Covariance structure analysis of ordinal ipsative data

Data are ipsative if they are subject to a constant-sum constraint for each individual. In the present study, ordinal ipsative data (OID) are defined as the ordinal rankings across a vector of variables. It is assumed that OID are the manifestations of their underlying nonipsative vector y, which are difficult to observe directly. A two-stage estimation procedure is suggested for the analysis of structural equation models with OID. In the first stage, the partition maximum likelihood (PML) method and the generalized least squares (GLS) method are proposed for estimating the means and the covariance matrix of A_cy, where A_c is a known contrast matrix. Based on the joint asymptotic distribution of the first stage estimator and an appropriate weight matrix, the generalized least squares method is used to estimate the structural parameters in the second stage. A goodness-of-fit statistic is given for testing the hypothesized covariance structure. Simulation results show that the proposed method works properly when a sufficiently large sample is available.This research was supported by National Institute on Drug Abuse Grants DA01070 and DA10017. The authors are indebted to Dr. Lee Cooper, Dr. Eric Holman, Dr. Thomas Wickens for their valuable suggestions on this study, and Dr. Fanny Cheung for allowing us to use her CPAI data set in this article. The authors would also like to acknowledge the helpful comments from the editor and the two anonymous reviewers.     

Vocational students' learning preferences: the interpretability of ipsative data

A number of researchers have argued that ipsative data are not suitable for statistical procedures designed for normative data. Others have argued that the interpretability of such analyses of ipsative data are little affected where the number of variables and the sample size are sufficiently large. The research reported here represents a factor analysis of the scores on the Canfield Learning Styles Inventory for 1,252 students in vocational education. The results of the factor analysis of these ipsative data were examined in a context of existing theory and research on vocational students and lend support to the argument that the factor analysis of ipsative data can provide sensibly interpretable results.     

Normative versus ipsative configural frequency analysis in personality research—their use discussed in a reanalysis of data on situation-bound anxiety

Configural frequency analysis (CFA) tests whether certain individual patterns in different variables are observed more frequently in a sample than expected by chance. In normative CFA, these patterns are derived from the subject's specific position in relation to sample characteristics such as the median or the mean. In ipsative CFA, patterns are defined within an individual reference system, e.g. relative to the subject's median of different variable scores. Normative CFA examines dimensionality of scales and is comparable to factor analysis in this respect. Ipsative CFA rather yields information about location of scores in different variables, in a similar way to ANOVA or Friedman testing. However, both normative and ipsative CFA may supply information not obtainable by means of the aforementioned methods. This is illustrated in a reanalysis of data in four scales of an anxiety inventory. © 1997 John Wiley & Sons, Ltd.     

Generalized canonical correlation analysis of matrices with missing rows: a simulation study

A method is presented for generalized canonical correlation analysis of two or more matrices with missing rows. The method is a combination of Carroll’s (1968) method and the missing data approach of the OVERALS technique (Van der Burg, 1988). In a simulation study we assess the performance of the method and compare it to an existing procedure called GENCOM, proposed by Green and Carroll (1988). We find that the proposed method outperforms the GENCOM algorithm both with respect to model fit and recovery of the true structure. The research of Michel van de Velden was partly funded through EU Grant HPMF-CT-2000-00664. The authors would like to thank the associate editor and three anonymous referees for their constructive comments and suggestions that led to a considerable improvement of the paper.     

Factor and ideal point analysis for interpersonally incomparable data

Interpersonally incomparable responses pose a significant problem for survey researchers. If the manifest responses of individuals differ from their underlying true responses by monotonic transformations which vary from person to person, then the covariances of the manifest responses tools such as factor analysis may yield incorrect results. Satisfactory results for interpersonally incomparable ordinal responses can be obtained by assuming that rankings are based upon a set of multivariate normal latent variables which satisfy the factor or ideal point models of choice. Two statistical methods based upon these assumptions are described; their statistical properties are explored; and their computational feasibility is demonstrated in some simulations. We conclude that is possible to develop methods for factor and ideal point analysis of interpersonally incomparable ordinal data.This research was begun in the supportive enviroment of the Survey Research Center at the University of California, Berkeley. Financial support was provided by Percy Tannenbaum, Director of the Center, by Allan Sindler, Dean of the Graduate School of Public Policy at Berkeley, by the Data Center of Harvard University, and by the National Science Foundation through grant number SES-84-03056. Chris Achen, Doug Rivers, and members of the Harvard-MIT econometrics seminar provided useful comments.     

