F tests for the absolute invariance of dominance and composition scales

Significance tests are developed for evaluating the absolute invariance of the dominance and composition scales presented in a previous paper [Bechtel, 1967]. These tests derive from the multivariate normality of the estimated scale values—this multinormality stemming from that of the observations upon which these estimated scale parameters are based. The scales compared by means of the present techniques will typically be constructed under distinct experimental conditions, which may take the concrete form of treatments, occasions, individuals, or groups. Thus the present tests possess a wide range of applicability including various experimental designs in which scale configuration is the dependent variable. Illustrative data are used in statistically comparing the scale structures of two different individuals.This research was supported in part by National Institutes of Health Grant MH-04439-06. The author would like to express his appreciation to Fred C. Andrews of the University of Oregon and J. E. Keith Smith of the University of Michigan for their helpful comments concerning aspects of this work. Computing assistance was obtained from the Health Sciences Computing Facility, UCLA, sponsored by NIH Grant FR-3.     

A dual scaling analysis for paired compositions

A paired composition is a response (upon a dependent variable) to the ordered pair <j, k> of stimuli, treatments, etc. The present paper develops an alternative analysis for the paired compositions layout previously treated by Bechtel's [1967] scaling model. The alternative model relaxes the previous one by including row and column scales that provide an expression of bias foreach pair of objects. The parameter estimation and hypothesis testing procedures for this model are illustrated by means of a small group analysis, which represents a new approach to pairwise sociometrics and personality assessment.This study was supported by Grant Nos. MH 12972, MH 10822, and MH 15506 from the National Institute of Mental Health, U. S. Public Health Service. Computing assistance was obtained from the Health Sciences Computing Facility, UCLA, sponsored by N.I.H. special research resources Grant RR-3.The motivation of this effort has been enhanced by Gerald Patterson and his associates, who have kindly provided the illustrative data at the end of the paper. The author would also like to express his appreciation to Wei-Ching Chang of the Oregon Research Institute and the University of Oregon for his substantive contributions to the paper, and to William Chaplin and Mark Layman of the Oregon Research Institute for the programming of the data analytic method. FORTRAN IV program listings for this analysis are available upon request to the author.     

A covariance analysis of multiple paired comparisons

In the method of multiple paired comparisons the dominance of objectj over objectk is observed uponp attributes. The present paper develops a covariance analysis for these paired comparisons in terms of a linear model which includes scale, bias, and interaction effects, along withs covariants upon which the comparisons are presumably dependent. The covariance model gives rise to adjusted parameter estimates and hypothesis tests for the residual pairwise layout from which the effects of thes covariants have been removed. These estimation and testing procedures are illustrated with an analysis of political judgment data, and their relevance to the general problem of residual scaling is discussed.This research was supported by National Institute of Mental Health grants MH 12972 and MH 15506. The author would like to express his appreciation to Jerry Solomon and Wei-Ching Chang of the Oregon Research Institute for the data analysis reported at the end of the paper. Computing assistance was obtained from the Health Sciences Computing Facility, UCLA, sponsored by N.I.H. Grant FR-3.     

A theory of appropriate statistics

A formal theory of appropriateness for statistical operations is presented which incorporates features of Stevens' theory of appropriate statistics and Suppes' theory of empirical meaningfulness. It is proposed that a statistic be regarded as appropriate relative to statements made about it in case the truths of these statements are invariant under permissible transformations of the measurement scale. It is argued that the use of inappropriate statistics leads to the formulation of statements which are either semantically meaning-less or empirically nonsignificant.This research was supported in part by each of the following grants: National Science Foundation Grant GS-333 to the University of Oregon; National Science Foundation Grant to the Institute of Human Learning, University of California, Berkeley; and National Institute of Mental Health Grant MH-08055-01 (under the direction of Ernest W. Adams), also to the Institute of Human Learning. Work on this project was carried out in part during Robert F. Fagot's tenure as Public Health Service Special Fellow (No. MSP-15800) at the University of California, Berkeley, 1962-63; and during Richard E. Robinson's tenure as National Science Foundation Science Faculty Fellow at Stanford University, 1962–63.     

