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.     

Essential independence and likelihood-based ability estimation for polytomous items

A definition ofessential independence is proposed for sequences of polytomous items. For items satisfying the reasonable assumption that the expected amount of credit awarded increases with examinee ability, we develop a theory ofessential unidimensionality which closely parallels that of Stout. Essentially unidimensional item sequences can be shown to have a unique (up to change-of-scale) dominant underlying trait, which can be consistently estimated by a monotone transformation of the sum of the item scores. In more general polytomous-response latent trait models (with or without ordered responses), anM-estimator based upon maximum likelihood may be shown to be consistent for under essentially unidimensional violations of local independence and a variety of monotonicity/identifiability conditions. A rigorous proof of this fact is given, and the standard error of the estimator is explored. These results suggest that ability estimation methods that rely on the summation form of the log likelihood under local independence should generally be robust under essential independence, but standard errors may vary greatly from what is usually expected, depending on the degree of departure from local independence. An index of departure from local independence is also proposed.This work was supported in part by Office of Naval Research Grant N00014-87-K-0277 and National Science Foundation Grant NSF-DMS-88-02556. The author is grateful to William F. Stout for many helpful comments, and to an anonymous reviewer for raising the questions addressed in section 2. A preliminary version of section 6 appeared in the author's Ph.D. thesis.     

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.     

Infants’ behavioral styles in joint attention situations and parents’ socio-economic status

In this study the eco-cultural model of parenting (Keller, H. (2007). Cultures of infancy. Mahwah, NJ: Erlbaum) was applied to the study of joint attention behavior of children from families with different socio-economic status (SES). It was hypothesized that infants’ early communication styles would differ with SES reflecting more independent or interdependent interactions with their caregivers. It was also hypothesized that infants would use the same types of behaviors whether they have declarative or imperative communication goals. The Early Social Communication Scales (ESCS, Mundy et al., 2003) was administered to 103 typically developing infants of 12 months (approximately half of them siblings of children with autism). A factor analysis, yielding four behavioral factors, namely pointing, eye contact, actions and following points, confirmed the hypothesis that infants use behaviors consistently across situations independent of their communicative intent. MANOVAs (comprising parental education and income) revealed that higher SES infants showed actions more frequently in the ESCS whereas lower SES infants followed experimenter's points more frequently. The results are discussed in the context of presumably differing socialization goals for infants and the divergent contribution of parental education and income that seem to have additive contribution to some factors (actions, following points) but divergent contributions to others (pointing, eye contact).     

Changing the Criminal Justice System Response to Sexual Assault: An Empirical Study of a Participatory Action Research Project

In jurisdictions throughout the United States, thousands of sexual assault kits (SAKs; also known as a “rape kits”) have not been submitted by the police for forensic DNA testing. DNA evidence may be helpful to sexual assault investigations and prosecutions by identifying perpetrators, revealing serial offenders through DNA matches across cases, and exonerating those who have been wrongly accused. This paper describes a longitudinal action research project conducted in Detroit, Michigan after that city discovered approximately 11,000 untested sexual assault kits in a police department storage facility. We conducted a root cause analysis to examine individual, organizational, community, and societal factors that contributed to the development of the rape kit backlog in Detroit. Based on those findings, we implemented and evaluated structural changes to increase staffing, promote kit testing, and retrain police and prosecutors so that cases could be reopened for investigation and prosecution. As we conducted this work, we also studied how this action research project impacted the Detroit criminal justice system. Participating in this project changed stakeholders’ attitudes about the utility of research to address community problems, the usefulness of DNA evidence in sexual assault cases, and the impact of trauma on survivors. The results led to new protocols for SAK testing and police investigations, and new state legislation mandating SAK forensic DNA testing.     

Enhancing the care of children with chronic diseases through the narratives of patient,physician, nurse and carer

We tested the hypothesis that a narrative approach may enhance a bio‐psycho‐social model (BPS) in caring for chronically ill children. Forty‐eight narratives were collected from 12 children with six different medical conditions, their mothers, physicians, and nurses. By a textual analysis, narratives were classified on their predominant focus as disease (biological focus), illness (psychologic focus), or sickness (social focus). Sixty‐one percent of narrative’ text were classified as illness, 28% as disease and 11% as sickness. All narratives had a degree of illness focus. Narratives by patients and physicians on the one hand, and nurses’ and mothers’ on the other were disease focused. Narratives were also evaluated with respect to the type of medical condition: Illness was largely prevalent in all but Crohn’s disease and HIV infection, the latter having a predominance of sickness most probably related to stigma. Narrative exploration proved a valuable tool for understanding and addressing the needs of children with complex conditions. Narrative approaches allow identification of the major needs of different patients according to health conditions and story tellers. In the narratives, we found a greater illness and disease focus and surprisingly a low sickness focus, except with HIV stories. Narrative medicine provides a tool to strengthen the BPS model in health care.