Assessing sources of error in structural equation models: The effects of sample size,reliability, and model misspecification

This study used Monte Carlo methods to investigate the accuracy and utility of estimators of overall error and error due to approximation in structural equation models. The effects of sample size, indicator reliabilities, and degree of misspecification were examined. The rescaled noncentrality parameter (McDonald & Marsh, 1990) was examined as a measure of approximation error, whereas the one‐ and two‐sample cross‐validation indices and a sample estimator of overall error (EFo) proposed by Browne and Cudeck (1989, 1993) were presented as measures of overall error. The rescaled noncentrality parameter and EFo provided extremely accurate estimates of the amounts of approximation and overall error, respectively. However, although models with errors of omission produced larger estimates of approximation and overall error, the presence of errors of inclusion had little or no effect on estimates of either type of error. The cross‐validation indices and sample estimator of overall error reached minimum values for the same model as an empirically derived measure of overall error only for models with large amounts of specification error. Implications for the use of these estimators in choosing among competing models were discussed.     

Analysis of a load application point in spline coupling teeth

The objective of this paper is to investigate the position of the resultant force in involute spline coupling teeth due to the contact pressure distribution for both ideal and misaligned conditions. In general, spline coupling teeth are in contact all along the involute profile and the load is far from uniform along the contact line. Theoretical models available in publications consider the resultant contact force as it is applied at the pitch diameter, and this study aims to evaluate the error introduced within the confines of a common approximation environment. This analysis is carried out through using finite element method （FEM） models, considering spline couplings in both ideal and misaligned conditions. Results show that the differences between the load application diameter and pitch diameter are not very obvious in both ideal and misaligned conditions; however, this ap- proximation becomes more important for the calculation of the tooth stiffness.     

基于几何质量和后验误差的网格优化设计

给出了偏微分方程的h型有限元分析的双层网格最优精化设计方法。第一层是细化后验误差相对大的单元？后验误差是通过简化计算由单元平均流量为连接的单元Neumann型子问题而得到的误差界。简化计算就是只把由1／2单元尺寸所构成的网格上的泛函作为单元残余误差方程的试探函数，这样计算成本将非常小。某些精化后的网格的几何性质将变得很差，所以第二层又用Laplace光顺算法对网格的质量进行改进，并用两个例题验证了该方法。结果表明，算法达到最优收敛率，并提高了精度。     

Using Fit Indexes to Select a Covariance Model for Longitudinal Data

This study investigated the performance of fit indexes in selecting a covariance structure for longitudinal data. Data were simulated to follow a compound symmetry, first-order autoregressive, first-order moving average, or random-coefficients covariance structure. We examined the ability of the likelihood ratio test (LRT), root mean square error of approximation (RMSEA), comparative fit index (CFI), and Tucker–Lewis Index (TLI) to reject misspecified models with varying degrees of misspecification. With a sample size of 20, RMSEA, CFI, and TLI are high in both Type I and Type II error rates, whereas LRT has a high Type II error rate. With a sample size of 100, these indexes generally have satisfactory performance, but CFI and TLI are affected by a confounding effect of their baseline model. Akaike's Information Criterion (AIC) and Bayesian Information Criterion (BIC) have high success rates in identifying the true model when sample size is 100. A comparison with the mixed model approach indicates that separately modeling the means and covariance structures in structural equation modeling dramatically improves the success rate of AIC and BIC.     

How to measure research efficiency in higher education? Research grants vs. publication output

An ongoing debate in the literature on the efficiency of higher education institutions concerns the indicator for research output for use in empirical analysis. While several studies have chosen to use the number of publications as this indicator, others rely on the amount of research grants. The present study investigates whether both measures lead to a similar assessment of universities. In addition, the number of publications belonging to the 10% and 1% most frequently cited papers in the corresponding subject category and publication year are evaluated. We show that there is a high correlation of efficiency values between the estimations using these indicators. This correlation is slightly higher when the efficiency values result from a data envelopment analysis than when they are determined with a stochastic frontier analysis. The results of this study provide helpful guidelines for researchers evaluating the efficiency of universities and are valueable for decision-makers in science policy.     

L~2(R)的分解及其函数逼近

本文利用多分辨力逼近理论讨论了任意不同子空间对L2（R）中函数的逼近误差,给出了比[1]中对L2（R）的分解更一般的形式．     

Fork-Join program response time on multiprocessors with exchangeable join

INTRODUCTION With the prevalence of distributed computing and parallel programming languages (Barry and Allen, 1998), performance evaluation of the parallel execu-tion systems becomes important. In this work we derive bounds and an approximation of the mean response time of a particular type parallel program: program with Fork-Join tasks and executed in multi-processor with first come first served (FCFS) policy. This kind of program is general in large-scale simu-lation and numerical …     

Goodness of Fit in Item Factor Analysis: Effect of the Number of Response Alternatives

The power of the chi-square test statistic used in structural equation modeling decreases as the absolute value of excess kurtosis of the observed data increases. Excess kurtosis is more likely the smaller the number of item response categories. As a result, fit is likely to improve as the number of item response categories decreases, regardless of the true underlying factor structure or χ²-based fit index used to examine model fit. Equivalently, given a target value of approximate fit (e.g., root mean square error of approximation ≤ .05) a model with more factors is needed to reach it as the number of categories increases. This is true regardless of whether the data are treated as continuous (common factor analysis) or as discrete (ordinal factor analysis). We recommend using a large number of response alternatives (≥ 5) to increase the power to detect incorrect substantive models.     

