Conditions for rasch-dichotomizability of the unidimensional polytomous rasch model

Jansen and Roskam (1986) discussed the compatibility of the unidimensional polytomous Rasch model with dichotomization of the response continuum. They derived a rather strict condition in which dichotomization of multicategory data that fit the unidimensional polytomous Rasch model, results in dichotomous data which fit the dichotomous Research model with effectively the same subject parameter. In this paper a more general dichotomization condition is derived for the polytomous Rasch model, which appears less restrictive, but upholds that the intrinsic logic of the unidimensional polytomous Rasch model defies dichotomization in general. The robustness of dichotomous analysis investigated in a simulation study. It shows a close relation with the two-parameters (Birnbaum) model. Theoretical and methodological implications are discussed.The authors are indebted to H. Müller (personal communication, August 1986), for giving an example which pointed toward the core equation in this paper. The authors also acknowledge the critical comments of Th. Bezambinder and P. Wakker, and of Psychometrika's reviewers to an earlier version of this paper.     

A SCATTER PLOT FOR IDENTIFYING STIMULUS CONTROL OF PROBLEM BEHAVIOR

Line graphs that average response frequency over long periods obscure the major rate changes that indicate sources of behavioral control. A scatter plot can make patterns of responding identifiable and, in turn, suggest environmental features that occasion undesirable behavior. Use of scatter diagrams is illustrated in three cases.     

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.     

On the use of ridit analysis

Ridit analysis is statistical method for comparing ordinal-scale responses. In this paper, the extact variance and asymptotic distribution of the average ridit is developed, including the cases in which the reference group is sampled or the comparison group is finite. The appropriate use and interpretation of ridit analysis is also discussed.The authors wish to thank Andrew Klugh for this support, and the references and David Feigenbaum for their very helpful comments.     

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.