Power of the likelihood ratio test in covariance structure analysis

A procedure for computing the power of the likelihood ratio test used in the context of covariance structure analysis is derived. The procedure uses statistics associated with the standard output of the computer programs commonly used and assumes that a specific alternative value of the parameter vector is specified. Using the noncentral Chi-square distribution, the power of the test is approximated by the asymptotic one for a sequence of local alternatives. The procedure is illustrated by an example. A Monte Carlo experiment also shows how good the approximation is for a specific case.This research was made possible by a grant from the Dutch Organization for Advancement of Pure Research (ZWO). The authors also like to acknowledge the helpful comments and suggestions from the editor and anonymous reviewers.     

Preference for unsegmented interreinforcement intervals in concurrent chains

Five pigeons were trained under concurrent-chain schedules in which a pair of independent, concurrent variable-interval 60-s schedules were presented in the initial link and either both variable-interval or both fixed-interval schedules were presented in the terminal link. Except for the baseline, one of the terminal-link schedules was always a two-component chained schedule and the other was either a simple or a tandem schedule of equal mean interreinforcement interval. The values of the fixed-interval schedules were either 15 s or 60 s; that of the variable-interval schedules was always 60 s. A 1.5-s changeover delay operated during the initial link in some conditions. The pigeons preferred a simple or a tandem schedule to a chain. For the fixed-interval schedules, this preference was greater when the fixed interval was 60 s than when it was 15 s. For the variable-interval schedules, the preferences were less pronounced and occurred only when the changeover delay was in effect. For a given type of schedule and interreinforcement interval, similar preferences were obtained whether the nonchained schedule was a tandem or simple schedule. The changeover delay generally inflated preference and lowered the changeover rate, especially when the terminal-link schedules were either short (15 s) or aperiodic (variable-interval). The results were consistent with the notion that segmenting the interreinforcement interval of a schedule into a chain lowers the preference for it.     

4~8年级学生分数数量表征的准确性及形式

在分数学习中,分数数量表征是非常重要的方面。本研究利用数字线估计任务对四到八年级学生分数数量表征的情况进行探索。研究结果表明：随着年级升高,被试分数数量表征的准确性也随之提高;被试对单位分数和非单位分数表征的准确性存在显著差异,表现为对单位分数表征的准确性显著高于对非单位分数的表征,这种差异在低年级显著,随着年级的增长,差异逐渐消失;四到八年级学生在0~3数字线上,对分数数量的表征表现为线性形式而非对数形式,且这种线性表征形式是在六年级开始出现并随着年龄增长逐渐发展起来的。中西方儿童在分数数量表征的准确性和形式上有相似的发展路径,但是在表征准确性上中国儿童更高、线性形式出现年级上中国儿童可能更早。     

时间赋义对数字空间表征的影响：来自数字线估计任务的证据

数字线估计任务的大量研究以纯数字为研究对象而忽视了赋义数字。本研究以Siegler等的数字线估计任务为原型,探讨在对数字时间赋义条件下小学二、四和六年级儿童的数字表征形式是否发生变化。结果表明,小学二年级是0-1000范围内数字表征从对数形式转换为线性形式的转折点,对数字赋予时间含义后,三个年级均出现了赋义效应。在线性模型和对数模型中时间赋义的作用相反,时间赋义表现出抑线升对（抑制线性模型提升对数模型解释力）的效果。     

Time-related processes in time-based prospective memory and in time-interval production

Time-based prospective memory tasks require the retrieval of previously formed plans (e.g., call me on my mobile phone) either at a specified time (e.g., at 3 p.m.) or after a specified period of time has elapsed (e.g., in 3 min). In the present study, we investigated whether the same time-related processes are recruited for a short-duration time-based prospective memory task and for a time-interval production task. In a dual-task paradigm, we required young adult participants to make category-membership decisions, while they were simultaneously engaged either in a time-based prospective memory tasks or in a time-interval production task. Under one set of conditions, participants were instructed to allocate attention equally to the two tasks, whereas in another set of conditions, they allocated attention primarily to the time-relevant task. The findings revealed that time estimates were not affected by the attention allocation manipulation, although it influenced performance on the concurrent category membership decision making task, and as expected time estimates were more accurate on the prospective memory task than on the time-production task. Based on the preponderance of the findings, we suggest that timing is managed by different mechanisms and/or strategies on time-interval production tasks and on short-duration time-based prospective memory tasks.     