Comparison of the One‐ and Bi‐Direction Chained Equipercentile Equating

This study investigated differences between two approaches to chained equipercentile (CE) equating (one‐ and bi‐direction CE equating) in nearly equal groups and relatively unequal groups. In one‐direction CE equating, the new form is linked to the anchor in one sample of examinees and the anchor is linked to the reference form in the other sample. In bi‐direction CE equating, the anchor is linked to the new form in one sample of examinees and to the reference form in the other sample. The two approaches were evaluated in comparison to a criterion equating function (i.e., equivalent groups equating) using indexes such as root expected squared difference, bias, standard error of equating, root mean squared error, and number of gaps and bumps. The overall results across the equating situations suggested that the two CE equating approaches produced very similar results, whereas the bi‐direction results were slightly less erratic, smoother (i.e., fewer gaps and bumps), usually closer to the criterion function, and also less variable.     

Value added based on educational positions in Dutch secondary education

Estimating added value as an indicator of school effectiveness in the context of educational accountability often occurs using test or examination scores of students. This study investigates the possibilities for using scores of educational positions as an alternative indicator. A number of advantages of a value added indicator based on educational positions of students can be formulated, such as: (a) the societal significance of educational position as output measure; (b) the fact that a single indicator can be estimated for an entire school in a differentiated educational system, where not all schools provide education in all tracks; and (c) the expectation that value added based on educational positions leads to other incentives for schools than value added based on test scores. Empirical analysis of Dutch cohort data (VOCL'99) for secondary education showed considerable differences in effectiveness between schools in the positions of students. Furthermore, differential school effects were found for both socio‐economic status and prior achievement. The phenomena of differential school effects for socio‐economic status and prior achievement are linked to differences between schools in the kind of tracks in which the schools provide schooling.     

Evaluating Model Fit With Ordered Categorical Data Within a Measurement Invariance Framework: A Comparison of Estimators

A paucity of research has compared estimation methods within a measurement invariance (MI) framework and determined if research conclusions using normal-theory maximum likelihood (ML) generalizes to the robust ML (MLR) and weighted least squares means and variance adjusted (WLSMV) estimators. Using ordered categorical data, this simulation study aimed to address these queries by investigating 342 conditions. When testing for metric and scalar invariance, Δχ² results revealed that Type I error rates varied across estimators (ML, MLR, and WLSMV) with symmetric and asymmetric data. The Δχ² power varied substantially based on the estimator selected, type of noninvariant indicator, number of noninvariant indicators, and sample size. Although some the changes in approximate fit indexes (ΔAFI) are relatively sample size independent, researchers who use the ΔAFI with WLSMV should use caution, as these statistics do not perform well with misspecified models. As a supplemental analysis, our results evaluate and suggest cutoff values based on previous research.     

Comparing the Fit of Item Response Theory and Factor Analysis Models

Linear factor analysis (FA) models can be reliably tested using test statistics based on residual covariances. We show that the same statistics can be used to reliably test the fit of item response theory (IRT) models for ordinal data (under some conditions). Hence, the fit of an FA model and of an IRT model to the same data set can now be compared. When applied to a binary data set, our experience suggests that IRT and FA models yield similar fits. However, when the data are polytomous ordinal, IRT models yield a better fit because they involve a higher number of parameters. But when fit is assessed using the root mean square error of approximation (RMSEA), similar fits are obtained again. We explain why. These test statistics have little power to distinguish between FA and IRT models; they are unable to detect that linear FA is misspecified when applied to ordinal data generated under an IRT model.     

A Note on Extending Steiger's (1998) Multiple Sample RMSEA Adjustment to Other Noncentrality Parameter-Based Statistics

This article considers the implications for other noncentrality parameter-based statistics from Steiger's (1998) multiple sample adjustment to the root mean square error of approximation (RMSEA) measure. When a structural equation model is fitted simultaneously in more than 1 sample, it is shown that the calculation of the noncentrality parameter used in tests of approximate fit and in point and interval estimators of other noncentral fit statistics (except the expected cross-validation index) also requires a likeminded adjustment. Furthermore, it is shown that an adjustment is needed in multiple sample models for correctly calculating MacCallum, Browne, and Sugawara's (1996) approach to power analysis. The accuracy of these proposals is investigated and demonstrated in a small Monte Carlo study in which particular attention is paid to using appropriately constructed covariance matrices that give specified nonzero population discrepancy values under maximum likelihood estimation.     

