项目反应理论多级记分模型参数估计的实现

项目反应理论中参数估计程序的实现,一直是研究现代测量理论的学者们关注的问题。该研究从理论上探讨了多级模型参数估计的实现途径,并模拟了5批不同数量及分布情形的项目及被试参数,生成相应的原始得分矩阵,对自编程序及国际流行的相关程序进行了严格的比较校验,验证结果证明本程序具有精确、稳定的性能,并且发现被试量太少将影响参数估计的精确性及稳定性     

教育和心理研究中的多层线性模型

多层线性模型是分析具有层次结构数据的一种新型统计分析技术,与传统统计方法相比,具有模型假设与实际更吻合、结果解释更合理等特点。近年来这一方法的应用逐渐在社会科学的研究中受到重视。文章从多层线性模型的基本假设入手,较系统地介绍了模型参数估计和假设检验的方法,并通过一个具体例子将这一方法与传统回归分析方法相比,进一步说明了多层线性模型在分析具有层次结构数据时的优点。     

Oral drug self-administration in rhesus monkeys: interactions between drug amount and fixed-ratio size.

During daily 3-hr sessions, 5 rhesus monkeys drank drug solutions and water that were concurrently available. The drug solutions were: 1 milligram per milliliter (mg/mL) pentobarbital (2 monkeys), 1 mg/mL pentobarbital plus 0.5% ethanol (1 monkey), 1 mg/mL pentobarbital plus 1% ethanol (1 monkey), and 8% ethanol (1 monkey). The drug solution and water were available under identical two-component tandem fixed-ratio continuous-reinforcement N schedules. Two variables were manipulated: the size of the fixed-ratio component and the number of liquid deliveries (N) in the second component. Deliveries of the drug solution maintained higher rates of responding than did deliveries of the drug vehicle, water. The number of drug deliveries per session increased with increases in the number of deliveries per fixed ratio and decreased with increases in fixed-ratio size. Analysis of the results in terms of the proportion of deliveries to responses showed that the number of drug deliveries per session was directly related to the size of this quotient. Finally, when fixed-ratio size was repeatedly doubled, the following orderly relationship emerged: The greater the number of available drug deliveries per fixed ratio, the less was the percent decrease in the number of fixed ratios completed per session. It was concluded that increases in the number of liquid deliveries per fixed ratio resulted in increases in reinforcing efficacy.     

A constrained spline estimator of a hazard function

A constrained quadratic spline is proposed as an estimator of the hazard function of a random variable. A maximum penalized likelihood procedure is used to fit the estimator to a sample of psychological response times. The results of a small simulation study suggest that, with a sample size of 500, the procedure may provide a reasonably precise estimate of the shape of a hazard function.This research was conducted under the auspices of the Naval Postgraduate School during the author's sabbatical from Vanderbilt University and was partially supported by the Navy Personnal Research and Development Center. The author wishes to thank Jules Borack, Richard Sorenson, and two anonymous reviewers for a number of useful and stimulating comments on the work reported here. Thanks are also due to David Kohfeld for providing the data which were used in the empirical example.     

Bayesian estimation in the three-parameter logistic model

A joint Bayesian estimation procedure for the estimation of parameters in the three-parameter logistic model is developed in this paper. Procedures for specifying prior beliefs for the parameters are given. It is shown through simulation studies that the Bayesian procedure (i) ensures that the estimates stay in the parameter space, and (ii) produces better estimates than the joint maximum likelihood procedure as judged by such criteria as mean squared differences between estimates and true values. The research reported here was performed pursuant to Grant No. N0014-79-C-0039 with the Office of Naval Research. A related article by Robert J. Mislevy (1986) appeared when the present paper was in the printing stage.     

