Item Response Theory with Estimation of the Latent Population Distribution Using Spline-Based Densities

The purpose of this paper is to introduce a new method for fitting item response theory models with the latent population distribution estimated from the data using splines. A spline-based density estimation system provides a flexible alternative to existing procedures that use a normal distribution, or a different functional form, for the population distribution. A simulation study shows that the new procedure is feasible in practice, and that when the latent distribution is not well approximated as normal, two-parameter logistic (2PL) item parameter estimates and expected a posteriori scores (EAPs) can be improved over what they would be with the normal model. An example with real data compares the new method and the extant empirical histogram approach.     

Lakatos’s Challenge? Auxiliary Hypotheses and Non-Monotonous Inference

Summary  Gerhard Schurz [2001, Journal for General Philosophy of Science, 32, 65–107] has proposed to reconstruct auxiliary hypothesis addition, e.g., postulation of Neptune to immunize Newtonian mechanics, with concepts from non-monotonous inference to avoid the retention of false predictions that are among the consequence-set of the deductive model. However, the non-monotonous reconstruction retains the observational premise that is indeed rejected in the deductive model. Hence, his proposal fails to do justice to Lakatos’ core-belt model, therefore fails to meet what Schurz coined “Lakatos’ challenge”. It is argued that Lakatos’s distinction between core and belt of a research program is not mapable onto premise-set and consequence-set and that Schurz’s understanding of a ceteris paribus clause as a transfinite list of (absent) interfering factors is problematic. I propose a simple reading of Lakatos’s use of the term ceteris paribus clause and motivate why the term hypothesis addition, despite not being interpretable literally, came to be entrenched.

It is not that we propose a theory and Nature may shout NO; rather we propose a maze of theories and Nature may shout INCONSISTENT. Lakatos (1978, p. 45)

     

存在问题的逻辑语言维度

存在问题在分析哲学的背景下取得了深入细致的研究成果。在“何谓存在”问题上,围绕“存在”是不是个体的属性从而是不是逻辑谓词的争论呈现出三派观点:弗雷格、罗素等从一阶逻辑出发,认为“存在”不是逻辑谓词,而是量词;皮尔士、斯特劳森等结合精致的自然语言分析,认为“存在”在某些特殊情况下表达了个体的属性,是一种特殊的谓词;自由逻辑学家则从自由逻辑的角度给出了肯定的答案。在“何物存在”问题上,蒯因“存在就是约束变项的值”的本体论承诺标准机智地揭示了存在问题的语言学实质。可以说,利用一阶逻辑解释存在问题的方法是比较成功的。如果将弗雷格、罗素的一阶语言扩展到高阶语言,则既能与蒯因的理论连贯一致,又能避免无谓的“存在”本体论纷争。这种做法的结果是“存在”具有了层次性的特征。掌握一定的逻辑学基础知识,有助于我们深入研究西方哲学。     

Maximizing present value: A model to explain why moderate response rates obtain on variable-interval schedules

In Phases 1 and 3, two Japanese monkeys responded on a multiple variable-ratio 80 variable-interval X schedule, where the value of X was adjusted to ensure equal between-schedule reinforcement rates. Components strictly alternated following the delivery of a food pellet, and each session ended following 50 components. Phase 2 differed from the others only in that the 50 pellets previously earned during the session were delivered together at session's end. Variable-ratio response rates did not decrease across phases, but variable-interval response rates decreased substantially during the Phase 2 procedure. This rate decrease was attributed to the food-at-session's-end manipulation removing the greater immediacy of reinforcement provided by short interresponse times relative to long interresponse times. Without this time preference for short interresponse times, the variable-interval interresponse-time reinforcement feedback function largely controlled response emission, dictating a response-rate reduction. This result was explained in terms of the economic notion of “maximizing present value.”     