An age-related view of the role of object and spatial cognitive styles in distance estimation

Distance estimations require identifying characteristics of the object and its spatial surroundings. With the present study, we examined the relationship between visual object and spatial (cognitive) styles and distance estimations in children and adults. Participants were administered the Object-Spatial Imagery Questionnaire (OSIQ) and two distance estimation tasks—one required estimating reach distance (reach task [RT]) from the self and the other required estimating distance between targets (perceptual task[PT]). Overall, our findings indicated that age was the best predictor of estimation for RT and PT tasks, and individuals were more accurate in the task requiring an egocentric frame of reference (RT) compared to tasks that require allocentric judgements (PT). In addition, children had higher ratings on cognitive styles in comparison to adults, but both object and spatial styles only related to RT accuracy in adults. Cognitive styles seem to be associated to distance estimation accuracy, but only when there is a clear preference.     

Human performance on negative slope schedules of points exchangeable for money: a failure of molar maximization

Panel pressing was generated and maintained in 5 adult humans by schedules of points exchangeable for money. Following exposure to a variable-interval 30-s schedule and to a linear variable-interval 30-s schedule (which permitted points to accumulate in an unseen "store" in the absence of responding), subjects were exposed to a series of conditions with a point-subtraction contingency arranged conjointly with the linear variable-interval schedule. Specifically, points were added to the store according to the linear-variable interval 30-s schedule and were subtracted from the store according to a ratio schedule. Ratio value varied across conditions and was determined individually for each subject such that the subtraction contingency would result in an approximately 50% reduction in the rate of point delivery. Conditions that included the subtraction contingency were termed negative slope schedules because the feedback functions were negatively sloped across all response rates greater than the inverse of the variable-interval schedule, in this case, two per minute. Overall response rates varied inversely with the subtraction ratio, indicating sensitivity to the negative slope conditions, but were in excess of that required by accounts based on strict maximization of overall reinforcement rate. Performance was also not well described by a matching-based account. Detailed analyses of response patterning revealed a consistent two-state pattern in which bursts of high-rate responding alternated with periods of prolonged pausing, perhaps reflecting the joint influence of local and overall reinforcement rates.     

Cognitive distance of stairways: a multi-stairway investigation

The present study had two major purposes. First it sought to determine to what extent in an earlier study of distance estimation in stairways (Hanyu & Itsukushima, 1995) would generalize to other types of stairway. Second, it sought to examine which hypothesis, information storage or effort, better explain the earlier results, in which people overestimated distance and traversed time estimates. We obtained four distance and time measures: distance estimate, traversal time estimate, mental walking time and actual traversal time. To measure information, we had participants rate each stairway for complexity (simple-complex) and effort (effortless-effortful) before and after the distance and time measurement tasks. The results revealed that the earlier findings (Hanyu & Itsukushima, 1995) did not fully generalize. The results also did not support either the information storage or the effort hypothesis.     

Effects of cocaine on performance under fixed-interval schedules with a small tandem ratio requirement

Daily administration of cocaine often results in the development of tolerance to its effects on responding maintained by fixed-ratio schedules. Such effects have been observed to be greater when the ratio value is small, whereas less or no tolerance has been observed at large ratio values. Similar schedule-parameter-dependent tolerance, however, has not been observed with fixed-interval schedules arranging comparable interreinforcement intervals. This experiment examined the possibility that differences in rate and temporal patterning between the two types of schedule are responsible for the differences in observed patterns of tolerance. Five pigeons were trained to key peck on a three-component multiple (tandem fixed-interval fixed-ratio) schedule. The interval values were 10, 30, and 120 s; the tandem ratio was held constant at five responses. Performance appeared more like that observed under fixed-ratio schedules than fixed-interval schedules. Effects of various doses of cocaine given weekly were then determined for each pigeon. A dose that reduced responding was administered prior to each session for 50 days. A reassessment of effects of the range of doses revealed tolerance. The degree of tolerance was similar across components of the multiple schedule. Next, the saline vehicle was administered prior to each session for 50 days to assess the persistence of tolerance. Tolerance diminished in all subjects. Overall, the results suggested that schedule-parameter-dependent tolerance does not depend on the temporal pattern of responding engendered by fixed-ratio schedules.     

Time and rate measures in choice transitions

Three experiments with pigeons studied the relation between time and rate measures of behavior under conditions of changing preference. Experiment 1 studied a concurrent chain schedule with random-interval initial links and fixed-interval terminal links; Experiment 2 studied a multiple chained random-interval fixed-interval schedule; and Experiment 3 studied simple concurrent random-interval random-interval schedules. In Experiment 1, and to a lesser extent in the other two experiments, session-average initial-link wait-time differences were linearly related to session-average response-rate differences. In Experiment 1, and to a lesser extent in Experiment 3, ratios of session-average initial-link wait times and response rates were related by a power function. The weaker relations between wait and response measures in Experiment 2 appear to be due to the absence of competition between responses. In Experiments 1 and 2, initial-link changes lagged behind terminal-link changes. These findings may have implications for the relations between fixed- and variable-interval procedures and suggest that more attention should be paid to temporal measures in studies of free-operant choice.