On the estimation of parameters in latent structure analysis

In this note, we describe the iterative procedure introduced earlier by Goodman to calculate the maximum likelihood estimates of the parameters in latent structure analysis, and we provide here a simple and direct proof of the fact that the parameter estimates obtained with the iterative procedure cannot lie outside the allowed interval. Formann recently stated that Goodman's algorithm can yield parameter estimates that lie outside the allowed interval, and we prove in the present note that Formann's contention is incorrect.This research was supported in part by Research Contract No. NSF SOC 76-80389 from the Division of the Social Sciences of the National Science Foundation. The author is indebted to C. C. Clogg for helpful comments and for the numerical results reported here (see, e.g., Table 1).     

Continuous and discrete latent structure models for item response data

Relations are examined between latent trait and latent class models for item response data. Conditions are given for the two-latent class and two-parameter normal ogive models to agree, and relations between their item parameters are presented. Generalizationss are then made to continuous models with more than one latent trait and discrete models with more than two latent classes, and methods are presented for relating latent class models to factor models for dichotomized variables. Results are illustrated using data from the Law School Admission Test, previously analyzed by several authors.     

Contingency and choice: The implications of matching theory for classroom instruction

This paper describes a mathematical account of behavior known as matching theory. Matching theory evolved out of basic operant research and assumes that individuals can engage in a variety of behaviors at any moment, but they choose one to the exclusion of others. According to the matching equation, choices in behavior match the relative amount of reinforcement provided for each alternative. Although the principles of matching theory have proven useful in developing novel treatment strategies, few data exist validating the matching equation in natural human environments. Recent applications of matching theory to children's classroom behavior are described, and the implications of matching theory for classroom management and effective teaching are discussed.     

Ecobehavioral analysis in the classroom: Review and implications

A rapidly developing area within applied behavior analysis that has implications for classroom instruction and behavior management is ecobehavioral analysis. Ecobehavioral analysis adds to behavior analysis the assessment of situational or contextual factors, such as classroom physical arrangements, instructional materials used by students, and teacher's behavior. Its eventual importance and contribution to behavior analysis and to education, however, has yet to be realized. In fact, it is difficult to find adequate accounts of exactly what ecobehavioral analysis entails (Morris & Midgley, 1990). To date, it has led to a number of interesting contributions. These include the development and validation of specific classroom instructional procedures, the development of a number of approaches to the reduction of challenging behaviors, an improved understanding of the components of effective instruction including the identification of instructional risk factors within regular and special education, as well as providing a better understanding of how the quality of implementation functions as a mediating variable for student outcomes. In this paper, we discuss the theory and principles that support ecobehavioral analysis, review research literature concerning its use in educational settings, describe emerging applications by school personnel (e.g., teachers, school psychologists), and examine a number of future research directions and their implications.     

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.     

The latent structure of occupations

Triads of occupations were given to 1300 high-school pupils of both sexes in order to find the affinities of the occupations and the values they used to arrive at the affinities. The values used to perceive occupations come from the subject; nevertheless they could be categorized into a scheme of 20 different values, with the residue category containing less than 1% of the answers. In accordance with previous research in this field, an almost universal structure of occupations was found. The following variables had no influence on the choice of occupational affinities: age, trend of study, SES, father's occupation, mother's occupation, vocational maturity, and preferred occupation. Only the pupils of one school were significantly different in affiliating the occupations in the triads. Furthermore, girls perceive the world of occupations more uniformly than boys.Underlying this universal structure of occupations there exists a latent structure, specific to each individual, which explains why the world of occupations is seen in the way it is. This latent structure of occupations is influenced by the individual's specific background.     

A nonparametric approach for assessing latent trait unidimensionality

Assuming a nonparametric family of item response theory models, a theory-based procedure for testing the hypothesis of unidimensionality of the latent space is proposed. The asymptotic distribution of the test statistic is derived assuming unidimensionality, thereby establishing an asymptotically valid statistical test of the unidimensionality of the latent trait. Based upon a new notion of dimensionality, the test is shown to have asymptotic power 1. A 6300 trial Monte Carlo study using published item parameter estimates of widely used standardized tests indicates conservative adherence to the nominal level of significance and statistical power averaging 81 out of 100 rejections for examinee sample sizes and psychological test lengths often incurred in practice.The referees' comments were remarkably detailed and greatly enhanced the writeup and sensitized the author to certain pertinent issues. Discussions with Fritz Drasgow, Lloyd Humphreys, Dennis Jennings, Brian Junker, Robert Linn, Ratna Nandakumar, and Robin Shealy were also very useful.This research was supported by the Office of Naval Research under grant N00014-84-K-0186; NR 150-533, and by the National Science Foundation under grant DMS 85-03321.     

