An algorithm for generating artificial test clusters

An algorithm for generating artificial data sets which contain distinct nonoverlapping clusters is presented. The algorithm is useful for generating test data sets for Monte Carlo validation research conducted on clustering methods or statistics. The algorithm generates data sets which contain either 1, 2, 3, 4, or 5 clusters. By default, the data are embedded in either a 4, 6, or 8 dimensional space. Three different patterns for assigning the points to the clusters are provided. One pattern assigns the points equally to the clusters while the remaining two schemes produce clusters of unequal sizes. Finally, a number of methods for introducing error in the data have been incorporated in the algorithm.     

Where do hypotheses come from?

Why are human inferences sometimes remarkably close to the Bayesian ideal and other times systematically biased? In particular, why do humans make near-rational inferences in some natural domains where the candidate hypotheses are explicitly available, whereas tasks in similar domains requiring the self-generation of hypotheses produce systematic deviations from rational inference. We propose that these deviations arise from algorithmic processes approximating Bayes’ rule. Specifically in our account, hypotheses are generated stochastically from a sampling process, such that the sampled hypotheses form a Monte Carlo approximation of the posterior. While this approximation will converge to the true posterior in the limit of infinite samples, we take a small number of samples as we expect that the number of samples humans take is limited. We show that this model recreates several well-documented experimental findings such as anchoring and adjustment, subadditivity, superadditivity, the crowd within as well as the self-generation effect, the weak evidence, and the dud alternative effects. We confirm the model’s prediction that superadditivity and subadditivity can be induced within the same paradigm by manipulating the unpacking and typicality of hypotheses. We also partially confirm our model’s prediction about the effect of time pressure and cognitive load on these effects.     

How Do Propensity Score Methods Measure Up in the Presence of Measurement Error? A Monte Carlo Study

Considering that the absence of measurement error in research is a rare phenomenon and its effects can be dramatic, we examine the impact of measurement error on propensity score (PS) analysis used to minimize selection bias in behavioral and social observational studies. A Monte Carlo study was conducted to explore the effects of measurement error on the treatment effect and balance estimates in PS analysis across seven different PS conditioning methods. In general, the results indicate that even low levels of measurement error in the covariates lead to substantial bias in estimates of treatment effects and concomitant reduction in confidence interval coverage across all methods of conditioning on the PS.     

Estimation and visualization of confusability matrices from adaptive measurement data

We present a simple but effective method based on Luce’s choice axiom [Luce, R.D. (1959). Individual choice behavior: A theoretical analysis. New York: John Wiley & Sons] for consistent estimation of the pairwise confusabilities of items in a multiple-choice recognition task with arbitrarily chosen choice-sets. The method combines the exact (non-asymptotic) Bayesian way of assessing uncertainty with the unbiasedness emphasized in the classical frequentist approach.We apply the method to data collected using an adaptive computer game designed for prevention of reading disability. A player’s estimated confusability of phonemes (or more accurately, phoneme-grapheme connections) and larger units of language is visualized in an easily understood way with color cues and explicit indication of the accuracy of the estimates. Visualization of learning-related changes in the player’s performance is considered.The empirical validity of the choice axiom is evaluated using the game data itself. The axiom appears to hold reasonably well although a small systematic violation is observable for the smallest choice-set sizes.     

Exact tests for the rasch model via sequential importance sampling

Rasch proposed an exact conditional inference approach to testing his model but never implemented it because it involves the calculation of a complicated probability. This paper furthers Rasch’s approach by (1) providing an efficient Monte Carlo methodology for accurately approximating the required probability and (2) illustrating the usefulness of Rasch’s approach for several important testing problems through simulation studies. Our Monte Carlo methodology is shown to compare favorably to other Monte Carlo methods proposed for this problem in two respects: it is considerably faster and it provides more reliable estimates of the Monte Carlo standard error.This Research was supported in part by National Science Foundation grant DMS-0203762 and a University of Pennsylvania Research Foundation grant.The authors are grateful to Don Burdick for helpful comments. In addition, the authors wish to thank the editor, the associate editor, and the referees for their helpful suggestions.This revised article was published online in August 2005 with the PDF paginated correctly.     

A Bayesian hierarchical model for the measurement of working memory capacity

Working memory is the memory system that allows for conscious storage and manipulation of information. The capacity of working memory is extremely limited. Measurements of this limit, and what affects it, are critical to understanding working memory. Cowan (2001) and Pashler (1988) suggested applying multinomial tree models to data from change detection paradigms in order to estimate working memory capacity. Both Pashler and Cowan suggested simple formulas for estimating capacity with these models. However, in many cases, these simple formulas are inadequate, and may lead to inefficient or biased estimation of working memory capacity. I propose a Bayesian hierarchical alternative to the Pashler and Cowan formulas, and show that the hierarchical model outperforms the traditional formulas. The models are easy to use and appropriate for a wide range of experimental designs. An easy-to-use graphical user interface for fitting the hierarchical model to data is available.     

Enumeration and simulation methods for 0–1 matrices with given marginals

Data in the form of zero-one matrices where conditioning on the marginals is relevant arise in diverse fields such as social networks and ecology; directed graphs constitute an important special case. An algorithm is given for the complete enumeration of the family of all zero-one matrices with given marginals and with a prespecified set of cells with structural zero entries. Complete enumeration is computationally feasible only for relatively small matrices. Therefore, a more useable Monte Carlo simulation method for the uniform distribution over this family is given, based on unequal probability sampling and ratio estimation. This method is applied to testing reciprocity of choices in social networks.The author wishes to thank Cajo ter Braak and John Birks for pointing out the relevance of this subject for ecology; and also Albert Verbeek and Ivo Molenaar, a referee, the Editor, and the Associate Editor for their comments. An earlier version of this paper was presented at the Stockholm Conference on Random Graphs and Applications (April 25–27, 1989), organized with financial support from the Swedish Council of Research in the Humanities and the Social Sciences.     

中介效应的点估计和区间估计:乘积分布法、非参数Bootstrap和MCMC法

针对中介效应ab的抽样分布往往不是正态分布的问题,学者近年提出了三类无需对ab的抽样分布进行任何限制且适用于中、小样本的方法,包括乘积分布法、非参数Bootstrap和马尔科夫链蒙特卡罗(MCMC)方法.采用模拟技术比较了三类方法在中介效应分析中的表现.结果发现:1)有先验信息的MCMC方法的ab点估计最准确;2)有先验信息的MCMC方法的统计功效最高,但付出了低估第Ⅰ类错误率的代价,偏差校正的非参数百分位Bootstrap方法的统计功效其次,但付出了高估第Ⅰ类错误率的代价;3)有先验信息的MCMC方法的中介效应区间估计最准确.结果表明,当有先验信息时,推荐使用有先验信息的MCMC方法;当先验信息不可得时,推荐使用偏差校正的非参数百分位Bootstrap方法.     

EM and beyond

The basic theme of the EM algorithm, to repeatedly use complete-data methods to solve incomplete data problems, is also a theme of several more recent statistical techniques. These techniques—multiple imputation, data augmentation, stochastic relaxation, and sampling importance resampling—combine simulation techniques with complete-data methods to attack problems that are difficult or impossible for EM.A preliminary version of this article was the Keynote Address at the 1987 European Meeting of the Psychometric Society June 24–26, 1987 in Enschede, The Netherlands. The author wishes to thank the editor and reviewers for helpful comments.