Analysis of clustered data in community psychology: With an example from a worksite smoking cessation project

Although it is common in community psychology research to have data at both the community, or cluster, and individual level, the analysis of such clustered data often presents difficulties for many researchers. Since the individuals within the cluster cannot be assumed to be independent, the use of many traditional statistical techniques that assumes independence of observations is problematic. Further, there is often interest in assessing the degree of dependence in the data resulting from the clustering of individuals within communities. In this paper, a random-effects regression model is described for analysis of clustered data. Unlike ordinary regression analysis of clustered data, random-effects regression models do not assume that each observation is independent, but do assume data within clusters are dependent to some degree. The degree of this dependency is estimated along with estimates of the usual model parameters, thus adjusting these effects for the dependency resulting from the clustering of the data. Models are described for both continuous and dichotomous outcome variables, and available statistical software for these models is discussed. An analysis of a data set where individuals are clustered within firms is used to illustrate fetatures of random-effects regression analysis, relative to both individual-level analysis which ignores the clustering of the data, and cluster-level analysis which aggregates the individual data. Preparation of this article was supported by National Heart, Lung, and Blood Institute Grant R18 HL42987-01A1, National Institutes of Mental Health Grant MH44826-01A2, and University of Illinois at Chicago Prevention Research Center Developmental Project CDC Grant R48/CCR505025.     

The influence of communality,factor strength,and loading size on the sampling characteristics of factor loadings

A Monte Carlo approach is employed in determining whether or not certain variables produce systematic effects on the sampling variability of individual factor loadings. A number of sample correlation matrices were generated from a specified population, factored, and transformed to a least-squares fit to the population values. Influences of factor strength, communality and loading size are discussed in relation to the statistics summarizing the results of the above procedures. Influences producing biased estimators of the population values are also discussed.This study was supported in part by NSF Grant GB 4230. Computing assistance was obtained from the Western Data Processing Center and Health Sciences Computing Facility, UCLA, sponsored by NIH Grant FR-3.     

Sex-role attitudes as predictors of contraceptive use among unmarried university students

Through a review of existing theory and research a set of propositions explaining contraceptive behavior among unmarried young women was developed. The paper tests the propositions with survey research data drawn from a stratified random sample of male and female students at a large Midwestern university. Findings suggest that nontraditional sex-role-related attitudes in conjunction with an internal locus of control orientation are predictive of effective contraception for women respondents. Neither variable alone or jointly explained contraceptive behavior of men respondents.Revised version of a paper presented at the annual meeting of the National Council on Family Relations, Salt Lake City, August 20–23, 1975. The research upon which this paper is based was performed pursuant to National Institute of Mental Health Grant No. RO3 MH26526-01. The author wishes to acknowledge the Bowling Green State University Faculty Research Committee and the Department of Sociology for their assistance in the early stages of this study.     

Generalizability of scores influenced by multiple sources of variance

Generalizability theory concerns the adequacy with which a universe score can be inferred from a set of observations. In this paper the theory is applied to a universe in which observations are classifiable according to two independent variable aspects of the measuring procedure. Several types of universe scores are developed and the variance components ascertained for each type. The composition of expected observed-score variance and the adequacy of inference to a particular type of universe score is a function of the procedure used in gathering data. A generalizability study provides estimates of variance components which can be used in designing an efficient procedure for a particular decision purpose.This study was conducted under Grant M-1839 from the National Institute of Mental Health while the authors were on the staff of the University of Illinois. Dr. Rajaratnam shared responsibility for the technical report of July, 1961 on which this paper is based. The present revision was made subsequent to her death in 1963. The present addresses of the other authors are: Goldine C. Gleser, Department of Psychiatry, Central Clinic, Cincinatti, 29, Ohio; Lee J. Cronbach, School of Education, Stanford University.     

Estimating the standard errors of rotated factor loadings by jackknifing

The jackknife by groups and modifications of the jackknife by groups are used to estimate standard errors of rotated factor loadings for selected populations in common factor model maximum likelihood factor analysis. Simulations are performed in whicht-statistics based upon these jackknife estimates of the standard errors are computed. The validity of thet-statistics and their associated confidence intervals is assessed. Methods are given through which the computational efficiency of the jackknife may be greatly enhanced in the factor analysis model.Computing assistance was obtained from the Health Sciences Computing Facility, UCLA, sponsored by NIH Special Research Resources Grant RR-3.The author wishes to thank his doctoral committee co-chairmen, Drs James W. Frane and Robert I. Jennrich, UCLA, for their contributions to this research.     

Estimation for structural equation models with missing data

A direct method in handling incomplete data in general covariance structural models is investigated. Asymptotic statistical properties of the generalized least squares method are developed. It is shown that this approach has very close relationships with the maximum likelihood approach. Iterative procedures for obtaining the generalized least squares estimates, the maximum likelihood estimates, as well as their standard error estimates are derived. Computer programs for the confirmatory factor analysis model are implemented. A longitudinal type data set is used as an example to illustrate the results.This research was supported in part by Research Grant DAD1070 from the U.S. Public Health Service. The author is indebted to anonymous reviewers for some very valuable suggestions. Computer funding is provided by the Computer Services Centre, The Chinese University of Hong Kong.     

