From eye movement to cognition: Toward a general framework of inference comment on Liechty et al., 2003

Liechty, Pieters & Wedel (2003) developed a hidden Markov Model (HMM) to identify the states of an attentional process in an advertisement viewing task. This work is significant because it demonstrates the benefits of stochastic modeling and Bayesian estimation in making inferences about cognitive processes based on eye movement data. One limitation of the proposed approach is that attention is conceptualized as an autonomous random process that is affected neither by the overall layout of the stimulus nor by the visual information perceived during the current fixation. An alternative model based on the input-output hidden Markov model (IOHMM; Bengio, 1999) is suggested as an extension of the HMM. The need for further studies that validate the HMM classification results is also discussed.     

Binary action based estimation of propensities

An observer is to make inference statements about a quantityp, called apropensity and bounded between 0 and 1, based on the observation thatp does or does not exceed a constantc. The propensityp may have an interpretation as a proportion, as a long-run relative frequency, or as a personal probability held by some subject. Applications in medicine, engineering, political science, and, most especially, human decision making are indicated. Bayes solutions for the observer are obtained based on prior distributions in the mixture of beta distribution family; these are then specialized to power-function prior distributions. Inference about logp and log odds is considered. Multiple-action problems are considered in which the focus of inference shifts to theprocess generating the propensitiesp, both in the case of a process parameter known to the subject and unknown. Empirical Bayes techniques are developed for observer inference aboutc when is known to the subject. A Bayes rule, a minimax rule and a beta-minimax rule are constructed for the subject when he is uncertain about.This research was partially supported by the Defense Advanced Research Projects Agency of the Department of Defense and was monitored by ONR under Contract No. N00014-77-C-0095. Any opinions, findings, conclusions or recommendations expressed herein are those of the author and do not necessarily reflect the views of the Defense Advanced Research Projects Agency, the Office of Naval Research, or Carnegie-Mellon University.     

Estimation in the power law

Most psychophysicists neglect to consider how error should be characterized in applications of the power law. Failures of the power law to agree with certain theoretical predictions may be due to bias of parameter estimates. A power law with lognormal product structure is proposed and approximately unbiased parameter estimates are given for several common estimation situations.     

Grading distractor-identification tests

On distractor-identification tests students mark as many distractors as possible on each test item. A grading scale is developed for this type testing. The scale is optimal in that it is the unique scale giving an unbiased estimate of the student's true score, i.e., the score that would result if no guessing occurred. If the test is administered as a usual multiple choice test and graded using the usual correction for guessing scale, the expected item score is the same as for the distractor-identification testing using the optimal grading scale. However, the variance of the item score is shown to be less for distractor-identification testing than for usual multiple choice testing under certain conditions.     

A numerical approach to the approximate and the exact minimum rank of a covariance matrix

A concept of approximate minimum rank for a covariance matrix is defined, which contains the (exact) minimum rank as a special case. A computational procedure to evaluate the approximate minimum rank is offered. The procedure yields those proper communalities for which the unexplained common variance, ignored in low-rank factor analysis, is minimized. The procedure also permits a numerical determination of the exact minimum rank of a covariance matrix, within limits of computational accuracy. A set of 180 covariance matrices with known or bounded minimum rank was analyzed. The procedure was successful throughout in recovering the desired rank.The authors are obliged to Paul Bekker for stimulating and helpful comments.     

On the Bock-Aitkin procedure—From an EM algorithm perspective

The relationship between the EM algorithm and the Bock-Aitkin procedure is described with a continuous distribution of ability (latent trait) from an EM-algorithm perspective. Previous work has been restricted to the discrete case from a probit-analysis perspective. The author is grateful to Bradley A. Hanson for valuable discussion and comments. Thanks also go to Terry A. Ackerman, Meichu Fan, Subrata Kundu, and Robert K. Tsutakawa for their help and encouragement in this study.     

On the loss of information in conditional maximum likelihood estimation of item parameters

In item response models of the Rasch type (Fischer & Molenaar, 1995), item parameters are often estimated by the conditional maximum likelihood (CML) method. This paper addresses the loss of information in CML estimation by using the information concept of F-information (Liang, 1983). This concept makes it possible to specify the conditions for no loss of information and to define a quantification of information loss. For the dichotomous Rasch model, the derivations will be given in detail to show the use of the F-information concept for making comparisons for different estimation methods. It is shown that by using CML for item parameter estimation, some information is almost always lost. But compared to JML (joint maximum likelihood) as well as to MML (marginal maximum likelihood) the loss is very small. The reported efficiency in the use of information of CML to JML and to MML in several comparisons is always larger than 93%, and in tests with a length of 20 items or more, larger than 99%.     

Children acquire the later‐greater principle after the cardinal principle

Many have proposed that the acquisition of the cardinal principle (CP) is a result of the discovery of the numerical significance of the order of the number words in the count list. However, this need not be the case. Indeed, the CP does not state anything about the numerical significance of the order of the number words. It only states that the last word of a correct count denotes the numerosity of the counted set. Here, we test whether the acquisition of the CP involves the discovery of the later‐greater principle – that is, that the order of the number words corresponds to the relative size of the numerosities they denote. Specifically, we tested knowledge of verbal numerical comparisons (e.g., Is ‘ten’ more than ‘six’?) in children who had recently learned the CP. We find that these children can compare number words between ‘six’ and ‘ten’ only if they have mapped them onto non‐verbal representations of numerosity. We suggest that this means that the acquisition of the CP does not involve the discovery of the correspondence between the order of the number words and the relative size of the numerosities they denote.     

主体关联性对贝叶斯推理概率估计的影响

用贝叶斯推理问题为实验材料,探讨了主体关联性对贝叶斯推理概率估计的影响。结果表明,当估计的事件与主体有关时,被试对消极事件概率估计较低,对积极事件概率估计值;当估计的事件与主体无关时,被试对消极事件和积极事件的概率估计无显著差异。反应时分析表明,被试对消极事件的概率估计比对积极事件的概率估计时间显著地长,当消极事件与主体有关时概率估计时间就更长;而对积极事件的概率估计,与主体有关和与主体无关时反应时差异不显著。这表明,被试对消极事件的概率估计(特别是消极事件与己有关时)更为慎重。     

短时距估计中刺激物的动态变化效应

用两个实验考查了时距估计中刺激物的动态变化效应。结果发现,刺激物的运动、速度和旋转角度显著地影响着被试的时间判断,刺激物速度的时距延长效应对于较长时距(18s-24s)来说更加明显;运动刺激与较短、较准确的时距判断相关联;旋转角度的减少使得被试低估时距,而旋转角度的增加使得时距估计呈高估倾向。被试在时间估计过程中表现出长时距低估和短时距高估现象,本研究得到的时间估计转换点是11.4s,此点与先前的有关研究基本一致。