An extension of the rasch model for ratings providing both location and dispersion parameters

An elaboration of a psychometric model for rated data, which belongs to the class of Rasch models, is shown to provide a model with two parameters, one characterising location and one characterising dispersion. The later parameter, derived from the idea of a unit of scale, is also shown to reflect the shape of rating distributions, ranging from unimodal, through uniform, and then to U-shaped distributions. A brief case is made that when a rating distribution is treated as a random error distribution, then the distribution should be unimodal.     

Positive and negative contrast as a function of component duration for key pecking and treadle pressing

Pigeons responded on several multiple schedules for food reinforcers. The duration of the components varied from four seconds to 16 minutes. The absolute size of positive (Experiment 1) and negative (Experiment 2) behavioral contrast varied inversely with component duration when key pecks produced the reinforcers. The absolute size of negative contrast varied directly with component duration, when treadle presses produced the reinforcers (Experiment 3). These results conform to theories that suggest that positive and negative contrast are symmetrical when pigeons peck keys. They also conform to theories that suggest that the same principles do not govern contrast when pigeons peck keys as when they press treadles. Finally, the results support the measurement of behavioral contrast by the differences between baseline rates of responding and the rates emitted when contrast is present.     

Relationship between response rate and reinforcement frequency in variable-interval schedules: III. The effect of d-amphetamine.

Four rats were exposed to variable-interval schedules specifying a range of different reinforcement frequencies. The effects of two doses of d-amphetamine (1.6 and 3.2 mumol/kg) upon performance maintained under each schedule were examined. In the case of each rat, the response rates observed under control conditions (no injection or injection of the vehicle alone) were increasing, negatively accelerated functions of reinforcement frequency, the data conforming closely to Herrnstein's (1970) equation. In each rat, d-amphetamine (3.2 mumol/kg) significantly reduced the value of the constant Rmax, which expresses the theoretical maximum response rate. In each rat, the value of KH, which expresses the reinforcement frequency needed to obtain the half-maximal response rate, was also reduced, although this only achieved statistical significance in the case of one rat. When the proportional change in response rate in the presence of the drug was plotted against the response rate under control conditions on double logarithmic co-ordinates, linear functions of negative slope were obtained; in each rat the slope was steeper and the value of the control response rate at which d-amphetamine exerted no effect was lower in the case of the higher dose (3.2 mumol/kg) than in the case of the lower dose (1.6 mumol/kg).     

运用回归旋转设计研究倒摄抑制的实验研究

用回归旋转设计研究倒摄抑制。实验数据最后用二次方程逼近并取得拟合检验的显著性水平(P<0.01)。本实验揭示了(1)影响倒摄抑制的四个因素中,先前材料的学习程度(A)和后继学习材料的长度(C)这两个因素起主要作用。当A足够时,不论C的长短,倒摄抑制相对而言总是最小。这说明A因素起最主要作用;(2)在A足够的前提下,C因素与倒摄抑制成正比函数关系。本研究的成功实验表明,回归旋转设计不仅适用于心理学研究而且能揭示心理现象在多因素共同作用下变化的函数关系。因此,它比心理学研究的传统设计方法又前进了一步。     

The nontruncated marginal of a truncated bivariate normal distribution

Inference is considered for the marginal distribution ofX, when (X, Y) has a truncated bivariate normal distribution. TheY variable is truncated, but only theX values are observed. The relationship of this distribution to Azzalini's skew-normal distribution is obtained. Method of moments and maximum likelihood estimation are compared for the three-parameter Azzalini distribution. Samples that are uniformative about the skewness of this distribution may occur, even for largen. Profile likelihood methods are employed to describe the uncertainty involved in parameter estimation. A sample of 87 Otis test scores is shown to be well-described by this model.     