An analysis of daily report cards and parent-managed privileges in the improvement of adolescents' classroom performance

A daily report-card system, involving home privileges administered by parents, was developed for use with "problem" junior-high students. In Experiment I, when home privileges and parent praise were contingent on improved school conduct, classwork, daily grades, and teacher satisfaction, the school performance of three students improved considerably. In Experiment II, a similar report-card system was employed with two additional students, except only parent praise was contingent on improved school performance. Under these conditions, one of the students did not bring the report card home, and class performance did not improve until contingent home privileges were added. The school performance of the second student improved with the card and praise alone. However, there appeared to be a slow decline of classwork performance over time. For Experiment III, an instructional manual, describing the report-card program, was written for school guidance counsellors. Two guidance counsellors read the program, used it with one student each, and found that the school performance of both students improved. These results suggest that the daily report-card program with home consequences administered by parents can improve the school performance of, and teacher satisfaction about, students having considerable difficulty in school.     

The complement of a point subset in a projective space and a Grassmann space

In a projective space we fix some set of points, a horizon, and investigate the complement of that horizon. We prove, under some assumptions on the size of lines, that the ambient projective space, together with its horizon, both can be recovered in that complement. Then we apply this result to show something similar for Grassmann spaces.     

Use of normative peer data as a standard for evaluating classroom treatment effects

This study illustrated the use of normative behavioral observation data as a standard for evaluating the practicality of treatment effects produced in other settings. Three groups of eight subjects each, displaying relatively low proportions of appropriate classroom behavior when compared with regular classroom peers, were selected for treatment within an experimental classroom setting. The three groups were exposed to intervention procedures designed to reinforce either direct academic performance and/or facilitative nonacademic classroom responses. The treatment was effective in changing levels of appropriate behavior (1) above baseline levels in the experimental classroom, and (2) to within normal peer-defined limits when reintegrated into the regular classroom. Further, the data reflect successful maintenance of these effects for a seven- to 12-week follow-up period. Several applications of a normative model for evaluating treatment, generalization, and maintenance effects were presented and discussed.     

Randomization-based inference about latent variables from complex samples

Standard procedures for drawing inferences from complex samples do not apply when the variable of interest cannot be observed directly, but must be inferred from the values of secondary random variables that depend on stochastically. Examples are proficiency variables in item response models and class memberships in latent class models. Rubin's multiple imputation techniques yield approximations of sample statistics that would have been obtained, had been observable, and associated variance estimates that account for uncertainty due to both the sampling of respondents and the latent nature of. The approach is illustrated with data from the National Assessment for Educational Progress.This research was supported by Grant No. NIE-G-83-0011 of the Office for Educational Research and Improvement, Center for Education Statistics, and Contract No. N00014-88-K-0304, R&T 4421552 from the Cognitive Sciences Program, Cognitive and Neural Sciences Division, Office of Naval Research. It does not necessarily reflect the views of either agency. I am grateful to R. Darrell Bock for calling my attention to the applicability of multiple imputation to the assessment setting; to Albert Beaton and Eugene Johnson for enlightening discussions on the topic; and to Henry Braun, Ben King, Debra Kline, Gary Phillips, Paul Rosenbaum, Don Rubin, John Tukey, Ming-Mei Wang, Kentaro Yamamoto, Rebecca Zwick, and two anonymous reviewers for comments on earlier drafts. Example 4 is based on the analysis of the 1984 National Assessment for Educational Progress reading survey, carried out at Educational Testing Service through the tireless efforts of too many people to mention by name, under the direction of Albert Beaton, Director of NAEP Data Analyses. David Freund, Bruce Kaplan, and Jennifer Nelson conducted additional analyses of the 1984 and 1988 data for the example.     

