Logistic加权模型的理论构建与模拟分析

试题难度、试题考查重要性程度加权是多级记分试题的两个基本属性, 因而在IRT项目特征函数中需用不同参数来表示。以往多级记分模型用多个难度参数来描述多级记分试题的难度, 不能有效的表达多级记分试题的分数权重作用。从多级记分试题的分数加权作用角度, 本文提出Logistic加权模型并论述了理论构建思想。在Logistic加权模型下对项目参数估计的EM算法进行推导并编写了相应的参数估计程序。在Logistic加权模型下进行测验模拟, 发现项目参数估计的模拟返真性能良好。     

A Monte Carlo simulation study of the reliability of intraindividual variability

Recent research has seen intraindividual variability become a useful technique to incorporate trial-to-trial variability into many types of psychological studies. Intraindividual variability, as measured by individual standard deviations (ISDs), has shown unique prediction to several types of positive and negative outcomes (Ram, Rabbit, Stollery, & Nesselroade, 2005). One unanswered question regarding measuring intraindividual variability is its reliability and the conditions under which optimal reliability is achieved. Monte Carlo simulation studies were conducted to determine the reliability of the ISD as compared with the intraindividual mean. The results indicate that ISDs generally have poor reliability and are sensitive to insufficient measurement occasions, poor test reliability, and unfavorable amounts and distributions of variability in the population. Secondary analysis of psychological data shows that use of individual standard deviations in unfavorable conditions leads to a marked reduction in statistical power, although careful adherence to underlying statistical assumptions allows their use as a basic research tool. (PsycINFO Database Record (c) 2012 APA, all rights reserved).     

Testing for robustness in Monte Carlo studies

Monte Carlo studies provide the information needed to help researchers select appropriate analytical procedures under design conditions in which the underlying assumptions of the procedures are not met. In Monte Carlo studies, the 2 errors that one could commit involve (a) concluding that a statistical procedure is robust when it is not or (b) concluding that it is not robust when it is. In previous attempts to apply standard statistical design principles to Monte Carlo studies, the less severe of these errors has been wrongly designated the Type I error. In this article, a method is presented for controlling the appropriate Type I error rate; the determination of the number of iterations required in a Monte Carlo study to achieve desired power is described; and a confidence interval for a test's true Type I error rate is derived. A robustness criterion is also proposed that is a compromise between W. G. Cochran's (1952) and J. V. Bradley's (1978) criteria.     

Bootstrap scree tests: A Monte Carlo simulation and applications to published data

A non‐parametric procedure for Cattell's scree test is proposed, using the bootstrap method. Bentler and Yuan developed parametric tests for the linear trend of scree eigenvalues in principal component analysis. The proposed method is for cases where parametric assumptions are not realistic. We define the break in the scree trend in several ways, based on linear slopes defined with two or three consecutive eigenvalues, or all eigenvalues after the k largest. The resulting scree test statistics are evaluated under various data conditions, among which Gorsuch and Nelson's bootstrap CNG performs best and is reasonably consistent and efficient under leptokurtic and skewed conditions. We also examine the bias‐corrected and accelerated bootstrap method for these statistics, and the bias correction is found to be too unstable to be useful. Using seven published data sets which Bentler and Yuan analysed, we compare the bootstrap approach to the scree test with the parametric linear trend test.     

A Monte Carlo evaluation of tests for comparing dependent correlations

The authors conducted a Monte Carlo simulation of 8 statistical tests for comparing dependent zero-order correlations. In particular, they evaluated the Type I error rates and power of a number of test statistics for sample sizes (Ns) of 20, 50, 100, and 300 under 3 different population distributions (normal, uniform, and exponential). For the Type I error rate analyses, the authors evaluated 3 different magnitudes of the predictor-criterion correlations (rho(y,x1) = rho(y,x2) = .1, .4, and .7). For the power analyses, they examined 3 different effect sizes or magnitudes of discrepancy between rho(y,x1) and rho(y,x2) (values of .1, .3, and .6). They conducted all of the simulations at 3 different levels of predictor intercorrelation (rho(x1,x2) = .1, .3, and .6). The results indicated that both Type I error rate and power depend not only on sample size and population distribution, but also on (a) the predictor intercorrelation and (b) the effect size (for power) or the magnitude of the predictor-criterion correlations (for Type I error rate). When the authors considered Type I error rate and power simultaneously, the findings suggested that O. J. Dunn and V. A. Clark's (1969) z and E. J. Williams's (1959) t have the best overall statistical properties. The findings extend and refine previous simulation research and as such, should have greater utility for applied researchers.     

