The nontruncated marginal of a truncated bivariate normal distribution

Inference is considered for the marginal distribution ofX, when (X, Y) has a truncated bivariate normal distribution. TheY variable is truncated, but only theX values are observed. The relationship of this distribution to Azzalini's skew-normal distribution is obtained. Method of moments and maximum likelihood estimation are compared for the three-parameter Azzalini distribution. Samples that are uniformative about the skewness of this distribution may occur, even for largen. Profile likelihood methods are employed to describe the uncertainty involved in parameter estimation. A sample of 87 Otis test scores is shown to be well-described by this model.     

Psychometric and information processing properties of selected response time models

This paper discusses the compatibility of some response time (RT) models with psychometric and with information processing approaches to response times. First, three psychometrically desirable properties of probabilistic models for binary data, related to the principle of specific objectivity, are adapted to the domain of RT models. One of these is the separability of item and subject parameters, and another is double monotonicity. Next, the compatibility of these psychometric properties with one very popular information processing approach, the serial-additive model, is discussed. Finally, five RT models are analyzed with respect to their compatibility with the psychometric properties, with serial-additive processing and with some alternative types of processing. It is concluded that (a) current psychometric models each satisfy one or more of the psychometric properties, but are not (easily) compatible with serial-additive processing, (b) at least one serial-additive processing model satisfies separability of item and subject parameters, and (c) RT models will more easily satisfy double monotonicity than the other two psychometric properties.     

A general model for preferential and triadic choice in terms of centralF distribution functions

A model for preferential and triadic choice is derived in terms of weighted sums of centralF distribution functions. This model is a probabilistic generalization of Coombs' (1964) unfolding model and special cases, such as the model of Zinnes and Griggs (1974), can be derived easily from it. This new form extends previous work by Mullen and Ennis (1991) and provides more insight into the same problem that they discussed.     

Specific effects of acute moderate exercise on cognitive control

The main issue of this study was to determine whether cognitive control is affected by acute moderate exercise. Twelve participants [4 females (VO_{2 max} = 42 ml/kg/min) and 8 males (VO_{2 max} = 48 ml/kg/min)] performed a Simon task while cycling at a carefully controlled workload intensity corresponding to their individual ventilatory threshold. The distribution-analytical technique and the delta plot analysis [Ridderinkhof, K. R. (2002). Activation and suppression in conflict tasks: Empirical clarification through distributional analyses. In W. Prinz & B. Hommel (Eds.), Common mechanisms in perception and action. Attention and performance (Vol. 19, pp. 494–519). Oxford: Oxford University Press.] were used to assess the role of selective response inhibition in resolving response conflict. Results showed that cognitive processes appeared to be differently affected by acute moderate exercise. Reaction time results confirmed that performance is better (faster without change in accuracy) when the cognitive task is performed simultaneously with exercise. Between-trial adjustments (post-conflict and post-error) highlighted that cognitive control adjustments are also fully efficient during exercise. However, the effect of congruency (Simon effect) appeared to be more pronounced during exercise compared to rest which suggests that the response inhibition is deteriorated during exercise. The present findings suggest that acute moderate exercise differently affects some specific aspects of cognitive functions.     

Asymptotic distributions of the estimators of communalities in factor analysis

Asymptotic distributions of the estimators of communalities are derived for the maximum likelihood method in factor analysis. It is shown that the common practice of equating the asymptotic standard error of the communality estimate to the unique variance estimate is correct for standardized communality but not correct for unstandardized communality. In a Monte Carlo simulation the accuracy of the normal approximation to the distributions of the estimators are assessed when the sample size is 150 or 300. This study was carried out in part under the ISM Cooperative Research Program (90-ISM-CRP-9).     

