On component analyses

Principal components analysis can be redefined in terms of the regression of observed variables upon component variables. Two criteria for the adequacy of a component representation in this context are developed and are shown to lead to different component solutions. Both criteria are generalized to allow weighting, the choice of weights determining the scale invariance properties of the resulting solution. A theorem is presented giving necessary and sufficient conditions for equivalent component solutions under different choices of weighting. Applications of the theorem are discussed that involve the components analysis of linearly derived variables and of external variables.Preparation of this article was supported in part by National Institute of Aging Grant NIA-AG03164-03 to William Meredith.     

An Extension of Multiple Correspondence Analysis for Identifying Heterogeneous Subgroups of Respondents

An extension of multiple correspondence analysis is proposed that takes into account cluster-level heterogeneity in respondents’ preferences/choices. The method involves combining multiple correspondence analysis and k-means in a unified framework. The former is used for uncovering a low-dimensional space of multivariate categorical variables while the latter is used for identifying relatively homogeneous clusters of respondents. The proposed method offers an integrated graphical display that provides information on cluster-based structures inherent in multivariate categorical data as well as the interdependencies among the data. An empirical application is presented which demonstrates the usefulness of the proposed method and how it compares to several extant approaches. The work reported in this paper was supported by Grant 290439 and Grant A6394 from the Natural Sciences and Engineering Research Council of Canada to the first and third authors, respectively. We wish to thank Ulf B?ckenholt, Paul Green, and Marc Tomiuk for their insightful comments on an earlier version of this paper. We also wish to thank Byunghwa Yang for generously providing us with his data.     

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.     

Redundancy analysis an alternative for canonical correlation analysis

A component method is presented maximizing Stewart and Love's redundancy index. Relationships with multiple correlation and principal component analysis are pointed out and a rotational procedure for obtaining bi-orthogonal variates is given. An elaborate example comparing canonical correlation analysis and redundancy analysis on artificial data is presented.A Fortran IV program for the method of redundancy analysis described in this paper can be obtained from the author upon request.     

内部分配改革的职务评价技术探新

建立工资标准系统的关键是确定职务工资率。职务间可比价值成分变异越大,对确定职务工资率的贡献也越大。根据以上研究设想采用方差分析方法进行职务评价。评价步骤包括：职务描述;对职务要素作主成分分析;对职务样本作聚类分析和判别分析;通过方差分析为可比价值各成分建构权重系数ωｉ。ωｉ‘满足：（１）ωｉ≥０;（２）Σωｉ＝１;（３）ωｉ,间可直接比较;（４）ωｉ的大小与对应的可比价值成分变异一致。最后将职务评价值线性变换为工资率。在线性方程中配一个常数。和调节系数α以适合组织的管理约束条件。配合两个企业内部分配改革的研究结果显示了方差分析法的有效性和实用性。     

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.     

A PROC MATRIX program for preference-dissimilarity multidimensional scaling

A computer program can be a means of communicating the structure of an algorithm as well as a tool for data analysis. From this perspective high-level matrix-oriented languages like PROC MATRIX in the SAS system are especially useful because of their readability and compactness. An algorithm for the joint analysis of dissimilarity and preference data using maximum likelihood estimation is presented in PROC MATRIX code.This research was supported by Grant APA 3020 from the Natural Sciences and Engineering Research Council of Canada.     

Peer facilitation of generalization in a preschool classroom

Two 5-year-old deviant preschoolers taught each other, as peer-tutors, to identify pictorial figures describing prepositional relationships. During training sessions monitored by the experimenter, the child in the peer-tutor role presented stimulus materials and provided consequences for the responses of the child in the tutee role. An assessment of generalization by each child to an academic classroom setting occurred each day. The data showed that the peer-tutor could facilitate generalization, when the tutee was probed in the peer-tutor's presence. However, it was found that the salience of the peer-tutor's presence was critical to this effect. In particular, when the peer presented the stimuli or offered occasional consequences for some correct responses, generalization was greatly enhanced.This research was supported in part by PHS Training Grant HD 00183, Research Grant MH 11739, and a Dissertation Fellowship from the University of Kansas. Appreciation is expressed to the classroom teachers, Scott Simmons, Janet Wedel, Sue Parker, and Tena McEachern, for their patience and cooperation in the implementation of these procedures, and to Merril Stokes, for her help and encouragement during this study.     

Cracks in a postdisaster service delivery network

Poor linkage cracks are defined and identified empirically in a postdisaster service delivery network. These cracks exist when essential services are provided only by isolated or peripheral clusters of organizations. Network analysis is used to identify the isolated and peripheral clusters of organizations. Measures of experience in responding to disasters and service capacity are used to identify the organizations whose services are essential in the network. Cracks prevent the network from responding effectively in the aftermath of a disaster. Suggestions are made for using network analysis to identify cracks and to improve planning and coordination in all kinds of service networks. Collection of the data for this work was supported by the National Science Foundation (NSF), Societal Response to Earthquake Hazards Mitigation Program, Grant No. CEE-8314421. The analysis and writing were accomplised with support from the National Science Foundation, Grant No. BCS-8920472. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the National Science Foundation. An early version of this paper was presented at the annual meetings of the Midwest Sociological Society, Des Moines, Iowa, April 1991. This paper was distinctly improved through our response to extensive and perceptive suggestions given by the editor and reviewers of theAmerican Journal of Community Psychology. We thank them for the help.     

