A functional equation analysis of two learning models

One-absorbing barrier random walks arising from Luce's nonlinear beta model for learning and a linear commuting-operator model (called the alpha model) are considered. Functional equations for various statistics are derived from the branching processes defined by the two models. Solutions to general functional equations, satisfied by statistics of the alpha and beta models, are obtained. The methods presented have application to other learning models.Abstracted from portions of the author's doctoral dissertation, University of Pennsylvania, June 1960. The author is indebted to Robert R. Bush, his dissertation supervisor for the valuable help and encouragement received from him and to R. Duncan Luce for many helpful discussions and for partial support from an NSF grant.The author is grateful to J. G. Brainerd, S. Gorn, and C. N. Weygandt of the Moore School, and N. F. Finkelstein, D. Parkhill and A. A. Wolf of General Dynamics for their encouragement.     

Latent partition analysis

Latent partition analysis has been formulated to study the relationships between two or more partitions of the same set of items. The major structural hypothesis is that a latent partition underlies the manifest partitions; that is, it is assumed that each item belongs to a latent category and that the manifest categories are derived by dividing and combining the latent categories. We have found that by examining manifest categories it is possible to reconstruct information about the latent partition and about its relation to the manifest partitions.The research reported herein was originally supported through the U. S. O. E. Cooperative Research Project 5-1005-2-12-1, directed by Donald M. Miller, at the Instructional Research Laboratory, University of Wisconsin. Further work has been supported by the National Science Foundation Grant No. GS-1025 at The University of Chicago. The author wishes to acknowledge the invaluable assistance of Richard G. Wolfe in the final statement of the theory and the assistance of Robert M. Pruzek in certain early formulations.     

Sex role orientation and social skill: A naturalistic assessment of assertion and conversational skill

This study evaluated the relationship between sex role orientation and social skill, improving upon previous research by utilizing a more naturalistic role-play assessment, and by assessing both assertion and conversational skills. Fifty-nine female psychology students were classified as masculine, feminine, androgynous, or undifferentiated based on the PRF-ANDRO scale. These subjects interacted with a confederate who engaged them in a standardized conversation including requests to borrow psychology class notes. The masculine, feminine, and androgynous groups displayed similar levels of assertion and conversational skill, even though masculine subjects rated themselves as more skillful and had fewer negative thoughts associated with being assertive than feminine subjects. Correlational analyses among continuous sex role and behavioral measures revealed that both masculinity and femininity scores were positively correlated with overall conversational skill. These results are interpreted in light of methodological difficulties in previous research, and in light of recent evidence that both masculine and feminine capabilities contribute to social competence in certain behavioral domains.This research was supported in part by a Baylor University sabbatical grant awarded to the first author. Both authors wish to thank Jack Baty for statistical consultation, Ross Williams for serving as the confederate, and Elaine McFarlane for serving as a rater.     

Some models for individual-group comparisons and group behavior

In problem solving situations, it has been suggested the superiority of groups over individuals is due simply to the fact that groups consist of several individuals. In this paper, the Lorge and Solomon [1955] approach to such situations is reexamined using the method of maximum likelihood. Extensions to trichotomous response situations are also presented, and the resulting models are applied to data gathered by Staub [1970]. The partitioning of the likelihood ratio goodness-of-fit statistic is then discussed in order that the effects of additional variables on the response variate can be assessed. Finally, the small sample behavior of the likelihood ratio statistic is examined.This research was supported in part by Research Contract No. NSF GS-2818 from the Division of Social Sciences of the National Science Foundation to the Department of Statistics, The University of Chicago.Now at the University of Minnesota.     

The effect of difficulty and chance success on item-test correlation and on test reliability

An equation is derived for predicting the effect of chance success, relative to item difficulty, on item-test correlation. The values predicted by this equation and by equations derived by Guilford and Carroll for predicting the effect of chance success on item difficulty and test reliability are compared with empirical values in an experiment which used identical test items in multiple-choice and answer-only form.Condensation of a dissertation presented in partial fulfillment of the requirements for the Ph.D. degree to the University of Chicago. Grateful acknowledgment is made to Professor Harold Gulliksen for his guidance as thesis advisor and to Professor L. L. Thurstone and Dr. D. W. Fiske of the University of Chicago who served as members of the thesis committee. The author is also indebted to Professor S. S. Wilks for review of the derivations and development of statistical tests used in the thesis, to Dr. L. R Tucker for technical advice, and to Dr. W. G. Mollenkopf for critical comments on the derivations and interpretations. The writer expresses appreciation to the Educational Testing Service for making available its technical facilities, and to the University of Chicago for the flexible administrative arrangement which made this thesis possible.     

