关于Dirichlet L─函数的一个加权均值

利用经典的Kloostermann和估计、三角和估计及其解析方法研究了Dirichlet L─函数的二次加权均值分布,给出一个有趣的二次加权均值分布的渐近公式.     

Dirichlet L-函数的一个四次加权均值分布

利用Kloostermann和估计及其解析方法研究了Dirichlet L-函数的一个四次加权均值分布，得到一个有趣的加权均值分布的渐近公式．     

Dirichlet L-函数加权均值公式的推广

用Gauss和的性质、三角和估计、特征和的性质及其解析方法讨论了Dirichlet L-函数的2k次加权均值分布问题，得到一个推广的加权均值分布的分布公式。     

Dirichlet L-函数的一个加权均值公式

利用Gauss和的定义、三角和估计及其解析方法研究了DirichletL一函数的二次加权均值分布，给出一个有趣的二次加权均值公式．     

关于Dirichlet L-函数与Gauss和

利用解析方法及其三角和估计给出DirichletL－函数二次加权均值的一个较强的渐近公式。     

估计有序约束均值的一个非参数方法

对k个总体,其均值被简单半序约束时的估计问题进行了讨论.把单个总体均值的H-L估计应用到多个总体的情况,定义了加权保序H-L估计,给出了算法及性质.     

缺失数据下线性模型响应变量均值估计的渐近正态性

考虑响应变量随机缺失下线性模型响应变量均值的估计问题,分别获得了基于完全观测样本数据、线性回归插补后的"完全样本"和逆概率加权插补后的"完全样本"得到的响应变量均值估计,并证明了其渐近正态性.     

Dirichlet L-函数加权均值

利用三角和估计及其解析方法讨论了Dirichlet L函数的二次加权均值,得到了一个有趣的均值公式:∑χ mod pχ(-1)=-1|G(m,χ)|2|L(1,χ)|2=(π2)/(12p2)(p-2)(p-1)3 O(pln2p).     

模拟偏差对自助法估计的影响探讨

文中探讨了模拟偏差对自助法均值估计的影响.首先,从分布N（1,12）中产生样本数据,利用自助法,得到自助法均值的估计.然后讨论了样本数据均值和总体分布均值的偏差对自助法估计的影响.结果表明,当偏差的绝对值小于等于0.54时,模拟结果较好,当偏差的绝对值大于等于0.56时,模拟结果很差.     

Sarmanov相依随机变量随机加权和的渐近估计

文章考虑Sarmanov分布的随机变量序列{(X_i,Y_i),i≥1}的随机加权和(∑ni=1θiXi,n∑j=1θjYj)尾概率的渐近估计问题,所得结果推广了一维随机变量加权和渐近估计结果.     

The Role of Centering for Interaction of Level 1 Variables in Multilevel Structural Equation Models

This article examined the role of centering in estimating interaction effects in multilevel structural equation models. Interactions are typically represented by product term of 2 variables that are hypothesized to interact. In multilevel structural equation modeling (MSEM), the product term involving Level 1 variables is decomposed into within-cluster and between-cluster random components. The choice of centering affects the decomposition of the product term, and therefore affects the sample variance and covariance associated with the product term used in the maximum likelihood fitting function. The simulation study showed that for an interaction between a Level 1 variable and a Level 2 variable, the product term of uncentered variables or the product term of grand mean centered variables produced unbiased estimates in both Level 1 and Level 2 models. The product term of cluster mean centered variables produced biased estimates in the Level 1 model. For an interaction between 2 Level 1 variables, the product term of cluster mean centered variables produced unbiased estimates in the Level 1 model, whereas the product term of grand mean centered variables produced unbiased estimates for the Level 1 model. Recommendations for researchers who wish to estimate interactions in MSEM are provided.     

Parameter Estimation Accuracy of the Effort-Moderated Item Response Theory Model Under Multiple Assumption Violations

As low-stakes testing contexts increase, low test-taking effort may serve as a serious validity threat. One common solution to this problem is to identify noneffortful responses and treat them as missing during parameter estimation via the effort-moderated item response theory (EM-IRT) model. Although this model has been shown to outperform traditional IRT models (e.g., two-parameter logistic [2PL]) in parameter estimation under simulated conditions, prior research has failed to examine its performance under violations to the model’s assumptions. Therefore, the objective of this simulation study was to examine item and mean ability parameter recovery when violating the assumptions that noneffortful responding occurs randomly (Assumption 1) and is unrelated to the underlying ability of examinees (Assumption 2). Results demonstrated that, across conditions, the EM-IRT model provided robust item parameter estimates to violations of Assumption 1. However, bias values greater than 0.20 SDs were observed for the EM-IRT model when violating Assumption 2; nonetheless, these values were still lower than the 2PL model. In terms of mean ability estimates, model results indicated equal performance between the EM-IRT and 2PL models across conditions. Across both models, mean ability estimates were found to be biased by more than 0.25 SDs when violating Assumption 2. However, our accompanying empirical study suggested that this biasing occurred under extreme conditions that may not be present in some operational settings. Overall, these results suggest that the EM-IRT model provides superior item and equal mean ability parameter estimates in the presence of model violations under realistic conditions when compared with the 2PL model.     