A hierarchical bayesian statistical framework for response time distributions

This paper provides a statistical framework for estimating higher-order characteristics of the response time distribution, such as the scale (variability) and shape. Consideration of these higher order characteristics often provides for more rigorous theory development in cognitive and perceptual psychology (e.g., Luce, 1986). RT distribution for a single participant depends on certain participant characteristics, which in turn can be thought of as arising from a distribution of latent variables. The present work focuses on the three-parameter Weibull distribution, with parameters for shape, scale, and shift (initial value). Bayesian estimation in a hierarchical framework is conceptually straightforward. Parameter estimates, both for participant quantities and population parameters, are obtained through Markov Chain Monte Carlo methods. The methods are illustrated with an application to response time data in an absolute identification task. The behavior of the Bayes estimates are compared to maximum likelihood (ML) estimates through Monte Carlo simulations. For small sample size, there is an occasional tendency for the ML estimates to be unreasonably extreme. In contrast, by borrowing strength across participants, Bayes estimation shrinks extreme estimates. The results are that the Bayes estimators are more accurate than the corresponding ML estimators.We are grateful to Michael Stadler who allowed us use of his data. This research is supported by (a) National Science Foundation Grant SES-0095919 to J. Rouder, D. Sun, and P. Speckman, (b) University of Missouri Research Board Grant 00-77 to J. Rouder, (c) National Science Foundation grant DMS-9972598 to Sun and Speckman, and (d) a grant from the Missouri Department of Conservation to D. Sun.     

Does visual working memory work as a few fixed slots?

The present study investigated whether visual working memory (VWM) functions as a few (about 3?～ 4) fixed slots by examining how the distribution of VWM is adjusted. Adopting a change-detection paradigm, we required subjects to memorize four items, one of which was prioritized. If VWM functions as 3?～?4 slots, allocating multiple slots to the prioritized item would leave no slot for some other items; consequently no information would be stored for them, leading to a substantial decrease in change-detection performance no matter whether small or large changes occurred. The result showed that small changes on the unfavoured items were detected less accurately, indicating that more VWM was allocated to the favoured item. Yet meanwhile large changes that occurred on those unfavoured items could still be detected as well as those on the favoured one, indicating that each of them was still stored to some extent rather than completely discarded. The results suggested that VWM may not work as 3?～?4 fixed slots. Possible mechanisms were discussed based on the present results, including a modified slot model with more available slots, a continuous resource model, and a hierarchical model that assumes storage of ensemble information in addition to the information of individual items.     

Bilateral Reminiscence in Inverted-Reversed Printing

Reported is a study of bilateral reminiscence in printing inverted-reversed alphabetic letters. Independent variables were the printing-Hand Sequence (left-to-right vs. right-to-left), and the Interpolated Activity (control vs. upright reading vs. inverted reading). These variables were factorially combined in a 2 × 3 design with 30 Ss per cell. On second-hand performance, the upright groups were found to be superior to the combined inverted and control groups under both sequence conditions. However, the inverted group was superior to the control group only in the left-to-right condition and not in the right-to-left condition. This latter result was discussed as possibly being due to the specialization of the cerebral hemispheres for certain types of processing activities. Implications of this hypothesis were pointed out for further research, and for possible mechanisms producing reactive inhibition in the central nervous system.     

A model for repeat trial product tests

A non-forced choice model is developed that describes subject behavior on repeat trial discrimination tests of the pick 1 ofk form. The model is developed from the Dirichlet distribution, and it allows for the derivation of individual true scores and of sampling properties for various constructs of interest. These results permit the analysis and comparison of test designs. The model is applied to issues such as forced vs. non-forced choice formats, the best number of alternatives at a choice point, and the selection of expert panels.     

Bug distribution and statistical pattern classification

A model (called the rule space model) which permits measuring cognitive skill acquisition, diagnosing cognitive errors, detecting the weaknesses and strengths of knowledge possessed by individuals was introduced earlier. This study further discusses the theoretical foundation of the model by introducing bug distribution and hypothesis testing (Bayes' decision rules for minimum errors) for classifying subjects into their most plausible latent state of knowledge. The model is illustrated with the domain of fraction arithmetic and compared with the results obtained from a conventional artificial intelligence approach.The authors would like to acknowledge Mr. Robert Baillie for developing several computer programs used for this research.This research was sponsored by the Personnel and Training Research Program, Psychological Sciences Division, Office of Naval Research.Some of the analyses presented in this report were performed on the PLATO® system. The PLATO® system is a development of the University of Illinois and PLATO® is a service mark of the Control Data Corporation.