Choice in a variable environment: effects of unequal reinforcer distributions

Six pigeons were trained in a procedure in which sessions included seven unsignaled components, each offering two pecking keys, and each providing a potentially different reinforcer ratio between the two keys. Across conditions, various combinations of reinforcer ratios and reinforcer-magnitude ratios were used to create unequal reinforcer distributions between the two alternatives when averaged across a session. The results extended previous research using the same basic procedure that had included only reinforcer distributions symmetrical around 1:1. Data analyses suggested that the variables controlling choice operated at a number of levels: First, individual reinforcers had local effects on choice; second, sequences of successive reinforcers obtained at the same alternative (continuations) had cumulative effects; and, third, when these sequences themselves occurred with greater frequency, their effects further cumulated. A reinforcer obtained at the other alternative following a sequence of continuations (a discontinuation) had a large effect and apparently reset choice to levels approximating the sessional reinforcer ratio.     

项目等距呈现过程中的系列位置效应

以中国汉字为材料,利用刘英茂提出的向前和向后联想的方法,证明在不同呈现时间和不同间隔时间条件下,系列位置曲线中首因效应和近因效应性质的分化过程。结果说明,系列位置曲线的近因部分对时间变化更为敏感,表现为绝对记忆的性质。系列位置曲线中首因效应和近因效应性质的分化,取决于项目呈现时间、项目间隔时间和系列包含的项目数。     

Tests of sphericity of normal distributions and the analysis of repeated measures designs

The locally best invariant test statistic for testing sphericity of normal distributions is shown to be a simple function of the Box/Geisser-Greenhouse degrees of freedom correction factor in a repeated measures design. Because of this relationship it provides a more intuitively appealing test of the necessary and sufficient conditions for valid F-tests in repeated measures analysis of variance than the likelihood ratio test. The properties of the two tests are compared and tables of the critical values of the Box/Geisser-Greenhouse correction factor are given.     

Concurrent ratio schedules: Fixed vs. variable response requirements

Rats were trained on concurrent fixed-ratio variable-ratio or concurrent fixed-ratio mixed-ratio schedules of food reinforcement. The variable-ratio schedule was composed of an arithmetic sequence of 11 ratios that averaged 50; the mixed-ratio schedule consisted of equiprobable ratios of 1 and 99. Fixed-ratio values, varied over experimental conditions, included 25, 35, 50, 60, and 99. The proportion of responses and time allocated to the variable- or mixed-ratio schedule increased as the size of the fixed ratio increased. For most subjects, higher proportions of responses and time were maintained on the fixed-ratio schedule at fixed-ratio values of 25 and 35; higher proportions of responses and time were maintained on the variable- or mixed-ratio schedule at fixed-ratio values of 50 or higher. On concurrent variable-ratio fixed-ratio schedules, the tendency for responding to be maintained exclusively by one schedule was related to the difference in local reinforcement rates obtained from those schedules. Exclusive responding was approximated when the difference in local reinforcement rates obtained from those schedules was large; responding was more evenly distributed between the schedules as the difference in the rates at which reinforcement was obtained from each decreased.     

Local response-rate constancy on concurrent variable-interval schedules of reinforcement

Concurrent variable-interval schedules were arranged with a main key that alternated in color and schedule assignment, along with a changeover key on which a small fixed ratio was required to changeover. Acceptable matching was observed with pigeons in two replications, but there was a tendency toward overmatching. Local response rates were found to differ for unequal schedules of a concurrent pair: local response rate was greater for the variable-interval schedule with the smaller average interreinforcement interval, but qualifications based on an interresponse-time analysis were discussed. In a second experiment, two 3-minute variable-interval schedules were arranged concurrently, and the experimental variable was the changeover procedure: either a changeover delay was incurred by each changeover or a small fixed ratio on a changeover key was required to complete a changeover. Changeover delays of 2 and 5 seconds were compared with a fixed-ratio changeover of five responses. The response output on the main key (associated with the variable-interval schedules) was greater when a changeover delay was arranged than when a fixed ratio was required to changeover. A detailed analysis of stripchart records showed that a 2-second delay generated an increased response rate for 3 seconds after a changeover, while the fixed-ratio requirement generated an increased rate during the first second only, followed by a depressed response rate for 2 seconds.     

