A model for repeat trial product tests

A non-forced choice model is developed that describes subject behavior on repeat trial discrimination tests of the pick 1 ofk form. The model is developed from the Dirichlet distribution, and it allows for the derivation of individual true scores and of sampling properties for various constructs of interest. These results permit the analysis and comparison of test designs. The model is applied to issues such as forced vs. non-forced choice formats, the best number of alternatives at a choice point, and the selection of expert panels.     

Differential effects of pentobarbital and cocaine on punished and nonpunished responding.

Similar rates of punished and nonpunished responding, maintained with equated rates of reinforcement, were established in pairs of rats. One subject of each pair was exposed to a random-ratio schedule of food presentation. The interreinforcement intervals for this subject comprised the intervals of a random-interval schedule of reinforcement for the other (yoked) rat. The random-ratio schedule maintained rates of responding higher than those maintained by the same rate of reinforcement schedule according to the yoked random-interval contingency. A random-ratio schedule of electric foot shock added to the random-ratio schedule of food presentation suppressed rates of responding such that similar rates of responding were observed in rats of both groups. Pentobarbital (3.0 to 17.0 mg/kg) increased punished responding at doses that had little effect on or decreased nonpunished responding, whereas cocaine (5.6 to 30 mg/kg) increased nonpunished responding at doses that decreased or did not alter punished responding. Qualitatively different effects of pharmacological agents on punished and nonpunished responding can be obtained using procedures that generate similar rates and temporal patterns of punished and nonpunished responding. The effects of pentobarbital and cocaine on responding can be determined by factors other than simply the baseline rate of responding.     

Logit models and logistic regressions for social networks: I. An introduction to Markov graphs andp

Spanning nearly sixty years of research, statistical network analysis has passed through (at least) two generations of researchers and models. Beginning in the late 1930's, the first generation of research dealt with the distribution of various network statistics, under a variety of null models. The second generation, beginning in the 1970's and continuing into the 1980's, concerned models, usually for probabilities of relational ties among very small subsets of actors, in which various simple substantive tendencies were parameterized. Much of this research, most of which utilized log linear models, first appeared in applied statistics publications.But recent developments in social network analysis promise to bring us into a third generation. The Markov random graphs of Frank and Strauss (1986) and especially the estimation strategy for these models developed by Strauss and Ikeda (1990; described in brief in Strauss, 1992), are very recent and promising contributions to this field. Here we describe a large class of models that can be used to investigate structure in social networks. These models include several generalizations of stochastic blockmodels, as well as models parameterizing global tendencies towards clustering and centralization, and individual differences in such tendencies. Approximate model fits are obtained using Strauss and Ikeda's (1990) estimation strategy.In this paper we describe and extend these models and demonstrate how they can be used to address a variety of substantive questions about structure in social networks.This research was supported by grants from the Australian Research Council and the National Science Foundation (#SBR93-10184). This paper was presented at the 1994 Annual Meeting of the Psychometric Society, Champaign, Illinois, June 1994. Special thanks go to Sarah Ardu for programming assistance, Laura Koehly and Garry Robins for help with this research, and to Shizuhiko Nishisato and three reviewers for their comments. INTERNETemail addresses:pattison@psych.unimelb.edu.au (PP);stanwass@uiuc.edu (SW). Affiliations: Department of Psychology, University of Melbourne (PP); Department of Psychology, Department of Statistics, and The Beckman Institute for Advanced Science and Technology, University of Illinois (SW).     

Testing the conditional independence and monotonicity assumptions of item response theory

When item characteristic curves are nondecreasing functions of a latent variable, the conditional or local independence of item responses given the latent variable implies nonnegative conditional covariances between all monotone increasing functions of a set of item responses given any function of the remaining item responses. This general result provides a basis for testing the conditional independence assumption without first specifying a parametric form for the nondecreasing item characteristic curves. The proposed tests are simple, have known asymptotic null distributions, and possess certain optimal properties. In an example, the conditional independence hypothesis is rejected for all possible forms of monotone item characteristic curves.The author acknowledges Paul W. Holland for valuable conversations on the subject of this paper; Henry Braun and Fred Lord for comments at a presentation on this subject which led to improvements in the paper; Carl H. Haag for permission to use the data in §4; Bruce Kaplan for assistance with computing; and two referees for helpful suggestions. Requests for reprints should be sent to Paul R. Rosenbaum     

