Fitting and testing carroll's weighted unfolding model for preferences

A quadratic programming algorithm is presented for fitting Carroll's weighted unfolding model for preferences to known multidimensional scale values. The algorithm can be applied directly to pairwise preferences; it permits nonnegativity constraints on subject weights; and it provides a means of testing various preference model hypotheses. While basically metric, it can be combined with Kruskal's monotone regression to fit ordinal data. Monte Carlo results show that (a) adequacy of true preference recovery depends on the number of data points and the amount of error, and (b) the proportion of data variance accounted for by the model sometimes only approximately reflects true recovery.This study is based on a doctoral dissertation submitted to the University of Illinois at Urbana-Champaign. The author wishes to thank the members of his dissertation committee—Lawrence E. Jones, Chairman, Charles Lewis, Stephen Golding, Ledyard Tucker, and Nancy Wiggins—for their helpful comments.     

Producing a change from competition to sharing: effects of large and adjusting response requirements

Pairs of high-school students matched-to-sample for money. On each trial, the first pair member to complete a fixed ratio of knob-pulling responses could work the matching problem on that trial. Competition occurred when both pair members responded for the problem. Sharing occurred when only one pair member responded on each trial, and the subjects alternated trials. Hence, sharing requires less responding and still allows a moderate number of reinforcers for each subject. Recent research has shown that increasing the response requirement to the point that it may have aversive properties will produce a change from competition to sharing. A related variable is an adjusting schedule that adjusts the subjects' response requirements so that their abilities to take reinforcers are equal. In this way, subjects might learn that competition requires more responding but produces no more reinforcers. However, recent research also suggests that competition decreases over sessions without experimental manipulations. Because of this possibility of a time-related variable, ratio size and an adjusting schedule were studied in a group design. Competition did decrease for all groups over sessions, but the large-ratio groups switched from competition to sharing sooner than the low-ratio groups. The adjusting schedule had a similar but smaller effect.     

Stopping rules for multi-category computerized classification testing

Computerized classification testing (CCT) aims to classify persons into one of two or more possible categories to make decisions such as mastery/non-mastery or meet most/meet all/exceed. A defining feature of CCT is its stopping criterion: the test terminates when there is enough confidence to make a decision. There is abundant research on CCT with a single cut-off, and two common stopping criteria are the sequential probability ratio test (SPRT) statistic and the generalized likelihood ratio statistic (GLR). However, there is a relative scarcity of research extending the SPRT to the multi-hypothesis case for when there is more than one cut-off. In this paper, we propose a new multi-category GLR (mGLR) statistic as well as a stochastically curtailed version of the CCT with three or more categories. A simulation study was conducted to show that the mGLR statistic outperformed the existing stopping rules by generating shorter average test length without sacrificing classification accuracy. Results also revealed that the stochastically curtailed mGLR successfully increased test efficiency in certain testing conditions.     

非符号数量表征和符号分数表征的关系

个体学习符号分数的一个关键是能对其数值形成准确表征。现有研究假设符号分数表征的认知基础是人类自婴幼儿期就具有的非符号数量表征(如表征两个集合各自的数量, 或两个数量的比例)。其证据包括表征非符号数量(尤其是非符号数量比例关系)和表征符号分数在行为和大脑神经活动层面上都表现出相关性。然而要说明非符号数量表征是符号分数表征的认知基础, 还需更多研究表明两者在数量概念上的独特相关和因果联系, 并阐明符号分数表征形成的认知机制。     

Testing two variances for superiority/non-inferiority and equivalence: Using the exhaustion algorithm for sample size allocation with cost

The equality of two group variances is frequently tested in experiments. However, criticisms of null hypothesis statistical testing on means have recently arisen and there is interest in other types of statistical tests of hypotheses, such as superiority/non-inferiority and equivalence. Although these tests have become more common in psychology and social sciences, the corresponding sample size estimation for these tests is rarely discussed, especially when the sampling unit costs are unequal or group sizes are unequal for two groups. Thus, for finding optimal sample size, the present study derived an initial allocation by approximating the percentiles of an F distribution with the percentiles of the standard normal distribution and used the exhaustion algorithm to select the best combination of group sizes, thereby ensuring the resulting power reaches the designated level and is maximal with a minimal total cost. In this manner, optimization of sample size planning is achieved. The proposed sample size determination has a wide range of applications and is efficient in terms of Type I errors and statistical power in simulations. Finally, an illustrative example from a report by the Health Survey for England, 1995–1997, is presented using hypertension data. For ease of application, four R Shiny apps are provided and benchmarks for setting equivalence margins are suggested.     

Assessing depressive symptoms with the Borg centiMax Scale® in a Swedish sample of patients and students

The Borg centiMax Scale, is a psychophysically composed general intensity ratio scale, which could enable more precise inter- and intraindividual comparisons of the intensity of depressive symptoms. In the present study, the properties of the centiMax scale were examined in 38 patients with clinical depression and 109 students. Additionally, preliminary centiMax cut-off scores for mild, moderate and severe depression were estimated. The psychometric properties of the centiMax were found to be satisfactory regarding internal consistency, convergent, discriminative and predictive validity. Moreover, the centiMax was demonstrated to provide meaningful comparisons of symptom intensity, which makes it possible to evaluate the relative importance of individual symptoms in a profile and make more precise comparisons within and between individuals. With regard to intraindividual comparisons, patients rated , for example, the intensity of feeling “guilt” twice as strong as feelings of “being punished,” and the intensity of “loss of pleasure” almost three times as strong as “being punished.” With regard to interindividual comparisons, patients rated e.g., the intensity of “being punished” as 12 times stronger than controls, and the intensity of “worthlessness” about nine times stronger. In conclusion, the centiMax was shown to be reliable and valid for assessing depressive symptoms. The centiMax with level anchored ratio data, appears to be highly advantageous as it permits rather precise values of symptom intensity for intra- and interindividual comparisons that could be useful in the diagnostic process and in treatment planning.     

