An analysis and synthesis of multiple correspondence analysis,optimal scaling,dual scaling,homogeneity analysis and other methods for quantifying categorical multivariate data

We discuss a variety of methods for quantifying categorical multivariate data. These methods have been proposed in many different countries, by many different authors, under many different names. In the first major section of the paper we analyze the many different methods and show that they all lead to the same equations for analyzing the same data. In the second major section of the paper we introduce the notion of a duality diagram, and use this diagram to synthesize the many superficially different methods into a single method.The ideas in this paper were worked out by the first author, with some suggestions provided by the second. The current version of this paper has evolved from three previous versions, the first two written by the first author.     

Testing equality of correlated proportions with incomplete data on both responses

Two test statistics are proposed for testing the equality of two correlated proportions when some observations are missing on both responses. The performance of these tests in terms of size and power is compared with other tests by means of Monte Carlo simulations. The proposed tests are easily computed and compare favorably with other tests.     

EMG scanning: Normative data

Surface EMG was recorded from both right and left aspects of 18 muscle groups for the purpose of establishing a data base of normative EMG levels. A scanning electrode permitted easy and rapid EMG measurement from 52 male and 51 female college students, both sitting and standing. Several a posteriori analyses of variance revealed sex differences in the masseter, occipital, posterior cervical, upper trapezius, latissimus dorsi, and anterior tibialis. Similarly, there were side differences for the anterior temporalis, occipitalis, splenius capitus, trapezius, paraspinalis, and soleus. The analyses also revealed interactions among sex, position, and side for various measures on the trapezius. The data show that females tend to muscle brace more than males in the upper extremities. The study provides data for normative comparisons and helps to plan and interpret future EMG studies.     

Exploratory analysis of contingency tables by loglinear formulation and generalizations of correspondence analysis

Goodman's (1979, 1981, 1985) loglinear formulation for bi-way contingency tables is extended to tables with or without missing cells and is used for exploratory purposes. A similar formulation is done for three-way tables and generalizations of correspondence analysis are deduced. A generalized version of Goodman's algorithm, based on Newton's elementary unidimensional method is used to estimate the scores in all cases.This research was partially supported by National Science and Engineering Research Council of Canada, Grant No. A8724. The author is grateful to the reviewers and the editor for helpful comments.     

Social skills training for juvenile delinquents

Twenty-seven incarcerated juvenile delinquents matched on the number of previous offenses, age, WISC-R IQ, and locus of control were assigned to a Social Skills. Discussion or Control group. Social skills training consisted of instruction, feedback, modeling, behavior rehearsal, social reinforcement and graduated homework assignments. All subjects were assessed before and after treatment on a variety of self-report, role-play and behavioral measures. Analyses of variance for difference scores indicated that the Social Skills group improved significantly more than the Discussion and Control groups, which did not differ. Appropriate interpersonal skills were learned, state anxiety was reduced, internal locus of control was increased, and significant shifts in adjustment to the institutional program were evidenced for the Social Skills group.     

Evaluating interobserver reliability of interval data

Previous recommendations to employ occurrence, nonoccurrence, and overall estimates of interobserver reliability for interval data are reviewed. A rationale for comparing obtained reliability to reliability that would result from a random-chance model is explained. Formulae and graphic functions are presented to allow for the determination of chance agreement for each of the three indices, given any obtained per cent of intervals in which a response is recorded to occur. All indices are interpretable throughout the range of possible obtained values for the per cent of intervals in which a response is recorded. The level of chance agreement simply changes with changing values. Statistical procedures that could be used to determine whether obtained reliability is significantly superior to chance reliability are reviewed. These procedures are rejected because they yield significance levels that are partly a function of sample sizes and because there are no general rules to govern acceptable significance levels depending on the sizes of samples employed.     

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.     

Intervention effects and relative variation as dimensions in experts' use of visual inference

Recent research indicates that when analyzing graphically presented single-subject data, subjects trained in visual inference appear to attend to large changes between phases regardless of relative variation and do not differentiate among common intervention effect patterns. In this follow-up study, experts in applied behavior analysis completed a free-sort task designed to assess the effects of these dimensions on their use of visual inference. The results indicate that they tended to differentiate among common intervention effect patterns but did not attend to relative variation in the data.     

Social interest,extreme response style,and implications for adjustment

As part of a series of studies examining Adler's proposition that social interest, or interest and concern for others, is a major factor facilitating personal adjustment, the research investigated the relation between social interest and Extreme Response Style (ERS). ERS was chosen as an indirect measure of maladjustment since research has confirmed Adler's contention that it is especially prevalent among neurotic individuals. In three studies involving a total of 221 subjects, inverse relations were found between a measure of social interest and ERS scores derived from four questionnaires concerning attitudes toward self, others, and a wide variety of attitudinal issues. The data also indicated that the results were not due to either apathy or repression being associated with social interest. The results provided further evidence that positive relations between social interest and adjustment are not limited to self-reports of the latter.     

Structural analysis of subjective categorical data

A general approach to the analysis of subjective categorical data is considered, in which agreement matrices of two or more raters are directly expressed in terms of error and agreement parameters. The method provides focused analyses of ratings from several raters for whom ratings have measurement error distributions that may induce bias in the evaluation of substantive questions of interest. Each rater's judgment process is modeled as a mixture of two components: an error variable that is unique for the rater in question as well as an agreement variable that operationalizes the true values of the units of observation. The statistical problems of identification, estimation, and testing of such measurement models are discussed.The general model is applied in several special cases. The most simple situation is that underlying Cohen's Kappa, where two raters place units into unordered categories. The model provides a generalization and systematization of the Kappa-idea to correct for agreement by chance. In applications with typical research designs, including a between-subjects design and a mixed within-subjects, between-subjects design, the model is shown to disentangle structural and measurement components of the observations, thereby controlling for possible confounding effects of systematic rater bias. Situations considered include the case of more than two raters as well as the case of ordered categories. The different analyses are illustrated by means of real data sets.The authors wish to thank Lawrence Hubert and Ivo Molenaar for helpful and detailed comments on a previous draft of this paper. Thanks are also due to Jens Möller und Bernd Strauß for the data from the 1992 Olympic Games. We thank the editor and three anonymous reviewers for valuable comments on an earlier draft.