Parental relationships,socioeconomic status,and sex-role expectations

The responses of university women to a scale composed of items reflective of traditional expectations for females are examined. Women who reject such stereotyped expectations had poor childhood relationships with their fathers, and the women who endorse the expectations had good paternal relationships. This is a class-specific pattern most characteristic of those of lower socioeconomic background. No similar effect was found when childhood relationships with mothers were considered. Implications of fathers' influence on daughters' sex-role orientations are considered.An earlier version of this article was presented as a paper at the meeting of the Pacific Sociological Association in Victoria, British Columbia, April 1975. The patience and ideas of an anonymous reviewer have considerably strengthened this revision. This research was partially supported by NSF Grant ISP-8011449.     

A method of optimal scaling for multivariate ordinal data and its extensions

This paper develops a method of optimal scaling for multivariate ordinal data, in the framework of a generalized principal component analysis. This method yields a multidimensional configuration of items, a unidimensional scale of category weights for each item and, optionally, a multidimensional configuration of subjects. The computation is performed by alternately solving an eigenvalue problem and executing a quasi-Newton projection method. The algorithm is extended for analysis of data with mixed measurement levels or for analysis with a combined weighting of items. Numerical examples and simulations are provided. The algorithm is discussed and compared with some related methods.Earlier results of this research appeared in Saito and Otsu (1983). The authors would like to acknowledge the helpful comments and encouragement of the editor.     

Experimental design symbolization and model derivation

A method of design symbolization (DS) is given for a class of designs in which all factors are related by complete crossing or by nesting. Characterization of acceptable DS's, and logical relational properties are given. It is shown how the design model can be obtained from the DS.The preparation of this article was supported by NIH Grant GM-11128, and by grants to the Institute of Human Learning by NSF and NIH.     

Indclas: A three-way hierarchical classes model

A three-way three-mode extension of De Boeck and Rosenberg's (1988) two-way two-mode hierarchical classes model is presented for the analysis of individual differences in binary object × attribute arrays. In line with the two-way hierarchical classes model, the three-way extension represents both the association relation among the three modes and the set-theoretical relations among the elements of each model. An algorithm for fitting the model is presented and evaluated in a simulation study. The model is illustrated with data on psychiatric diagnosis. Finally, the relation between the model and extant models for three-way data is discussed.The research reported in this paper was partially supported by NATO (Grant CRG.921321 to Iven Van Mechelen and Seymour Rosenberg).     

On the effects of food deprivation and component reinforcer rates on multiple-schedule performance

Six pigeons were used to investigate the effects of varying body weight and component reinforcer rates in two-component multiple variable-interval variable-interval schedules. In Parts 1 and 3 of the experiment, unequal component reinforcer rates were arranged, and body weights were respectively increased and decreased. At 80% ad lib weight, response-rate ratios were closer to unity than reinforcer-rate ratios, but at 100% or more of ad lib weight, response-rate ratios generally equaled reinforcer-rate ratios. In Part 2, component reinforcer-rate ratios were varied over five conditions with the subjects maintained at 100% or more of their ad lib weights, and response-rate ratios matched reinforcer-rate ratios. The data thus support the empirical finding that response allocation in multiple schedules is a function of deprivation. Although this qualitative result is predicted by three models of multiple-schedule performance, only a model that assumes no direct component interaction adequately describes the data.     

Test selection with integral gross score weights

A new method of test selection, which attempts to combine the merits of the ToopsL-Method with those of the Wherry-Doolittle Method, is presented. It results in integral (unit if desired) positive and/or negative (optional) weights. This flexibility makes the method applicable to all kinds of material and for both selecting items for tests and tests for batteries. An explicit solution of one test construction problem is presented. Necessary changes in method for the solution of five other types of test construction problem are presented. A few cautions are provided for potential users.     

Maximum likelihood additivity analysis

A maximum likelihood estimation procedure was developed to fit unweighted and weighted additive models to conjoint data obtained by the categorical rating, the pair comparison or the directional ranking method. The scoring algorithm used to fit the models was found to be both reliable and efficient, and the program MAXADD is capable of handling up to 300 parameters to be estimated. Practical uses of the procedure are reported to demonstrate various advantages of the procedure as a statistical method.The research reported here was supported by Grant A6394 to the author from the Natural Sciences and Engineering Research Council of Canada. Portions of this research were presented at the Psychometric Society meeting in Iowa City, Iowa, in May, 1980.Thanks are due to Jim Ramsay, Justine Sergent and anonymous reviewers for their helpful comments.Two MAXADD programs which perform the computations discussed in this paper may be obtained from the author.     

On the composition of risk preference and belief

Prospect theory assumes nonadditive decision weights for preferences over risky gambles. Such decision weights generalize additive probabilities. This article proposes a decomposition of decision weights into a component reflecting risk attitude and a new component depending on belief. The decomposition is based on an observable preference condition and does not use other empirical primitives such as statements of judged probabilities. The preference condition is confirmed by most of the experimental findings in the literature. The implied properties of the belief component suggest that, besides the often-studied ambiguity aversion (a motivational factor reflecting a general aversion to unknown probabilities), perceptual and cognitive limitations play a role: It is harder to distinguish among various levels of likelihood, and to process them differently, when probabilities are unknown than when they are known.     

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.