A scalar product model for the multidimensional scaling of choice

A multidimensional scaling analysis is presented for replicated layouts of pairwise choice responses. In most applications the replicates will represent individuals who respond to all pairs in some set of objects. The replicates and the objects are scaled in a joint space by means of an inner product model which assigns weights to each of the dimensions of the space. Least squares estimates of the replicates' and objects' coordinates, and of unscalability parameters, are obtained through a manipulation of the error sum of squares for fitting the model. The solution involves the reduction of a three-way least squares problem to two subproblems, one trivial and the other solvable by classical least squares matrix factorization. The analytic technique is illustrated with political preference data and is contrasted with multidimensional unfolding in the domain of preferential choice.The present work was initiated at Oregon Research Institute under National Institute of Mental Health Grant MH 12972. It was reformulated and completed while the first author was a Visiting Research Fellow at Educational Testing Service.Presently at the Department of Mathematics, University of Toronto.     

Videotape modeling for preschool children with low levels of social interaction and low peer involvement in play

This research evaluated a videotape modeling intervention for six preschool children who showed low levels of social involvement with peers in natural free-play settings. Observations across 14 weeks gave frequency and topographic data on social interactions and assessment of social involvement in play using the Parten Scale. Simultaneous observation of three children gave data on two comparison children for each target child. A multiple-baseline across-subjects design was used with two data analysis strategies. Averaged group data showed statistically significant increases in both interactions and social involvement in play. Visual analysis of the single-subject data, however, indicated no clear treatment outcome for two children, while four subjects showed a variable increase in social responding after viewing the modeling videotape. Session-by-session variability was a feature of the interaction rate measure for comparison children and for posttreatment phase data for target subjects.This research was supported by Grant No. 62-262-98 from the Mental Health Foundation of New Zealand and by University of Otago Research Committee Grant No. 37-877. Grateful acknowledgment is extended to Dan McKerracher and Ted Glynn for valued comments at various stages of the research. Appreciation is extended to the teachers and children of the Dunedin Free Kindergartens who participated in the study.     

Testing a unidimensional,qualitative unfolding model for attitudinal or developmental data

Assuming that subject responses rank order stimuli by preference, statistical methods are presented for testing the hypothesis that responses conform to a unidimensional, qualitative unfolding model and to an a priori stimulus ordering. The model postulates that persons and stimulus variables are ordered along a single continuum and that subjects most prefer stimuli nearest their own position. The underlying continuum need not form an interval scale of the stimulus attribute. The general assumptions of the test for the unfolding model make it suitable for the analysis of structure in attitude responses, preference data, and developmental stage data.This research was supported by a grant from the U.S. Public Health Service (Grant No. 1-R01-MH27861-01) to the University of Minnesota. I wish to thank Sanford Weisberg for his helpful suggestions. I also wish to thank Karen Kitchener and Patricia King for letting me use their data.     

Matrix analysis of identifiability of some finite markov models

Methods developed by Bernbach [1966] and Millward [1969] permit increased generality in analyses of identifiability. Matrix equations are presented that solve part of the identifiability problem for a class of Markov models. Results of several earlier analyses are shown to involve special cases of the equations developed here. And it is shown that a general four-state chain has the same parameter space as an all-or-none model if and only if its representation with an observable absorbing state is lumpable into a Markov chain with three states.This research was supported by the U.S. Public Health Service under Grant MH-12717 to Indiana University and Grant GM-1231 to the University of Michigan.Now at the University of Texas, Austin.     

Solutions to some nonlinear equations from nonmetric data

A method is presented to provide estimates of parameters of specified nonlinear equations from ordinal data generated from a crossed design. The analytic method, NOPE, is an iterative method in which monotone regression and the Gauss-Newton method of least squares are applied alternatively until a measure of stress is minimized. Examples of solutions from artificial data are presented together with examples of applications of the method to experimental results.This work was begun while the author was on sabbatical leave during 1970–71 at the Department of Mathematical Psychology, University of Nijmegen, the Netherlands, where discussions with E. E. Roskam on the problem were very helpful. Support was provided by Grant A0151 from the Natural Sciences and Engineering Council, Canada.     

The relation between sample and population characteristic vectors

Data are reported which show the statistical relation between the sample and population characteristic vectors of correlation matrices with squared multiple correlations as communality estimates. Sampling fluctuations were found to relate only to differences in the square roots of characteristic roots and to sample size. A principle for determining the number of factors to rotate and interpret after rotation is suggested.This study was supported by the National Science Foundation, Grant GB 4230. The author wishes to express his appreciation for the use of Western Data Processing Center and the Health Sciences Computing Facility, UCLA. He also thanks Dr. Roger Pennell for extremely valuable assistance in a number of phases of the study.     