An analysis of adolescent suicidal ideation

The purpose of this study was to investigate the predominant variables (i.e., hopelessness, depression, anxiety, negative life stress, family social climate, coping behaviors) theorized to be etiologically significant in the production of adolescent suicidal ideation. Subjects were 433 normal, midwestern high school students. ANOVAs revealed significant sex differences in level of suicidal ideation over the past year. Therefore, separate path analyses were conducted for males and females. Various statistical tests revealed that assumptions of path analysis were upheld by the male and female models that emerged. For males, levels of depression and family cohesiveness were found to have direct effects on the criterion. For females, levels of depression and trait anxiety were found to have direct effects on the criterion. The remaining significant variables in both models only indirectly affected the criterion. This paper is based on the dissertation research completed by the first author. Portions of the paper were presented at the 98th Annual Convention of the American Psychological Association (Boston, MA), August 1990. This study was funded in part by a University of South Dakota General Research Fund grant awarded to the second author.     

Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm

Maximum likelihood estimation of item parameters in the marginal distribution, integrating over the distribution of ability, becomes practical when computing procedures based on an EM algorithm are used. By characterizing the ability distribution empirically, arbitrary assumptions about its form are avoided. The Em procedure is shown to apply to general item-response models lacking simple sufficient statistics for ability. This includes models with more than one latent dimension.Supported in part by NSF grant BNS 7912417 to the University of Chicago and by SSRC (UK) grant HR6132 to the University of Lancaster.We are indebted to Mark Reiser and Robert Gibbons for computer programming. David Thissen clarified a number of points in an earlier draft.     

Perceptions of date and stranger rape: A difference in sex role expectations and rape-supportive beliefs

The sex role expectations and rape-supportive beliefs which are differentially applied to date and stranger rape were assessed. A sample of 62 college females and 33 males read one of three rape scenarios which varied according to the victim-perpetrator relationship (steady dating partners/acquaintances on a first date/strangers). Then participants rated the extent to which several sex role expectations and rape-supportive attitudes were applicable to the assault. MANOVAS and univariate ANOVAS showed that females' and males' perceptions of date rape, more than stranger rape, incorporated sex role expectations and that rape-supportive beliefs, primarily of males, were stronger in relation to steady date than first date or stranger rape. These findings are discussed in the context of the sex role analysis of rape.This research was supported by the University of Connecticut Research Foundation Grant #1171-000-22-00215-35-760. The author thanks Laurin Hafner for his help with the data analysis.     

Turn-taking and speech act patterns in the discourse of senile dementia of the Alzheimer's type patients

Conversational discourse patterns of 11 normal elderly and 11 senile dementia of the Alzheimer's type (SDAT) patients engaged in dyadic interaction with an examiner were examined. Differences in word usage, turn taking, and speech act production were investigated both for the two-subject groups and for the examiner's conversations with each group. Compensatory shifts in discourse by participants are identified. For the subject, differences were shown on words per turn with SDAT subjects speaking in shorter turns and in nonverbal responses with SDAT subjects using this strategy more frequently. Speech act categories of Requestives and Assertives also differed with SDAT subjects using more Requestives and fewer Assertives. The SDAT subjects had significantly more occurrences of unintelligible utterances. For the examiner, words per turn differed with the examiner using shorter turns with SDAT subjects. No differences were shown in the examiner's patterns of speech act usage, nonverbal responses, or intelligibility. In general, these results indicate significant discourse differences in the words per turn level for all participants and speech act levels of conversation for SDAT subjects. They also indicate generally maintained interaction patterns by speakers so that the discourse genre of conversation is sustained. The pattern of compensatory shifts in discourse suggests retained flexibility in the communication system of early and mid stage SDAT patients.     