信度系数与观测分数和潜在特质的相关比

在经典真分数模型中,信度系数R=D(T)/D(X)。通常认为,信度系数与项目反应理论没有什么联系。事实上,信度系数恰好等于考生观测分数与潜在特质分数的非线性相关比η_(xθ)~2=1-MD(x|θ)/D(X),据此我们得出估计信度系数的一种新途径,同时讨论了x、θ的相关系数与相关比η_(xθ)~2的关系。     

Effects of search cost on foraging and feeding: a three-component chain analysis

An experiment determined whether pigeons minimize number of key pecks per food delivery and maintain their baseline intake of food while key pecking on a three-component chain schedule. Pigeons at either 80% or 100% body weight obtained all their food during baseline and contingency sessions. During baseline sessions, pecks on the left and center keys had no consequences; each peck on the right key activated the feeder. During contingency sessions, pigeons key pecked on a three-component chain schedule simulating components of a foraging chain. In the search component either 3, 9 or 15 key pecks (varied parametrically across blocks of sessions) on the left key produced a stimulus on the middle key, indicating an encounter with either the low-cost prey (3 key pecks) or an equally probable high-cost prey (21 key pecks). In the procurement component the pigeon pecked either: (a) the left key once, thus returning to the search component, or (b) the middle key either 3 or 21 times, which activated the right response key. In the handling component one peck on the right key operated the feeder. The pigeons always procured the low-cost prey and minimized the number of key pecks per hopper by procuring the high-cost prey when the search-cost ratio was high (15 key pecks) but not when it was low (3 key pecks). All pigeons maintained their baselines of eating during contingency sessions by key pecking more frequently and eating more efficiently. The 80% body-weight birds produced higher overall rates of key pecking and eating. These results have implications for ecological theories of optimal foraging and for psychological theories of learned performance.     

Stepwise variable selection in factor analysis

It is very important to choose appropriate variables to be analyzed in multivariate analysis when there are many observed variables such as those in a questionnaire. What is actually done in scale construction with factor analysis is nothing but variable selection.In this paper, we take several goodness-of-fit statistics as measures of variable selection and develop backward elimination and forward selection procedures in exploratory factor analysis. Once factor analysis is done for a certain numberp of observed variables (thep-variable model is labeled the current model), simple formulas for predicted fit measures such as chi-square, GFI, CFI, IFI and RMSEA, developed in the field of the structural equation modeling, are provided for all models obtained by adding an external variable (so that the number of variables isp + 1) and for those by deleting an internal variable (so that the number isp – 1), provided that the number of factors is held constant.A programSEFA (Stepwise variable selection in Exploratory Factor Analysis) is developed to actually obtain a list of the fit measures for all such models. The list is very useful in determining which variable should be dropped from the current model to improve the fit of the current model. It is also useful in finding a suitable variable that may be added to the current model. A model with more appropriate variables makes more stable inference in general.The criteria traditionally often used for variable selection is magnitude of communalities. This criteria gives a different choice of variables and does not improve fit of the model in most cases.The URL of the programSEFA is http://koko15.hus.osaka-u.ac.jp/~harada/factor/stepwise/.     

The use of item scores and response times to detect examinees who may have benefited from item preknowledge

According to Wollack and Schoenig (2018, The Sage encyclopedia of educational research, measurement, and evaluation. Thousand Oaks, CA: Sage, 260), benefiting from item preknowledge is one of the three broad types of test fraud that occur in educational assessments. We use tools from constrained statistical inference to suggest a new statistic that is based on item scores and response times and can be used to detect examinees who may have benefited from item preknowledge for the case when the set of compromised items is known. The asymptotic distribution of the new statistic under no preknowledge is proved to be a simple mixture of two χ² distributions. We perform a detailed simulation study to show that the Type I error rate of the new statistic is very close to the nominal level and that the power of the new statistic is satisfactory in comparison to that of the existing statistics for detecting item preknowledge based on both item scores and response times. We also include a real data example to demonstrate the usefulness of the suggested statistic.