Analysis of covariance structures

A general method is presented for estimating variance components when the experimental design has one random way of classification and a possibly unbalanced fixed classification. The procedure operates on a sample covariance matrix in which the fixed classes play the role of variables and the random classes correspond to observations. Cases are considered which assume (i) homogeneous and (ii) nonhomogeneous error variance, and (iii) arbitrary scale factors in the measurements and homogeneous error variance. The results include maximum-likelihood estimations of the variance components and scale factors, likelihood-ratio tests of the goodness-of-fit of the model assumed for the design, and large-sample variances and covariances of the estimates. Applications to mental test data are presented. In these applications the subjects constitute the random dimension of the design, and a classification of the mental tests according to objective features of format or content constitute the fixed dimensions.Preparation of this paper has been supported in part by NSF Grant GB-939 and U. S. P. H. Grant GM-1286-01. Computer time was donated by the Computation Center, University of Chicago.Now at the University of Chicago.Now at the University of Georgia.     

Aspects of preschoolers' comprehension of indoor and outdoor gender-typed toys

Forty-nine 44- to 81-month-old predominantly white children's classification of and clustering in recall of gender-typed indoor and outdoor toys, and their gender schematicity, were assessed. Consistent with predictions, children high in gender schematicity demonstrated significantly greater clustering in their recall by gender type than children low in schematicity. As expected, all children demonstrated more accurate classification of same-sex than other-sex gender-typed toys in general. However, boys and girls showed distinctively different patterns in their abilities to accurately classify same-sex and other-sex indoor and outdoor gender-typed toys. Results are discussed in terms of the different social and play contexts inhabited by preschool boys and girls.Completion of this project was facilitated by funds received when the author was a National Institute of Mental Health Postdoctoral Fellow at the University of Denver; Grant 5T32 MH 15780-09, in addition to an Academic Challenge Award from the University of Toledo. This support is gratefully acknowledged. Special thanks to Maryjo Jones for her data collection efforts and to the faculty, children, and parents of Iliff Preschool of Denver, Colorado, and especially to Director Jean True for assisting in the completion of this research. Thanks also to Joan M. Barth, Narina N. Nightingale, Kathy A. Park, and Peg Hull-Smith for their comments on earlier versions of this article. A shorter version of this paper was presented at the Conference on Human Development, Richmond, Virginia, March 1990.To whom reprint requests should be addressed at Department of Psychology, University of Wyoming, P.O. Box 3415, Room 135 Biological Sciences Building, Laramie, WY 82071-3415.     

A nonrandomized minimax solution for passing scores in the binomial error model

A nonrandomized minimax solution is presented for passing scores in the binomial error model. The computation does not require prior knowledge regarding an individual examinee or group test data for a population of examinees. The optimum passing score minimizes the maximum risk which would be incurred by misclassifications. A closed-form solution is provided for the case of constant losses, and tables are presented for a variety of situations including linear and quadratic losses. A scheme which allows for correction for guessing is also described.This work was performed pursuant to Grant No. NIE-G-78-0087 with the National Institute of Education, Department of Health, Education, and Welfare, Huynh Huynh, Principal Investigator. Points of view or opinions stated do not necessarily reflect NIE position or policy and no official endorsement should be inferred. The editorial assistance and comments of Anthony J. Nitko and of Joseph C. Saunders are gratefully acknowledged.     

Situational approach to assessment of guilt: Development and validation of a self-report measure

The present research developed and evaluated a self-report measure of guilt that encompassed diverse, typical guilt experiences. Behavior-analytic procedures were employed to construct the Situational Guilt Scale (SGS), in which 22 items assessed anticipated guilt feelings for a wide range of naturally occurring specific situations. The SGS was administered to young-adult college students (mean age, 24 years), along with measures of guilt in traditional moral contexts, depressive tendencies, and socially desirable responding. A test-retest study of the SGS was separately conducted. Results indicated that SGS scores had statisfactory internal consistencies and considerable stability. Correlational findings and comparisons of SGS scores in a typology of depressive experience showed relationships of SGS guilt scores with dependent and self-critical tendencies and support the validity of the measure. The findings and utility of the SGS are discussed.Grant 13487 from the PSC-CUNY Research Award Program of the City University of New York provided support for this project. The Committee on Research Computing of the City University of New York funded the use of computer facilities.