Model modification

An analysis of empirical data often leads to a rejection of a hypothesized model, even if the researcher has spent considerable efforts in including all available information in the formulation of the model. Thus, the researcher must reformulate the model in some way, but in most instances there is, at least theoretically, an overwhelming number of possible actions that could be taken. In this paper a modification index will be discussed which should serve as a guide in the search for a better model. In statistical terms, the index measures how much we will be able to reduce the discrepancy between model and data, as defined by a general fit function, when one parameter is added or freed or when one equality constraint is relaxed. The modification index discussed in this paper is an improvement of the one incorporated in the LISREL V computer program in that it takes into account changes in all the parameters of the model when one particular parameter is freed.The research reported in this paper has been supported by The Swedish Council for Research in the Humanities and Social Sciences under Research Program Multivariate Statistical Analysis, Project Director Karl G Jöreskog.     

Sizing Things Up: Colloquial Reflection as Practical Wisdom

This essay reintroduces Rhetoric as the principle art for giving emphasis and importance to contested matters; in other words, for making things matter. In a speculative reading of the Aristotelian rhetorical tradition, Aristotle's interpretations of magnitude, contengency and practical wisdom are critically examined from both an aesthetic and an ethical-political point of view. The concluding discussion attempts to apply these same concepts to a growing dilemma in the present age. The dilemma is that monumental changes in scale have all but eroded the prospects for engaged encounters with contemporary contingency. It remains the challenge of rhetorical practice to reframe actions and events so that they and we may hold some hope for an engaged civic life.     

On robust estimation of effect size under semiparametric models

Estimation of effect size is of interest in many applied fields such as Psychology, Sociology and Education. However there are few nonparametric estimators of effect size proposed in the existing literature, and little is known about the distributional characteristics of these estimators. In this article, two estimators based on the sample quantiles are proposed and studied. The first one is the estimator suggested by Hedges and Olkin (see page 93 of Hedges & Olkin, 1985) for the situation where a treatment effect is evaluated against a control group (Case A). A modified version of the robust estimator by Hedges and Olkin is also proposed for the situation where two parallel treatments are compared (Case B). Large sample distributions of both estimators are derived. Their asymptotic relative efficiencies with respect to the normal maximum likelihood estimators under several common distributions are evaluated. The robust properties of the proposed estimators are discussed with respect to the sample-wise breakdown points proposed by Akritas (1991). Simulation studies are provided in which the performing characteristics of the proposed estimator are compared to that of the nonparametric estimators by Kraemer and Andrews (1982). Interval estimation of the effect sizes is also discussed. In an example, interval estimates for the data set in Kraemer and Andrews (1982) are calculated for both cases A and B.     

Weighted least squares fitting using ordinary least squares algorithms

A general approach for fitting a model to a data matrix by weighted least squares (WLS) is studied. This approach consists of iteratively performing (steps of) existing algorithms for ordinary least squares (OLS) fitting of the same model. The approach is based on minimizing a function that majorizes the WLS loss function. The generality of the approach implies that, for every model for which an OLS fitting algorithm is available, the present approach yields a WLS fitting algorithm. In the special case where the WLS weight matrix is binary, the approach reduces to missing data imputation.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the author.     

Relative reinforcer magnitude under a nonindependent concurrent schedule of cocaine reinforcement in rhesus monkeys.

Lever pressing by three rhesus monkeys was maintained under a two-lever concurrent schedule of cocaine reinforcement. Responding on one lever (constant-dose lever) produced a constant dose of 0.05 or 0.1 mg/kg/injection arranged according to a variable-interval 1-min schedule. Responding on the other lever (variable-dose lever) produced a comparison dose of cocaine (0.013 to 0.8 mg/kg/injection), also under a variable-interval 1-min schedule. The two variable-interval schedules were made nonindependent by arranging that the assignment of a reinforcer by one schedule inactivated the second schedule until the assigned reinforcer had been obtained. This modification ensured that the two cocaine doses were obtained with approximately equal frequency, regardless of the distribution of the subject's responding. Preference, indicated by relative response frequency on the variable-dose lever, was almost always for the larger of the doses and was a monotonic function of the comparison dose, except at the highest doses. Preferences at the highest comparison doses may have resulted from the low overall response rates exhibited at these doses. Relative response frequencies on the variable-dose lever roughly matched relative reinforcer magnitude (mg/kg/injection available on the variable-dose lever divided by the sum of mg/kg/injections available on each lever).