An optimized facial stimuli paradigm for hybrid SSVEP+P300 brain computer interface

In this paper, hybrid BCI that merges Event Related Potentials (P300) and Steady State visual Evoked Potentials (SSVEP) simultaneously is proposed to enhance the performance of Four-choice command system. Here we integrate human facial structure in external visual stimulus to evoke stronger cortical responses in hybrid SSVEP+P300 BCI & compare it with non-face stimuli. We also addressed question of feasibility of eliciting one potential by face & other by non-face stimuli. To evoke SSVEP & P300 responses, paradigms with non-face stimuli, neutral face stimuli, and facial expression changes stimuli are proposed. We also projected additional paradigm where SSVEP is elicited by non-face and P300 by flashing different facial expressions. Results proved the last paradigm evoke stronger cortical potentials and thereby improve system accuracy and ITR than other paradigms. Author discussed external stimulus parameters that might affect simultaneous evocation of multiple brain potentials and their deterioration effect on individual potentials.     

Monte Carlo Evaluation of Two-Level Logistic Regression for Assessing Person Fit

Person fit is the degree to which an item response model fits for individual examinees. Reise (2000) Reise, S. P. 2000. Using multilevel logistic regression to evaluate person-fit in IRT models. Multivariate Behavioral Research, 35: 543–568. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar] described how two-level logistic regression can be used to detect heterogeneity in person fit, evaluate potential predictors of person fit heterogeneity, and identify potentially aberrant individuals. The method has apparently never been applied to empirical data or evaluated in a simulation study. The present research applies Reise's method to empirical data obtained from university undergraduates measured on the Fear of Negative Evaluation scale. Additionally, Reise's method is evaluated under conditions varying according to the type of aberrancy, level of test reliability, and scale length. Statistical power to detect aberrancy was highly dependent on manipulated variables, and some results were affected by bias in model parameters that was due to the aberrant responders. Nevertheless, Reise's method generally performed well and detected aberrant individuals either as well as, or better than, the well-established l _z person-fit statistic.     

Comments on Monte Carlo simulations of void-lattice formation

We study the coalescence of neighbouring voids along close-packed directions in recent computer simulation studies of void-lattice formation. The stability against coalescence of a developing void lattice is found to depend very much on the detailed geometry of the local void distribution. The possibility of void coalescence as an artifact, caused by the incorrect assumption of homogeneous void nucleation in these simulations, is suggested and discussed.     

TouchStat: A Monte Carlo program for calculating sequential touching probabilities

A growing number of child cognition researchers are using an object-manipulation, sequential-touching paradigm to explore young children’s conceptual abilities. Within this paradigm, it is essential to distinguish children’s intracategory touching sequences from those expected by chance. The sequentialtouching approach is congruent with a permutation testing model of statistical inference and is best modeled by sampled permutations as derived from Monte Carlo procedures. In this article, we introduce a computer program for generating Monte Carlo sequential-touching simulations. TouchStat permits users to determine their own specifications to simulate sequential touching to category exemplars across a wide range of task parameters. We also present Monte Carlo chance probabilities for the standard two-category, four-exemplar task, with sequences up to 30 touches long. Finally, we consider broader applications of the TouchStat program.     

The conditional power of randomization tests for single-case effect sizes in designs with randomized treatment order: A Monte Carlo simulation study

The conditional power (CP) of the randomization test (RT) was investigated in a simulation study in which three different single-case effect size (ES) measures were used as the test statistics: the mean difference (MD), the percentage of nonoverlapping data (PND), and the nonoverlap of all pairs (NAP). Furthermore, we studied the effect of the experimental design on the RT’s CP for three different single-case designs with rapid treatment alternation: the completely randomized design (CRD), the randomized block design (RBD), and the restricted randomized alternation design (RRAD). As a third goal, we evaluated the CP of the RT for three types of simulated data: data generated from a standard normal distribution, data generated from a uniform distribution, and data generated from a first-order autoregressive Gaussian process. The results showed that the MD and NAP perform very similarly in terms of CP, whereas the PND performs substantially worse. Furthermore, the RRAD yielded marginally higher power in the RT, followed by the CRD and then the RBD. Finally, the power of the RT was almost unaffected by the type of the simulated data. On the basis of the results of the simulation study, we recommend at least 20 measurement occasions for single-case designs with a randomized treatment order that are to be evaluated with an RT using a 5% significance level. Furthermore, we do not recommend use of the PND, because of its low power in the RT.     

Monte Carlo simulations and the chi-square test of independence

A Monte Carlo program for sampling 2 by 2 contingency tables from a user-specified population is discussed. Applications include computer-assisted instruction (CAI) of statistics, evaluation of actual vs nominal Type I error rates of the chi-square test of independence when expected frequencies are less than 10, and estimation of the power of the chi-square test.     

