Tests of symmetry in three-way contingency tables

Three-dimensional contingency tables are analyzed, with one variable (e.g., sex) as a factor, and with a natural relation between the other variables (e.g. left and right eye vision). Models of special interest, like symmetry and proportional symmetry between the related variables, and homogeneity across the factor levels, are investigated. Maximum likelihood estimators of parameters and partitions of chi-square goodness-of-fit statistics are explicitly presented; the independence of certain models is noted, and an example is discussed.     

Psychopathy and structure of primary mental abilities

The Comprehensive Ability Battery (CAB) was used to assess 18 primary mental abilities in 53 white, male prison inmates for whom highly reliable ratings of psychopathy were available. None of the correlations between ratings of psychopathy and scores on the CAB tests was significant, and the overall pattern or structure of abilities was the same for inmates with low and high ratings of psychopathy. The possibility is raised that the personality characteristics of psychopaths make them appear to be brighter and more creative than they actually are. Compared with norms for male high school students, the inmates as a group generally performed well, falling near the 50th percentile on 11 of the tests. The inmates performed significantly better than the normative sample on tests of verbal ability, esthetic judgment, aiming, and representational drawing, and significantly worse on tests of ideational fluency, spontaneous flexibility, and word fluency.This research was supported by Grant MT-4511 from the Medical Research Council of Canada.     

Robust estimation of ability in the Rasch model

Estimating ability parameters in latent trait models in general, and in the Rasch model in particular is almost always hampered by noise in the data. This noise can be caused by guessing, inattention to easy questions, and other factors which are unrelated to ability. In this study several alternative formulations which attempt to deal with these problems without a reparameterization are tested through a Monte Carlo simulation. It was found that although no one of the tested schemes is uniformly superior to all others, a modified jackknife stood out as the best one in general, it was also super efficient (more efficient than the asymptotically optimal estimator) for tests with forty or fewer items. It is proposed that this sort of jackknifing scheme for estimating ability be considered for practical work.This research was funded through a grant from the Law Enforcement Assistance Administration (78-NI-AX-0047) to the Bureau of Social Science Research, Howard Wainer, Principal Investigator. We would like to thank Ronald Mead, Anne Morgan and James Ramsay for kind, generous, and invaluable help at various stages of the project.     

Timing the second response in two-response avoidance.

Rats were trained on a free-operant avoidance task requiring two lever presses within R seconds, with the opportunity for each response distinguished by differing stimuli. Response latencies at a variety of response-shock intervals were found to be proportional to the time available for the response. These results are shown to be consonant with a scalar expectancy model of timing behavior.     

Parameter estimation in latent trait models

Latent trait models for binary responses to a set of test items are considered from the point of view of estimating latent trait parameters=( ₁, , _n ) and item parameters=( ₁, , _k ), where _j may be vector valued. With considered a random sample from a prior distribution with parameter, the estimation of (, ) is studied under the theory of the EM algorithm. An example and computational details are presented for the Rasch model.This work was supported by Contract No. N00014-81-K-0265, Modification No. P00002, from Personnel and Training Research Programs, Psychological Sciences Division, Office of Naval Research. The authors wish to thank an anonymous reviewer for several valuable suggestions.     

Choice, changeover, and travel: A quantitative model

Six pigeons were trained on concurrent variable-interval schedules in which responding on fixed-interval schedules was required to give access to the alternate schedule. Responding on the concurrent schedules was not allowed, after changing over had commenced, until the changeover schedule had been completed. In Parts 1 to 3 of the experiment, the changeover fixed-interval schedules were equal and were 0 s, 10 s, and 20 s, respectively. In each part, the relative frequency of reinforcement obtained on the concurrent schedules was varied over at least five conditions. In Part 4, the concurrent schedules were equal, and one changeover fixed-interval schedule was twice the other. Under these conditions, the absolute sizes of the changeover schedules were varied. Increasing the changeover requirement from 0 s to 10 s (Parts 1 and 2) resulted in increases in the sensitivity of behavior allocation to reinforcers obtained, but no further increase was obtained when the changeover schedules were increased to 20 s (Part 3). In Part 4, performance was biased towards the concurrent schedule that took less time to enter. These results are consistent with a subtractive punishment model of travel in which the degree of punishment is measured by the number of reinforcers apparently lost from a schedule when the subject changes to that schedule. Absolute times spent on the main keys could be accurately described by a previous model of changeover performance.     

Personality diagnostic questionnaire-revised (PDQ-R) personality disorder scores and negative life events independently predict changes in hopkins symptom checklist (SCL-90) Psychopathology Scores

The present study employed a prospective design to investigate whether Personality Diagnostic Questionnaire—Revised (PDQ-R) scores and/or Hassles Scale—Revised (HS-R) scores predict changes in Axis I psychopathology levels over 1 month, in a nonclinical sample of young adults. The PDQ-R, HS-R, and Hopkins Symptom Checklist (SCL-90) were administered to a mixed-sex sample of 100 undergraduate students on two occasions separated by 1 month. Hierarchical multiple regression analyses indicated that (1) time 1 PDQ-R composite scores predicted changes in scores on 11 SLC-90 scales; (2) time 1 PDQ-R impairment/distress index scores predicted changes in SCL-90 general symptom index scores; (3) only one of the individual PDQ-R personality disorder subscales—the schizotypal personality disorder subscale—predicted changes in SCL-90 general symptom index scores; (4) HS-R scores predicted changes in scores on 9 SCL-90 scales; and (5) in only 3 of the 27 analyses conducted did the statistical interaction between PDQ-R and HS-R scores predict changes in SCL-90 scores. These findings indicate that personality disorder symptomatology and negative life events may independently predict changes in Axis I psychopathology levels and, thus, support the continued inclusion of Axis II and Axis IV in future versions of the Diagnostic and Statistical Manual of Mental Disorders.     

Axiomatic and numerical conjoint measurement: An evaluation of diagnostic efficacy

Synthetic data are used to examine how well axiomatic and numerical conjoint measurement methods, individually and comparatively, recover simple polynomial generators in three dimensions. The study illustrates extensions of numerical conjoint measurement (NCM) to identify and model distributive and dual-distributive, in addition to the usual additive, data structures. It was found that while minimum STRESS was the criterion of fit, another statistic, predictive capability, provided a better diagnosis of the known generating model. That NCM methods were able to better identify generating models conflicts with Krantz and Tversky's assertion that, in general, the direct axiom tests provide a more powerful diagnostic test between alternative composition rules than does evaluation of numerical correspondence. For all methods, dual-distributive models are most difficult to recover, while consistent with past studies, the additive model is the most robust of the fitted models.Douglas Emery is now at the Krannert Graduate School of Management, Purdue University, West Lafayette, IN, on leave from the University of Calgary.     

Diagnostic Classification Models for a Mixture of Ordered and Non-ordered Response Options in Rating Scales

When developing ordinal rating scales, we may include potentially unordered response options such as “Neither Agree nor Disagree,” “Neutral,” “Don’t Know,” “No Opinion,” or “Hard to Say.” To handle responses to a mixture of ordered and unordered options, Huggins-Manley et al. (2018) proposed a class of semi-ordered models under the unidimensional item response theory framework. This study extends the concept of semi-ordered models into the area of diagnostic classification models. Specifically, we propose a flexible framework of semi-ordered DCMs that accommodates most earlier DCMs and allows for analyzing the relationship between those potentially unordered responses and the measured traits. Results from an operational study and two simulation studies show that the proposed framework can incorporate both ordered and non-ordered responses into the estimation of the latent traits and thus provide useful information about both the items and the respondents.