Sex differences in nonverbal communication

An experiment was conducted to determine the relationship between sex-role attitudes, affiliation, and dominance and nonverbal communication styles in men and women in same- and opposite-sex dyads. Women were found to elicit more warmth and men more anxiety from their partners. Evidence was found for a possible monitoring mechanism through which women adjust their nonverbal communications to fit the male in the interaction. Liberalism in sex-role attitudes was found to correlate with nonverbal warmth in men. The nonverbal presentations of men and women in the microprocesses of dyadic interaction were found to relate significantly to the macrostructure of societal sex roles.This research was supported by NSF Grant GS36814. The author wishes to express her special thanks to Harmon Hosch, Vivian Shayne, David Fineman, and Lee Braff for their help in the experiment and data analysis. An abbreviated version of this paper was presented at the meeting of the American Sociological Association, San Francisco, August 1975.     

A Linguistic Comparison of Letters of Recommendation for Male and Female Chemistry and Biochemistry Job Applicants

Letters of recommendation are central to the hiring process. However, gender stereotypes could bias how recommenders describe female compared to male applicants. In the current study, text analysis software was used to examine 886 letters of recommendation written on behalf of 235 male and 42 female applicants for either a chemistry or biochemistry faculty position at a large U.S. research university. Results revealed more similarities than differences in letters written for male and female candidates. However, recommenders used significantly more standout adjectives to describe male as compared to female candidates. Letters containing more standout words also included more ability words and fewer grindstone words. Research is needed to explore how differences in language use affect perceivers’ evaluations of female candidates. This research was supported by National Institute of Mental Health Grant #1R01MH071749 to the first author and a University of Arizona grant from the College of Science Millennium Report Oversight Committee awarded to the third author.     

Attachment Styles and Reactions to Nonverbal Involvement Change in Romantic Dyads Patterns of Reciprocity and Compensation

Attachment-theory principles suggest that those with different attachment styles will react to nonverbal involvement change in a manner consistent with their approach/avoidance orientations and mental working models of self and others. It was hypothesized that preoccupieds initially reciprocate increases in involvement, but compensate for decreases, whereas dismissives initially compensate for increases in involvement, but reciprocate decreases. A second hypothesis predicted that over time interactants reciprocate both increases and decreases in nonverbal involvement. Partners in enduring romantic relationships participated in two separate conversations. Between conversations, one member of each dyad was enlisted as a confederate who increased or decreased nonverbal immediacy and positive affect in the second conversation. Results indicated that, regardless of attachment style, targets reciprocated confederate behavior in the increase-involvement condition and displayed behavior indicative of both compensation and reciprocity in the decrease-involvement condition. However, preoccupieds showed the strongest pattern of reciprocating increases in involvement and compensating for decreases in involvement. Results also demonstrated a pull toward reciprocity over time. Findings are interpreted in light of the bidimensional model of distancing and interaction adaptation theory, with results most supportive of the latter theory.     

Sex roles and nonverbal communication skills

As a step toward understanding sex differences in nonverbal decoding and encoding abilities, the hypothesis that sex-role variables are related to these communication abilities was tested. An analysis was undertaken of 11 studies on the relationship of encoding and decoding abilities to sex roles, including several masculinity and femininity scales, a measure of attitudes toward women, and a questionnaire on sex roles in the home. Although the relationships of the masculinity and femininity measures to decoding were generally weak, more masculine people tended to be better decoders. Patterns also emerged showing that the magnitude of the correlations varied with age group, sex, sex-role scale, and channel of communication. In addition, among women, those who were more liberated according to several indices were better decoders, at least of a woman stimulus person. Differences between the sexes in encoding and decoding abilities were unaffected by partialling out the masculinity and femininity measures. A hypothesis concerning the adaptive uses of nonverbal sensitivity is advanced, as well as a hypothesis concerning overall sex differences in nonverbal communication skills.Part of this research was conducted while the authors held National Science Foundation Graduate Fellowships, and was supported by a National Science Foundation Dissertation Award to the first author and by a grant from the Biomedical Research Support Program, National Institutes of Health, to The Johns Hopkins University. This paper could not have been prepared without the generosity of several colleagues and students who made their unpublished results available. These people are (alphabetically): Bella M. DePaulo, Karen I. Fischer, Judith Harackiewicz, Leonard A. Kusnitz, Carol J. Mills, James G. Simmons, Ann L. Weber, and Miron Zuckerman. In addition, Bert F. Green, Jr., Bella M. DePaulo, and Marylee C. Taylor provided many appreciated suggestions and criticisms on an earlier draft.     