Multidimensional Equating

Equatings were performed on both simulated and real data sets using the common-examinee design and two abilities for each examinee (i.e., two dimensions). Item and ability parameter estimates were found by using the Multidimensional Item Response Theory Estimation (MIRTE) program. The amount of equating error was evaluated by a comparison of the mean difference and the mean absolute difference between the true scores and ability estimates found on both tests for the common examinees used in the equating. The results indicated that effective equating, as measured by comparability o f true scores, was possible with the techniques used in this study. When the stability o f the ability estimates was examined, unsatisfactory results were found.     

The Effect of Scale Referent on Tests of Mean Structure Parameters

Structured means analysis is a very useful approach for testing hypotheses about population means on latent constructs. In such models, a z test is most commonly used for testing the statistical significance of the relevant parameter estimates or of the differences between parameter estimates, where a z value is computed based on the asymptotic standard error estimate associated with the parameter of interest. In the current article, a series of population analyses demonstrate that the z tests for latent mean structure parameters or, more directly, the standard error estimates upon which those z tests are based are, not invariant to how factors are scaled. As such, circumstances exist in which latent mean inference is compromised solely as a result of scaling decisions. This problem is illustrated in the context of between-subjects (i.e., multisample) latent means models and within-subjects latent means models. Recommendations for practice are also offered.     

An undergraduate student flow model: Australian higher education

The probability of completing and the time to complete an undergraduate course are likely to vary by the age and sex of the student, and the field of study undertaken. In this paper a Markov chain is used to model the movement of undergraduates through the higher education system in Australia. Given the age of the student when they commence a course, this model provides estimates of the probability of them completing the course. It also provides estimates for the mean time a student takes to complete the course, and mean time they spend in the higher education system.     

一个Dirichlet L-函数的新的二次加权均值

本文利用特征和与解析的方法研究了广义二次高斯和六次方与D irich let函l-数的二次方的加权均值。     

OBTAINING MAXIMUM LIKELIHOOD TRAIT ESTIMATES FROM NUMBER-CORRECT SCORES FOR THE THREE-PARAMETER LOGISTIC MODEL

A procedure is presented for obtaining maximum likelihood trait estimates from number-correct (NC) scores for the three-parameter logistic model. The procedure produces an NC score to trait estimate conversion table, which can be used when the hand scoring of tests is desired or when item response pattern (IP) scoring is unacceptable for other (e.g., political) reasons. Simulated data are produced for four 20-item and four 40-item tests of varying difficulties. These data indicate that the NC scoring procedure produces trait estimates that are tau-equivalent to the IP trait estimates (i.e., they are expected to have the same mean for all groups of examinees), but the NC trait estimates have higher standard errors of measurement than IP trait estimates. Data for six real achievement tests verify that the NC trait estimates are quite similar to the IP trait estimates but have higher empirical standard errors than IP trait estimates, particularly for low-scoring examinees. Analyses in the estimated true score metric confirm the conclusions made in the trait metric.     

How 15 hundred is like 15 cherries: effect of progressive alignment on representational changes in numerical cognition

How does understanding the decimal system change with age and experience? Second, third, sixth graders, and adults (Experiment 1: N = 96, mean ages = 7.9, 9.23, 12.06, and 19.96 years, respectively) made number line estimates across 3 scales (0–1,000, 0–10,000, and 0–100,000). Generation of linear estimates increased with age but decreased with numerical scale. Therefore, the authors hypothesized highlighting commonalities between small and large scales (15:100::1500:10000) might prompt children to generalize their linear representations to ever‐larger scales. Experiment 2 assigned second graders (N = 46, mean age = 7.78 years) to experimental groups differing in how commonalities of small and large numerical scales were highlighted. Only children experiencing progressive alignment of small and large scales successfully produced linear estimates on increasingly larger scales, suggesting analogies between numeric scales elicit broad generalization of linear representations.     

Brief Research Report: A User Friendly Effect Size—When Normality Matters

There is a need for effect sizes that are readily interpretable by a broad audience. One index that might fill this need is π, which represents the proportion of scores in one group that exceed the mean of another group. The robustness of estimates of π to violations of normality had not been explored. Using simulated data, three estimates of π (π? _direct, r, and r_robust) were studied under varying conditions of sample size, distribution shape, and group mean difference. This study demonstrated that r and r_robust were biased estimates of π when data were nonnormal. We recommend that neither be used in estimating π unless data are normally distributed.