Optimal behavior and concurrent variable interval schedules

Behavior maintained with 2-component concurrent variable interval schedules of reinforcement (CONC VIVI) is described well by the matching law. Deviations from matching behavior have been handled by adding free parameters to the matching law equation. With CONC VIVI schedules there are infinitely many solutions to the matching law equation at each value of the procedural parameters. However, at each value of the procedural parameters, only one combination of durations of intervals spent in each VI component (dwell times) yields the combined maximum reinforcement rate. The equations that yield the optimal dwell times solution for CONC VIVI schedules are mathematically incompatible with the matching law. Optimal performance and matching coincide only when the parameter values of the two VI components are equal. It seems reasonable to use optimal behavior to assess performance in these schedules. Researchers have not compared optimal and empirical performances in CONC VIVI possibly because the equations for optimal dwell times (ODT) can be solved only numerically. We present a table of ODT for a wide range of VIs and changeover delays. We also derive a function m that can be used to compare matching data and the matching behavior predictions of optimization. We prove that 0.5<m<1.003502, and we describe some of the more nteresting properties of the function.     

Testing unidimensionality in polytomous Rasch models

A fundamental assumption of most IRT models is that items measure the same unidimensional latent construct. For the polytomous Rasch model two ways of testing this assumption against specific multidimensional alternatives are discussed. One, a marginal approach assuming a multidimensional parametric latent variable distribution, and, two, a conditional approach with no distributional assumptions about the latent variable. The second approach generalizes the Martin-Löf test for the dichotomous Rasch model in two ways: to polytomous items and to a test against an alternative that may have more than two dimensions. A study on occupational health is used to motivate and illustrate the methods.The authors would like to thank Niels Keiding, Klaus Larsen and the anonymous reviewers for valuable comments to a previous version of this paper. This research was supported by a grant from the Danish Research Academy and by a general research grant from Quality Metric, Inc.     

教师压力影响职业倦怠:教学效能感的调节作用

采用问卷法以743名中小学在职教师为被试研究了教学效能感在职业压力影响职业倦怠过程中的调节作用。结果发现:①教师的工作特征、学生等压力源能有效预测教师职业倦怠。随着从业年限的增加,影响职业倦怠的主要压力源从工作特征过渡到社会特征。②教学效能的调节作用因教师不同的人口学分布而异,其中一般教学效能和个体教学效能所表现出来的调节效应也不同。③个体教学效能表现出线性调节作用,一般教学效能表现出曲线调节作用,两种调节作用的性质取决于不同的压力源。     

重参数化多分属性DINA模型的多级评分拓广——基于等级反应模型

多分属性认知诊断模型（CDMs）比传统的二分属性CDMs提供更详细的诊断反馈信息,但现有大部分多分属性CDMs并不具备直接分析多级（或混合）评分数据的功能。本文基于等级反应模型对重参数化多分属性DINA模型进行多级评分拓广,开发一个可处理多级评分数据的等级反应多分属性DINA模型。首先通过实证数据分析呈现新模型的现实可应用性;然后通过模拟研究探究新模型的参数估计返真性。结果表明,新模型满足同时处理多分属性和多级评分数据的现实需求;且具备良好的心理计量学性能,但对测验质量有一定要求（如题目质量较高且测验Qp矩阵具有完备性等）。     

The unique correspondence of the item response function and item category response functions in polytomously scored item response models

The item response function (IRF) for a polytomously scored item is defined as a weighted sum of the item category response functions (ICRF, the probability of getting a particular score for a randomly sampled examinee of ability ). This paper establishes the correspondence between an IRF and a unique set of ICRFs for two of the most commonly used polytomous IRT models (the partial credit models and the graded response model). Specifically, a proof of the following assertion is provided for these models: If two items have the same IRF, then they must have the same number of categories; moreover, they must consist of the same ICRFs. As a corollary, for the Rasch dichotomous model, if two tests have the same test characteristic function (TCF), then they must have the same number of items. Moreover, for each item in one of the tests, an item in the other test with an identical IRF must exist. Theoretical as well as practical implications of these results are discussed.This research was supported by Educational Testing Service Allocation Projects No. 79409 and No. 79413. The authors wish to thank John Donoghue, Ming-Mei Wang, Rebecca Zwick, and Zhiliang Ying for their useful comments and discussions. The authors also wish to thank three anonymous reviewers for their comments.     