Randomization-based inference about latent variables from complex samples

Standard procedures for drawing inferences from complex samples do not apply when the variable of interest cannot be observed directly, but must be inferred from the values of secondary random variables that depend on stochastically. Examples are proficiency variables in item response models and class memberships in latent class models. Rubin's multiple imputation techniques yield approximations of sample statistics that would have been obtained, had been observable, and associated variance estimates that account for uncertainty due to both the sampling of respondents and the latent nature of. The approach is illustrated with data from the National Assessment for Educational Progress.This research was supported by Grant No. NIE-G-83-0011 of the Office for Educational Research and Improvement, Center for Education Statistics, and Contract No. N00014-88-K-0304, R&T 4421552 from the Cognitive Sciences Program, Cognitive and Neural Sciences Division, Office of Naval Research. It does not necessarily reflect the views of either agency. I am grateful to R. Darrell Bock for calling my attention to the applicability of multiple imputation to the assessment setting; to Albert Beaton and Eugene Johnson for enlightening discussions on the topic; and to Henry Braun, Ben King, Debra Kline, Gary Phillips, Paul Rosenbaum, Don Rubin, John Tukey, Ming-Mei Wang, Kentaro Yamamoto, Rebecca Zwick, and two anonymous reviewers for comments on earlier drafts. Example 4 is based on the analysis of the 1984 National Assessment for Educational Progress reading survey, carried out at Educational Testing Service through the tireless efforts of too many people to mention by name, under the direction of Albert Beaton, Director of NAEP Data Analyses. David Freund, Bruce Kaplan, and Jennifer Nelson conducted additional analyses of the 1984 and 1988 data for the example.     

Constrained latent class analysis: Simultaneous classification and scaling of discrete choice data

A reparameterization of a latent class model is presented to simultaneously classify and scale nominal and ordered categorical choice data. Latent class-specific probabilities are constrained to be equal to the preference probabilities from a probabilistic ideal-point or vector model that yields a graphical, multidimensional representation of the classification results. In addition, background variables can be incorporated as an aid to interpreting the latent class-specific response probabilities. The analyses of synthetic and real data sets illustrate the proposed method.The authors thank Yosiho Takane, the editor and referees for their valuable suggestions. Authors are listed in reverse alphabetical order.     

The essential process in a family of measurement models

Five members of the Rasch family of latent trait models which have appeared more or less independently in the literature are brought together and identified as one model. In addition to sharing the distinguishing characteristic of the dichotomous Rasch model—separable person and item parameters and hence sufficient statistics—all five models share a common algebraic form and have as their basic element the fundamental process defined by Rasch's simple logistic expression. In these models, the sufficient statistics for person and item parameters are counts of events constructed to be indicative of the variable being measured, and the measures they enable are ‘fundamental’.     

Feedback functions for variable-interval reinforcement

On a given variable-interval schedule, the average obtained rate of reinforcement depends on the average rate of responding. An expression for this feedback effect is derived from the assumptions that free-operant responding occurs in bursts with a constant tempo, alternating with periods of engagement in other activities; that the durations of bursts and other activities are exponentially distributed; and that the rates of initiating and terminating bursts are inversely related. The expression provides a satisfactory account of the data of three experiments.     

Inhibiting function of reinforcement: magnitude effects on variable-interval schedules

In two experiments, the performance of rats under constant-probability and arithmetic variable-interval schedules respectively was compared when the concentration of a liquid reinforcer was varied within sessions; in other sessions, half of the reinforcers were randomly omitted. When the discriminative function of the reinforcer as a signal for a decrease in the probability of reinforcement was attenuated (the constant-probability schedule) the postreinforcement pause duration was nevertheless an increasing function of reinforcer magnitude. This relationship was also present, but more marked, when the temporal discriminative function of the reinforcer was enhanced (the arithmetic schedule). These results suggested that reinforcement has an unconditioned suppressive effect on the reinforced response distinct from any discriminative function it may acquire. The reinforcement-omission effect, where response rate accelerates following omission, was observed when the reinforcer functioned as an effective temporal discriminative stimulus, but not when such temporal control was absent.