through the use of statistical assessments of both absolute and relative fit attained by these models. An application is presented to exemplify how this strategy may be used within the exploratory context.The author is obliged to Clifford Clogg, C. Mitchell, Dayton, and William Schafer for helpful comments made regarding a previous draft of this paper as well as to Mary Papageorgiou who provided access to the data which was considered in this study.     

Ordered binary trees constructed through an application of Kendall's tau

A procedure is described for orienting the nodes of a binary tree to maximize the Kendall rank order correlation (tau) between node order and a given external criterion. The procedure is computationally efficient and is based on application of an ordered set of node tests.     

Canonical analysis of longitudinal and repeated measures data with stationary weights

When measuring the same variables on different occasions, two procedures for canonical analysis with stationary compositing weights are developed. The first, SUMCOV, maximizes the sum of the covariances of the canonical variates subject to norming constraints. The second, COLLIN, maximizes the largest root of the covariances of the canonical variates subject to norming constraints. A characterization theorem establishes a model building approach. Both methods are extended to allow for Cohort Sequential Designs. Finally a numerical illustration utilizing Nesselroade and Baltes data is presented.The authors wish to thank John Nesselroade for permitting us to use the data whose analysis we present.     

The Headache Symptom Questionnaire: Discriminant classificatory ability and headache syndromes suggested by a factor analysis

A brief Headache Symptom Questionnaire was administered to 129 chronic headache Sufferers. The questionnaire accurately classified 68.42% of headache subjects in their proper diagnostic category, comparable to, but statistically less accurate than, the 86.4% agreement between expert headache diagnosticians using clinical interviews. Results of a factor analysis of the Headache Symptom Questionnaire lend support for their being two commonly accepted global headache categories—vascular/migraine and muscle contraction—and one headache dimension concerned with duration of headache pain. Combined migraine-muscle contraction headache was found to be related more to migraine than to muscle contraction headache, and cluster headaches emerged as a separate clinical entity, not loading positively on any factor and loading negatively on all three.This research was supported in part by Grant NS-15235 from the National Institute of Neurological and Communicative Disorders and Stroke.     

Standardized classroom management program: Social validation and replication studies in Utah and Oregon

A comprehensive validation study was conducted of the Program for Academic Survival Skills (PASS), a consultant-based, teacher-mediated program for student classroom behavior. The study addressed questions related to: (a) brief consultant training, (b) subsequent teacher training by consultants using PASS manuals, (c) contrasts between PASS experimental teachers and students and equivalent controls on measures of teacher management skills, student classroom behavior, teacher ratings of student problem behaviors, and academic achievement, (d) reported satisfaction of participants, and (e) replication of effects across two separate school sites. Results indicated that in both sites significant effects were noted in favor of the PASS experimental group for (a) teacher approval, (b) student appropriate classroom behavior, and (c) four categories of student inappropriate behavior. Program satisfaction ratings of students, teachers, and consultants were uniformly positive, and continued use of the program was reported a year later. Discussion focused upon issues of cost-effectiveness, differential site effects, and the relationship between appropriate classroom behavior and academic achievement.     

Peer tutoring among elementary students: educational benefits to the tutor

To determine whether tutoring might be academically beneficial to the tutor, this study investigated the acquisition of spelling words by three elementary students in a peer tutoring program. The experimental design allowed a simultaneous comparison of each child's gain in performance on comparable word lists on which the child tutored another child, was tutored by another child, or neither gave nor received tutoring. The children's spelling improved nearly an equivalent amount on those words on which they tutored another child as on the words on which they were tutored; no such change was noted on the words on which they neither gave nor received tutoring. These findings, that peer tutoring is profitable for the tutor as well as the tutee, provide a basis for recommending peer tutoring as one method of individualizing education.     

Community applications of instructional technology: teaching writers of instructional packages

A community education program, to develop a variety of performance competencies in large numbers of neighborhood residents, requires a technology for preparing learning units administerable by community members themselves. The effects of a writing manual, designed to teach nonprofessionals to prepare such instructional packages, were analyzed in two experiments. Experiment I employed a multiple-baseline design across three university student trainees. The results showed that appropriate program writing increased by 75% after completion of the manual. The results of Experiment II, with two low-income neighborhood residents serving as trainees, showed that packages produced by trained writers resulted in a greater increase in skill activities than sets of training stimuli produced by untrained writers.