Working memory in skilled and less skilled readers

This study assessed skilled and less skilled readers' working memory performance. Fifty skilled and less skilled readers at two age levels were presented with sentence span and concurrent memory tasks. The span task results indicated that working memory differences exist between reading groups. The concurrent task revealed performance deficits for less skilled readers across verbal and nonverbal conditions, suggesting a central processing deficiency. Age differences were isolated to skilled readers. It was concluded that less skilled readers' working memory deficiencies were pervasive in the sense that they involve deficiencies in memory components related to central executive processing.The authors are indebted to the University Laboratory School, University of Northern Colorado, and Greeley School District 6 for providing subjects for this study. Special appreciation is given to Dr. Neil Henderson, Sue Swaim, and Karen Cash for their administrative assistance. This study was supported by a grant from the U. S. Office of Special Education and Rehabilitative Services to the first author.     

Reading Their Book of Faith: North American Muslims and Their Interpretations of the Qur'an in the Post 9/11 Era

Abstract :  This article seeks to provide an overarching view of the North American Muslim conversation about interpreting the Qur'an in a post 9/11 world. While most Western critiques of Islam focus on reading the texts of Islam, the author argues that one must also listen to the contemporary intra-Muslim conversation about their own text, in order to faithfully understand the Muslim perspective. In this conversation, the author provides evidence for a plurality of social-political views among Muslims and notes that the post 9/11 North American context is alive and well with such faith conversations.     

Argument structure, argument content, and cognitive change in children's peer interaction

In this experimental study, the author examined whether children's conversations play a role in the processes of influence between peers. Children, aged 8 to 10 years, who were at different levels of moral development participated. The conversations of 120 children were coded and analyzed in terms of argument structure and content. Results indicated that the differences in structure between boys' and girls' arguments are stylistic and do not influence conversation outcomes. The children's use of the structural features of conversations suggested that when a more advanced position is adopted, the arguments themselves appear to inspire cognitive change. However, when a less advanced position is adopted, the children who influence their peers invoke a particular and insistent conversational style. Results are discussed in terms of transmission and constructivist accounts of the role of social interaction in cognitive development.     

Argument Structure,Argument Content,and Cognitive Change in Children's Peer Interaction

In this experimental study, the author examined whether children's conversations play a role in the processes of influence between peers. Children, aged 8 to 10 years, who were at different levels of moral development participated. The conversations of 120 children were coded and analyzed in terms of argument structure and content. Results indicated that the differences in structure between boys' and girls' arguments are stylistic and do not influence conversation outcomes. The children's use of the structural features of conversations suggested that when a more advanced position is adopted, the arguments themselves appear to inspire cognitive change. However, when a less advanced position is adopted, the children who influence their peers invoke a particular and insistent conversational style. Results are discussed in terms of transmission and constructivist accounts of the role of social interaction in cognitive development.     

PERCEPTIONS OF INFORMATION SEQUENCING IN RELATIONSHIP DEVELOPMENT1

Randomly selected adult residents (N = 204) of a Chicago suburb sorted 150 statements along a time continuum according to their estimate of when each statement would first be made during a two-hour conversation between two strangers. Analyses were conducted on the items employing the following variables: self-esteem, birth order, number of close friends, economic status, desired number of friends, age, sex, and education. Only the latter four variables produced significant differences.     

Is there a sex difference in lateralization for processing of humorous materials?

Leventhal and Cupchik (1976) reported an unpublished finding that women rate items funnier with left-ear input, while men give higher ratings with right-ear input. This finding, widely cited in the literature, has sometimes been quoted as evidence for a biological basis for sex differences in humor appreciation, in particular, and in information processing, in general. However, the effect has apparently never been replicated. In this study, 120 subjects rated the funniness of 35 monaurally-presented comedy excerpts, with half of the subjects receiving input over each ear. Although the experiment had several features intended to maximize replicability, the reported sex difference was not found. While failure to find an effect in a particular case is not definitive, it is troubling to see such widespread citation of an unpublished and apparently unreplicated effect and to see rather extreme conclusions based on it receive serious consideration in the literature.This research was supported by a University College of Cape Breton research grant and by a job internship grant awarded by Enterprise Cape Breton Corporation. I am very grateful to Wayne Baillie, Manager, UCCB Electronic Learning Center, for his assistance in conducting this experiment. An earlier version of this paper was presented at the annual meeting of the Canadian Psychological Association, Ottawa, June, 1990.