Monte Carlo studies in nonmetric scaling

In response to Arabie several random ranking studies are compared and discussed. Differences are typically very small, however it is noted that those studies which used arbitrary configurations tend to produce slightly higher stress values. The choice of starting configuration is discussed and we suggest that the use of a principal components decomposition of the doubly centered matrix of dissimilarities, or some transformation thereof, will yield an initial configuration which is superior to a randomly chosen one.This research was supported by the National Research Council of Canada (Grant No. A8351) and by the National Institute of Mental Health (Grant Nos. MH10006 and MH26504). The authorship order has been determined by Monte Carlo methods.     

A modified beta binomial model with applications to multiple choice and taste tests

A modified beta binomial model is presented for use in analyzing ramdom guessing multiple choice tests and certain forms of taste tests. Detection probabilities for each item are distributed beta across the population subjects. Properties for the observable distribution of correct responses are derived. Two concepts of true score estimates are presented. One, analogous to Duncan's empirical Bayes posterior mean score, is appropriate for assessing the subject's performance on that particular test. The second is more suitable for predicting outcomes on similar tests.This research was made possible by a grant from the Center for Food Policy Research, Graduate School of Business, Columbia University.     

随机截距潜在转变分析(RI-LTA)——个案自我转变与个案间差异的分离

传统的潜在转变分析属于单水平分析, 但其同样也可以看作二水平分析。Muthén和Asparouhov就以二水平分析的视角在单水平分析框架内提出了随机截距潜在转变分析(RI-LTA), 其中跨时间点产生的自我转变可以看作在水平1进行分析, 跨时间点不变的个案间差异可以看作在水平2进行分析, 使个案的自我转变和个案间的初始差异分离, 避免了高估保留在初始类别的概率。某研究型大学2016级本科生的追踪调查数据被用于演示使用随机截距潜在转变分析的过程。该方法的最大优势是通过引入随机截距避免了高估保留在本类别的转变概率。未来研究可以运用蒙特卡洛模拟研究探究随机截距潜在转变分析模型的适用性, 也可以用多水平分析的思路为灵感, 探究多水平随机截距潜在转变分析在统计软件中的实现。     

Estimation of a Latent Variable Regression Growth Curve Model for Individuals Cross-Classified by Clusters

The cross-classified multiple membership latent variable regression (CCMM-LVR) model is a recent extension to the three-level latent variable regression (HM3-LVR) model which can be utilized for longitudinal data that contains individuals who changed clusters over time (for instance, student mobility across schools). The HM3-LVR model can include the initial status on growth effect as varying across those clusters and allows testing of more flexible hypotheses about the influence of initial status on growth and of factors that might impact that relationship, but only in the presence of pure clustering of participants within higher-level units. This Monte Carlo study was conducted to evaluate model estimation under a variety of conditions and to measure the impact of ignoring cross-classified data when estimating the incorrectly specified HM3-LVR model in a scenario in which true values for parameters are known. Furthermore, results from a real-data analysis were used to inform the design of the simulation. Overall, it would be recommended for researchers to utilize the CCMM-LVR model over the HM3-LVR model when individuals are cross-classified, and to use a bare minimum of more than 100 clustering units in order to avoid overestimation of the level-3 variance component estimates.     

Dynamic probability of reinforcement for cooperation: Random game termination in the centipede game

Experimental games have previously been used to study principles of human interaction. Many such games are characterized by iterated or repeated designs that model dynamic relationships, including reciprocal cooperation. To enable the study of infinite game repetitions and to avoid endgame effects of lower cooperation toward the final game round, investigators have introduced random termination rules. This study extends previous research that has focused narrowly on repeated Prisoner's Dilemma games by conducting a controlled experiment of two‐player, random termination Centipede games involving probabilistic reinforcement and characterized by the longest decision sequences reported in the empirical literature to date (24 decision nodes). Specifically, we assessed mean exit points and cooperation rates, and compared the effects of four different termination rules: no random game termination, random game termination with constant termination probability, random game termination with increasing termination probability, and random game termination with decreasing termination probability. We found that although mean exit points were lower for games with shorter expected game lengths, the subjects' cooperativeness was significantly reduced only in the most extreme condition with decreasing computer termination probability and an expected game length of two decision nodes.