Progressing toward data intimacy: a review of within-session data analysis

Visual inspection of data is a common method for understanding, responding to, and communicating important behavior-environment relations in single-subject research. In a field that was once dominated by cumulative, moment-to-moment records of behavior, a number of graphic forms currently exist that aggregate data into larger units. In this paper, we describe the continuum of aggregation that ranges from distant to intimate displays of behavioral data. To aid in an understanding of the conditions under which a more intimate analysis is warranted (i.e., one that provides a richer analysis than that provided by condition or session aggregates), we review a sample of research articles for which within-session data depiction has enhanced the visual analysis of applied behavioral research.     

Validation of an ipsative personality measure (DISCUS)

The purpose of this study was to examine the construct validity of an ipsative personality test (DISCUS), and various effects of the ipsative format of the test. Both an ipsative and a normative version of the DISCUS test was administered to a sample of undergraduate students (N = 103), along with an adjective based personality test that measures the Big-Five personality traits (5PFa). The results indicated that the normative and the ipsative version of DISCUS are not equivalent, and caution is needed when using the ipsative version for psychometric evaluations as in validation studies. The four DISCUS dimensions (Dominance, Influence, Stability, and Carefulness) represented combinations of the Big-Five traits rather than independent traits as indicated by the correlations with the Big-Five measure.     

Fears of phobic patients: Factor analyses of self-report data

Fear questionnaires completed by 171 phobic patients were factor-analysed. Factors previously identified in student and non-phobic patients were replicated, and in addition an agoraphobia factor was found. Separate analyses of (i) a group of psychiatrically diagnosed agoraphobics and (ii) a group of miscellaneous phobics revealed that agoraphobics are generally more fearful and depressed than other phobics, and score more highly on a cluster of items which include ‘breathing difficulties’ and ‘dizziness’. A distinct agoraphobia factor was not identifiable in the group of miscellaneous phobics, pointing to the all-or-none nature of this fear.     

Factor analysis of a Venezuelan fear survey schedule

A Fear Survey Schedule, developed for use by university students in Venezuela, was administered to 871 first-year students at the Simón Bolivar University, Caracas, and subjected to several analyses to identify its factorial structure. Five factors were identified in the male group: Fear of aversive interpersonal events; of Violence and physical assault; of Loss of self-control; of Injuries and surgical operations; and of Animals and insects. Seven factors were identified in the female group, four of them coincided with the male group: Fear of interpersonal events; of Animals and insects; of Injuries and surgery; of Responsibility; of Death and physical threats; of Doctors and hospitals; of Violence and physical assault. The results were compared to those obtained with similar fear surveys of North American and Israeli University students.     

Using multilevel analyses with sibling data to increase analytic power: an illustration and simulation study

This study investigates the extent to which analytic power can be increased through the inclusion of siblings in a data set and the concomitant use of random coefficient multilevel models. Analyses of real-world data regarding the predictors of young adult alcohol use illustrate how parallel single-level analyses of a 1-child-per-family data set and multilevel analyses of a data set including all siblings in each family would be conducted. A simulation study, closely based on the illustrative analyses, compares the empirical power to detect main, moderation, and mediation effects under three conditions: (a) single-level analyses of 1-child-per-family data, (b) multilevel analyses of all-siblings data, and (c) single-level analyses of independent data with sample size equivalent to the all-siblings condition. Supplementary analyses are conducted to determine the conditions under which greater analytic power could be achieved with the addition of siblings to a data set than with the addition of a lesser number of independent individuals at equivalent cost.     

Factor analysis and Psychometrika: Major developments

Papers on factor analysis appearing inPsychometrika reflect the initial efforts of the Thurstonians to reformulate psychology as a quantitative science. The Thurstonians' emphasis on the development of factor analysis as an exploratory methodology was not new with them but was taken from British statisticians and psychologists who preceded them, whose literature the Thurstonians otherwise tended to ignore. The Thurstonians' rejection of general factors and focus on rotation to simple structure reflected an attempt to avoid statistical artifact and to identify factors with psychological substance. Much of the literature on factor analysis inPsychometrika concerned solving technical problems in the exploratory factor analysis method. Factor analysis took a major shift in direction in the 1970's with the development of confirmatory methodologies, many of which now receive greater attention than the method of exploratory factor analysis, most of the problems of which are now resolved.     

Factor copula models for mixed data

We develop factor copula models to analyse the dependence among mixed continuous and discrete responses. Factor copula models are canonical vine copulas that involve both observed and latent variables, hence they allow tail, asymmetric and nonlinear dependence. They can be explained as conditional independence models with latent variables that do not necessarily have an additive latent structure. We focus on important issues of interest to the social data analyst, such as model selection and goodness of fit. Our general methodology is demonstrated with an extensive simulation study and illustrated by reanalysing three mixed response data sets. Our studies suggest that there can be a substantial improvement over the standard factor model for mixed data and make the argument for moving to factor copula models.