得失情境下他人参照点及心理距离对自我-他人利益权衡的影响

以福利权衡率(WTR)为利他程度的指标, 通过3个实验逐步深入地考察了得失情境下他人参照点及心理距离对自我-他人利益权衡的影响。实验1的结果表明, 得失情境并未改变被试的WTR。实验2引入他人底线、现状和目标三个参照点变量, 发现被试获益情境下的WTR高于损失情境, 且WTR从高到低依次为他人临近底线、目标和现状; 他人临近底线时, 被试在获益情境下的WTR高于损失情境, 而他人临近现状和目标时, 个体在得失情境下的WTR无显著差异。实验3进一步引入心理距离变量, 发现心理距离较近他人的WTR高于较远他人, 且与得失情境和参照点发生了复杂的交互效应, 得失情境的主效应消失了, 但总体上并未改变实验2发现的参照点效应。这些结果对于更深入地理解得失不对称效应、三参照点理论及社会折扣和自我-他人决策差异研究的相关发现具有一定的启示意义。     

Pitch distribution,melodic contour or both? Modeling makam schema with multidimensional scaling and self-organizing maps

Experienced listeners internalize musical tonal knowledge via statistical learning of pitch distributions as a result of exposure to musical environment. Cross-cultural studies of music cognition offer new perspectives to investigate the acquisition of tonal schema. Makam music is a rich musical system characterized by modal structures defined by micro-tonal pitch sets, and melodic progression patterns (aka seyir features). Makam schema is possibly acquired by internalizing the seyir in addition to pitch features. In the current study, we examined whether an ideal model of makam schema is built with multidimensional scaling analysis and with self-organizing maps (SOMs). We were interested in whether statistical information about seyir features, in addition to pitch distributions, would form an acceptable makam schema model. We qualitatively analyzed topographical organizations in the models to understand whether they reflect complex relations between makams. Multidimensional scaling analyses did not produce an acceptable model for makam schema. The SOM trained with pitch distributions provided an adequate model for makam schema. However, the SOM trained with both pitch distributions and seyir features was better in capturing the complex relations between makams. Further behavioral research is necessary to understand whether melodic progression patterns are intrinsic features of the tonal knowledge of the experienced listeners of makam music.     

Drug discrimination under concurrent variable-ratio variable-ratio schedules

Pigeons were trained to discriminate 5 mg/kg pentobarbital from saline under concurrent variable-ratio (VR) VR schedules, in which responses on the pentobarbital-biased lever were reinforced under the VR schedule with the smaller response requirements when pentobarbital was given before the session, and responses on the saline-biased key were reinforced under the VR schedule with the larger response requirements. When saline was administered before the session, the reinforcement contingencies associated with the two response keys were reversed. When responding stabilized under concurrent VR 20 VR 30, concurrent VR 10 VR 40, or concurrent VR 5 VR 50 schedules, pigeons responded almost exclusively on the key on which fewer responses were required to produce the reinforcer. When other doses of pentobarbital and other drugs were substituted for the training dose, low doses of all drugs produced responding on the saline-biased key. Higher doses of pentobarbital and chlordiazepoxide produced responding only on the pentobarbital-biased key, whereas higher doses of ethanol and phencyclidine produced responding only on this key less often. d-Amphetamine produced responding primarily on the saline-biased key. When drugs generalized to pentobarbital, the shape of the generalization curve under concurrent VR VR schedules was more often graded than quantal in shape. Thus, drug discrimination can be established under concurrent VR VR schedules, but the shapes of drug-discrimination dose-response curves under concurrent VR VR schedules more closely resemble those seen under interval schedules than those seen under fixed-ratio schedules. Graded dose-response curves under concurrent VR VR schedules may relate to probability matching and difficulty in discriminating differences in reinforcement frequency.     

Progressive-ratio schedules: effects of later schedule requirements on earlier performances

Four rats were studied with variants of a progressive-ratio schedule with a step size of 6 in which different terminal components followed completion of the 20th ratio: (a) a reversal of the progression, (b) a fixed-ratio 6 schedule, or (c) extinction. Responding in the progressive-ratio components of these schedules was compared to performances under conventional progressive-ratio baselines. Under baseline conditions, postreinforcement pauses increased exponentially as a function of increasing ratio size, whereas running rates showed modest declines. The procedure of linking the progressive-ratio schedule to the reversed progression or to the fixed-ratio component resulted in decreased pausing. Linking the progressive-ratio schedule to the extinction component had the opposite effect, that of producing weakened progressive-ratio performances as evidenced by increased pausing. Subjects whose responses were reinforced on half of the ratios also showed exponential increases; however, pauses were substantially shorter following ratios on which the reinforcer was omitted. The results suggested that progressive-ratio pausing reflects the influence of remote as well as local contingencies.