Matching, maximizing, and hill-climbing

In simple situations, animals consistently choose the better of two alternatives. On concurrent variable-interval variable-interval and variable-interval variable-ratio schedules, they approximately match aggregate choice and reinforcement ratios. The matching law attempts to explain the latter result but does not address the former. Hill-climbing rules such as momentary maximizing can account for both. We show that momentary maximizing constrains molar choice to approximate matching; that molar choice covaries with pigeons' momentary-maximizing estimate; and that the “generalized matching law” follows from almost any hill-climbing rule.     

Additive conjoint isotonic probabilistic models (ADISOP)

The ISOP-model or model of twodimensional or bi-isotonicity (Scheiblechner, 1995) postulates that the probabilities of ordered response categories increase isotonically in the order of subject ability and item easiness. Adding a conventional cancellation axiom for the factors of subjects and items gives the ADISOP model where the c.d.f.s of response categories are functions of an additive item and subject parameter and an ordinal category parameter. Extending cancellation to the interactions of subjects and categories as well as of items and categories (independence axiom of the category factor from the subject and item factor) gives the CADISOP model (completely additive model) in which the parallel c.d.f.s are functions of the sum of subject, item and category parameters. The CADISOP model is very close to the unidimensional version of the polytomous Rasch model with the logistic item/category characteristic(s) replaced by nonparametric axioms and statistics. The axioms, representation theorems and algorithms for model fitting of the additive models are presented.     

Kernel smoothing approaches to nonparametric item characteristic curve estimation

The option characteristic curve, the relation between ability and probability of choosing a particular option for a test item, can be estimated by nonparametric smoothing techniques. What is smoothed is the relation between some function of estimated examinee ability rankings and the binary variable indicating whether or not the option was chosen. This paper explores the use of kernel smoothing, which is particularly well suited to this application. Examples show that, with some help from the fast Fourier transform, estimates can be computed about 500 times as rapidly as when using commonly used parametric approaches such as maximum marginal likelihood estimation using the three-parameter logistic distribution. Simulations suggest that there is no loss of efficiency even when the population curves are three-parameter logistic. The approach lends itself to several interesting extensions.The author wishes to acknowledge the support of the National Sciences and Engineering Research Council of Canada through grant A320 and the support of Educational Testing Service during his leave there.     

Aftereffects of reinforcement on variable-ratio schedules

On each of variable-ratio 10, 40, and 80 schedules of reinforcement, when rats' lever-pressing rates were stable, the concentration of a liquid reinforcer was varied within sessions. The duration of the postreinforcement pause was an increasing function of the reinforcer concentration, this effect being more marked the higher the schedule parameter. The running rate, calculated by excluding the postreinforcement pause, was unaffected by concentration. The duration of the postreinforcement pause increased with the schedule parameter, but the proportion of the interreinforcement interval taken up by the pause decreased. Consequently, the overall response rate was an increasing function of the schedule parameter; i.e., it was inversely related to reinforcement frequency, contrary to the law of effect. The running rate, however, decreased with the reinforcement frequency, in accord with the law of effect. When 50% of reinforcements were randomly omitted, the postomission pause was shorter than the postreinforcement pause, but the running rate of responses was not affected.     

Effects of magnitude of food reinforcement on free-operant response rates

In Experiment 1 rats were trained to press a lever on a variable-ratio schedule of food presentation and were then exposed to progressively increasing magnitudes of food reinforcement. Response running rates (rates exclusive of the postreinforcement pause) were found to increase as a function of increasing reinforcement magnitudes. The effect of reinforcement magnitude on response rates inclusive of the postreinforcement pause, however, was less pronounced. Increases in the magnitude of reinforcement were also found to increase the length of the postreinforcement pause. Rats in Experiment 2 were trained to respond on a chained differential-reinforcement-of-low-rate variable-ratio schedule, and were exposed to increasing magnitudes of reinforcement as in Experiment 1. Response running rates increased in the variable-ratio component but decreased in the other component of the schedule. The results are discussed with reference to incentive accounts of reinforcement and the action of reinforcement on the response units generated by the operative contingencies.