Discriminative properties of briefly presented stimuli

In Experiment I, pigeons' responses produced food according to a fixed-interval schedule while responses on the key also produced brief stimuli according to a variable-interval schedule. Each brief stimulus reset the fixed interval. Thus, a brief stimulus occurred irregularly but a fixed minimum time separated the occurrence of food from a brief stimulus. Pauses followed brief stimuli and were followed by an accelerated response rate until another brief stimulus or food occurred. In Experiment II, four control procedures were examined. (1) Brief-stimulus presentations were omitted, producing a loss of response patterning. (2) A second-order schedule was studied with fixed-interval components. This schedule produced patterning following brief stimuli similar in kind and degree to that found in Experiment I. (3) A conjoint schedule was arranged in which food was no longer separated from the stimulus by a fixed time; pauses following the stimulus no longer resulted. (4) A brief food reinforcer replaced the brief visual stimulus, resulting in a constant response rate with no pausing following the brief food stimulus. The results suggest that the brief-stimulus effects were due to discriminative functions produced by the fixed temporal relation separating the stimulus from food.     

Schedule-induced defecation.

Excessive defecation, typically considered to be a concomitant of stress, was experimentally induced or eliminated under specific schedules of positive reinforcement of lever pressing by rats. The schedules were, by and large, those under which polydipsia is typically induced. In the first of three experiments, rats under fixed-interval 32-second schedules and variable interval 32-second schedules for food and water reinforcers defecated profusely, but not under fixed-interval one-second schedules or other small interval schedules. Somewhat higher rates of defecation were observed on variable interval 32-second schedules than on fixed-interval 32-second schedules. In a second experiment, fixed-ratio schedules were used, some of which resulted in responding such that reinforcement densities were similar to those on the interval schedules that induced defecation. Defecation was not systematically induced by these ratio schedules. In a third experiment, fixed-time schedules of food presentations were utilized. High rates of defecation were induced comparable to those induced by interval schedules of the same time parameter. No other behavior commonly termed "emotional" was observed in any of these experiments.     

A COMPARISON OF THE EFFECTS OF FIXED AND VARIABLE RATIO SCHEDULES OF REINFORCEMENT ON THE BEHAVIOR OF DEAF CHILDREN

The performance of all five students in an adjustment class for deaf children was compared under fixed and variable ratio schedules of reinforcement. During the fixed ratio (FR) condition, students earned checks if they were attentive and did not engage in disruptive behavior. These checks could be exchanged for the opportunity to draw a prize from a grab bag. During the variable ratio (VR) condition, they earned a draw from the grab bag according to a variable ratio schedule with a mean ratio equal to the value of the preceding FR schedule. During the VR condition, students visually attended more and engaged in disruptive behavior less often than during the FR condition. The number of math problems completed per minute was also higher during the VR condition although no specific consequences were applied to math performance.     

Generalized bilinear models

Generalized bilinear models are presented for the statistical analysis of two-way arrays. These models combine bilinear models and generalized linear modeling, and yield a family of models that includes many existing models, as well as suggest other potentially useful ones. This approach both unifies and extends models for two-way arrays, including the ability to treat response and explanatory variables differently in the models, and the incorporation of external information about the variables directly into the analysis. A unifying framework for the generalized bilinear models is provided by considering four particular cases which have been proposed and used in the existing statistical literature. A three-step procedure is proposed to analyze data sets by generalized bilinear models. Two data sets of different nature are analyzed.     

Points of view analysis revisited: Fitting multidimensional structures to optimal distance components with cluster restrictions on the variables

Points of view analysis (PVA), proposed by Tucker and Messick in 1963, was one of the first methods to deal explicitly with individual differences in multidimensional scaling, but at some point was apparently superceded by the weighted Euclidean model, well-known as the Carroll and Chang INDSCAL model. This paper argues that the idea behind points of view analysis deserves new attention, especially as a technique to analyze group differences. A procedure is proposed that can be viewed as a streamlined, integrated version of the Tucker and Messick Process, which consisted of a number of separate steps. At the same time, our procedure can be regarded as a particularly constrained weighted Euclidean model. While fitting the model, two types of nonlinear data transformations are feasible, either for given dissimilarities, or for variables from which the dissimilarities are derived. Various applications are discussed, where the two types of transformation can be mixed in the same analysis; a quadratic assignment framework is used to evaluate the results.The research of the first author was supported by the Royal Netherlands Academy of Arts and Sciences (KNAW); the research of the second author by the Netherlands Organization for Scientific Research (NWO Grant 560-267-029). An earlier version of this paper was presented at the European Meeting of the Psychometric Society, Leuven, 1989. We wish to thank Willem J. Heiser for his stimulating comments to earlier versions of this paper, and we are grateful to the Editor and anonymous referees for their helpful suggestions.