An alternative approach to relapse analysis: Using Monte Carlo methods and proportional rates of response

Relapse is the recovery of a previously suppressed response. Animal models have been useful in examining the mechanisms underlying relapse (e.g., reinstatement, renewal, reacquisition, resurgence). However, there are several challenges to analyzing relapse data using traditional approaches. For example, null hypothesis significance testing is commonly used to determine whether relapse has occurred. However, this method requires several a priori assumptions about the data, as well as a large sample size for between‐subjects comparisons or repeated testing for within‐subjects comparisons. Monte Carlo methods may represent an improved analytic technique, because these methods require no prior assumptions, permit smaller sample sizes, and can be tailored to account for all of the data from an experiment instead of some limited set. In the present study, we conducted reanalyses of three studies of relapse (Berry, Sweeney, & Odum, 2014 ; Galizio et al., 2018 ; Odum & Shahan, 2004 ) using Monte Carlo techniques to determine if relapse occurred and if there were differences in rate of response based on relevant independent variables (such as group membership or schedule of reinforcement). These reanalyses supported the previous findings. Finally, we provide general recommendations for using Monte Carlo methods in studies of relapse.     

Assessing categorization performance at the individual level: a comparison of Monte Carlo simulation and probability estimate model procedures

Two analytical procedures for identifying young children as categorizers, the Monte Carlo Simulation and the Probability Estimate Model, were compared. Using a sequential touching method, children aged 12, 18, 24, and 30 months were given seven object sets representing different levels of categorical classification. From their touching performance, the probability that children were categorizing was then determined independently using Monte Carlo Simulation and the Probability Estimate Model. The two analytical procedures resulted in different percentages of children being classified as categorizers. Results using the Monte Carlo Simulation were more consistent with group-level analyses than results using the Probability Estimate Model. These findings recommend using the Monte Carlo Simulation for determining individual categorizer classification.     

An inexpensive CRT terminal controller/computer

An inexpensive CRT terminal controller/computer is described. The board integrates virtually any keyboard and CRT monitor into a work station with firmware-governed intelligence. The system is designed to fill the cost/functionality niche below the Apple microcomputer. It can be configured as a dumb or smart terminal (approximately $100 plus keyboard and CRT monitor), as a self-contained computer that runs ROM-based software such as a small BASIC or an assembler/disassembler fan additional $100 in chips), or as a word processor if aa audio cassette ($50) or dual digital cassettes with controller ($125) are added.     

分类精确性指数Entropy在潜剖面分析中的表现:一项蒙特卡罗模拟研究

本研究通过蒙特卡洛模拟考查了分类精确性指数Entropy及其变式受样本量、潜类别数目、类别距离和指标个数及其组合的影响情况。研究结果表明:(1)尽管Entropy值与分类精确性高相关,但其值随类别数、样本量和指标数的变化而变化,很难确定唯一的临界值;(2)其他条件不变的情况下,样本量越大,Entropy的值越小,分类精确性越差;(3)类别距离对分类精确性的影响具有跨样本量和跨类别数的一致性;(4)小样本(N=50~100)的情况下,指标数越多,Entropy的结果越好;(5)在各种条件下Entropy对分类错误率比其它变式更灵敏。     

Taxometric analysis of fuzzy categories: a Monte Carlo study

A small Monte Carlo study examined the performance of a form of taxometric analysis (the MAXCOV procedure) with fuzzy data sets. These combine taxonic (categorical) and nontaxonic (continuous) features, containing a subset of casts with intermediate degrees of category membership. Fuzzy data sets tended to yield taxonic findings on plot inspection and two popular consistency tests, even when the degree of fuzziness, i.e., the proportion of intermediate cases, was large. These results suggest that fuzzy categories represent a source of pseudotaxonic inferences, if on is understood in the usual binary, "either-or" fashion. This in turn implies that dichotomous causes cannot be confidently inferred when taxometric analyses yield apparently taxonic findings.     

Monte Carlo tests of the Rasch model based on scalability coefficients

For item responses fitting the Rasch model, the assumptions underlying the Mokken model of double monotonicity are met. This makes non‐parametric item response theory a natural starting‐point for Rasch item analysis. This paper studies scalability coefficients based on Loevinger's H coefficient that summarizes the number of Guttman errors in the data matrix. These coefficients are shown to yield efficient tests of the Rasch model using p‐values computed using Markov chain Monte Carlo methods. The power of the tests of unequal item discrimination, and their ability to distinguish between local dependence and unequal item discrimination, are discussed. The methods are illustrated and motivated using a simulation study and a real data example.