A multi-element analysis of the effect of teacher aides in an "open"-style classroom

Open classrooms with few rules, individualized instruction, and informal class organization present new problems for the application of behavior principles. The effects of three types of teacher aides on student achievement and on-task behavior were studied. Each was compared with a standard no-aide condition. Subjects were 54 third graders in two "open"-style classrooms. The three types of aide, helping adult, disciplinary adult, and helping fifth-grade aide, were compared in a multi-element design with a no-aide control. The helping-adult aide significantly affected the academic output of the class, when compared with the no-aide condition. All aide conditions produced more academic work and on-task behavior than did the standard no-aide condition.     

分类精确性指数Entropy在潜剖面分析中的表现:一项蒙特卡罗模拟研究

本研究通过蒙特卡洛模拟考查了分类精确性指数Entropy及其变式受样本量、潜类别数目、类别距离和指标个数及其组合的影响情况。研究结果表明:(1)尽管Entropy值与分类精确性高相关,但其值随类别数、样本量和指标数的变化而变化,很难确定唯一的临界值;(2)其他条件不变的情况下,样本量越大,Entropy的值越小,分类精确性越差;(3)类别距离对分类精确性的影响具有跨样本量和跨类别数的一致性;(4)小样本(N=50~100)的情况下,指标数越多,Entropy的结果越好;(5)在各种条件下Entropy对分类错误率比其它变式更灵敏。     

The views of migrant and non migrant students on cultural diversity in the Greek classroom

The aim of the present study is to explore the views of migrant and non migrant students living in Greece on cultural diversity in the classroom. It focuses on students of both the dominant (i.e. Greek) and nondominant (i.e. migrant) groups and investigates their views in comparison to one another. Data were collected in the context of a pilot action research program aiming at the empowerment of in-service teachers so that they actively support the migrant students’ integration into the regular classroom. Two hundred and seventy students participated in the study. Data were selected through three scales especially constructed for the purposes of the present study which explored (a) migrant and non migrant students’ views on cultural diversity in the classroom, (b) their expectations from the implementation of the above mentioned program, and (c) the reasons they consider important their participation in it. The results reveal the contradictions and the conflicting views of older students of the non migrant group and point to the necessity for intervention programs that will take into consideration not only the educational needs of students of diverse cultural backgrounds but also the psychological needs of all students of both the dominant and the nondominant groups.

The Structure of Negative Self-Statements in Children and Adolescents: A Confirmatory Factor-Analytic Approach

The aim of this study was to examine the nature and organization of a range of negative self-statements in children and adolescents, using a structural equations/confirmatory factor-analytic approach. A community sample of 978 children aged 7-16 years completed a questionnaire about the frequency with which they experienced a broad range of negative automatic thoughts. The outcome of comparative modeling provided strongest support for a model in which 4 distinct cognitive factors were all related to a single higher order factor. The 4 lower order factors related to cognitions on social threat, physical threat, personal failure, and hostility. The pattern of results was consistent across age and gender. Results were consistent with assumptions of cognitive specificity models of psychopathology, on the latent structure of automatic thoughts in children and adolescents.     

The structure of negative emotions in adolescents

This study examined the structure of negative emotions in a sample of nonclinical adolescents, using an approach that exclusively relied on child self-report. A large sample of adolescents (N = 968) completed self-report questionnaires measuring symptoms of fear, anxiety, and depression. Confirmatory factor analysis provided support for the notion that fear, anxiety, and depression are distinct yet correlated components of negative emotions. This result is in agreement with recent empirical findings and current theoretical notions on the structure of negative emotions in children and should be taken as an encouragement for researchers to develop more specific measures for assessing fear, anxiety, and depression in children.     

Classroom problem behavior and teacher-child relationships in kindergarten: The moderating role of classroom climate

Young children with problem behavior in the classroom are at risk for developing more conflictual and less close relationships with their teachers. Two studies in kindergarten (N = 3798; N = 237) shed light on some aspects of classroom climate that can moderate this risk for relational problems. Results showed problematic classroom compositions, in terms of high average levels of internalizing or externalizing behavior, to exacerbate the risk for teachers to form more conflictual relationships with children showing externalizing behavior. Additionally, observed emotional support of teachers was found to be protective for the relational functioning of children at risk due to maladjusted behavior. Specifically, with emotionally supportive teachers, children who expose internalizing or externalizing behavior are no longer at risk for developing less close or more conflictual relationships with their teachers respectively. Practical implications and limitations of the studies are reported and suggestions are made for future research.