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.     

Parental divorce as a factor in children''s perception of human relationships: An analysis of human movement responses in the Rorschach test

The subjects were 108 Swedish children between 10 and 12 years old, who constituted a divorce and a non-divorce group of 27 girls and 27 boys each. Rorschach Tests were administered individually and human movement responses were analysed. Non-divorce children perceived more cooperative and fewer hostile interactions than the divorce children. Responses containing figures engaged in hostile interaction were most common among divorce girls, whereas the divorce boys had difficulties in perceiving any interaction whatsoever. The different effect of parental divorce on the ability of girls and boys to develop satisfactory social relationships is discussed.     

Covariance structure analysis in several populations

This paper is concerned with the study of covariance structural models in several populations. Estimation theory of the parameters that are subject to general functional restraints is developed based on the generalized least squares approach. Asymptotic properties of the constrained estimator are studied; and asymptotic chi-square tests are presented to evaluate appropriate model comparisons. The method of multipliers and the standard reparametrization technique are discussed in obtaining the estimates. The methodology is demonstrated by a set of real data.Computer facilities were provided by the Computer Services Center, The Chinese University of Hong Kong. The authors are indebted to several anonymous reviewers for suggestions for improvement of this paper.     

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.     

Two simple classes of mastery scores based on the beta-binomial model

Two simple classes of mastery scores which are suitable for hand calculations are presented for beta-binomial test score distributions combined with linear and cubic referral success. The models provide a simple way to explore the consequences of selecting an arbitrary mastery score. Such assessment would be useful whenever the test user is not willing to posta priori a loss ratio, but wishes to look at the various consequences before aiming at a particular score.     

A note on the estimation of the level of predictive precision of a fitted linear equation

A procedure that utilizes the sample multiple correlation to form a lower bound for the level of predictive precision of a fitted regression equation is suggested. The procedure is shown to yield probability statements which are true at least 100(1–)% of the time.     

How a high working memory capacity can increase proactive interference

Previous findings suggested that a high working memory capacity (WMC) is potentially associated with a higher susceptibility to proactive interference (PI) if the latter is measured under high cognitive load. To explain such a finding, we propose to consider susceptibility to PI as a net effect of individual executive processes and the intrinsic potential for PI. With the latter, we refer to the amount of information that is activated at a given time and that has the potential to exert PI subsequently. In two studies deploying generalized linear mixed models, susceptibility to PI was modeled as the decline of performance over trials of a complex span task. The results revealed that a higher WMC was associated with a higher susceptibility to PI. Moreover, the number of stimuli recalled in one trial as a proxy variable for the intrinsic potential for PI negatively affected memory performance in the subsequent trial.     

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).