Reporting Valid and Reliable Overall Scores and Domain Scores

In educational assessment, overall scores obtained by simply averaging a number of domain scores are sometimes reported. However, simply averaging the domain scores ignores the fact that different domains have different score points, that scores from those domains are related, and that at different score points the relationship between overall score and domain score may be different. To report reliable and valid overall scores and domain scores, I investigated the performance of four methods using both real and simulation data: (a) the unidimensional IRT model; (b) the higher-order IRT model, which simultaneously estimates the overall ability and domain abilities; (c) the multidimensional IRT (MIRT) model, which estimates domain abilities and uses the maximum information method to obtain the overall ability; and (d) the bifactor general model. My findings suggest that the MIRT model not only provides reliable domain scores, but also produces reliable overall scores. The overall score from the MIRT maximum information method has the smallest standard error of measurement. In addition, unlike the other models, there is no linear relationship assumed between overall score and domain scores. Recommendations for sizes of correlations between domains and the number of items needed for reporting purposes are provided.     

基于改进支持向量机模型的交通拥堵情况预测

随着机动车数量的迅猛增加,城市交通拥堵状况日益严峻,城市道路拥堵严重影响着居民的日常工作和生活,因此研究道路拥堵程度,以及对道路拥堵变化进行预测则显得尤为重要。为此,构建一个基于拥堵指标的MM-SVR模型,在考虑下一时段可能到达路段的潜在车流量情况下,对道路拥堵情况进行深入探究。首先,融合速度、区域内交通流量构建道路拥堵程度指标,然后基于历史数据构建将马尔科夫链与支持向量机预测相结合的MM-SVR模型对道路拥堵进行预测,以向前[n]阶状态的交通流量和速度作为输入量,将道路拥堵程度指标作为输出量。在实例验证中,使用广州市某片区的实时交通流数据对模型效果进行评测,并且使用SVR以及Adaboosting模型进行对比实验。实验结果表明,该模型无论是在拟合优度还是预测误差上均优于对比模型,在实时反映交通流拥堵情况方面有着良好表现。     

一类m阶基数B一样条小波插值的误差估计

主要针对基数B-样条函数及其基本性质，研究一类m阶基数B-样条小波插值的误差估计，获得了关于一类m阶基数B-样条小波插值的误差表示以及该类插值误差关于步长h的若干结果，重点是计算、基数B-样条小波逼近和误差处理，特别，这里所说的基数B-样条函数是指具有等距单重节点的多项式样条函数．     

Formulation of the DETECT Population Parameter and Evaluation of DETECT Estimator Bias

The development of the DETECT procedure marked an important advancement in nonparametric dimensionality analysis. DETECT is the first nonparametric technique to estimate the number of dimensions in a data set, estimate an effect size for multidimensionality, and identify which dimension is predominantly measured by each item. The efficacy of DETECT critically depends on accurate, minimally biased estimation of the expected conditional covariances of all the item pairs. However, the amount of bias in the DETECT estimator has been studied only in a few simulated unidimensional data sets. This is because the value of the DETECT population parameter is known to be zero for this case and has been unknown for cases when multidimensionality is present. In this article, integral formulas for the DETECT population parameter are derived for the most commonly used parametric multidimensional item response theory model, the Reckase and McKinley model. These formulas are then used to evaluate the bias in DETECT by positing a multidimensional model, simulating data from the model using a very large sample size (to eliminate random error), calculating the large-sample DETECT statistic, and finally calculating the DETECT population parameter to compare with the large-sample statistic. A wide variety of two- and three-dimensional models, including both simple structure and approximate simple structure, were investigated. The results indicated that DETECT does exhibit statistical bias in the large-sample estimation of the item-pair conditional covariances; but, for the simulated tests that had 20 or more items, the bias was small enough to result in the large-sample DETECT almost always correctly partitioning the items and the DETECT effect size estimator exhibiting negligible bias.     

The Model Size Effect in SEM: Inflated Goodness-of-Fit Statistics Are Due to the Size of the Covariance Matrix

The size of a model has been shown to critically affect the goodness of approximation of the model fit statistic T to the asymptotic chi-square distribution in finite samples. It is not clear, however, whether this “model size effect” is a function of the number of manifest variables, the number of free parameters, or both. It is demonstrated by means of 2 Monte Carlo computer simulation studies that neither the number of free parameters to be estimated nor the model degrees of freedom systematically affect the T statistic when the number of manifest variables is held constant. Increasing the number of manifest variables, however, is associated with a severe bias. These results imply that model fit drastically depends on the size of the covariance matrix and that future studies involving goodness-of-fit statistics should always consider the number of manifest variables, but can safely neglect the influence of particular model specifications.     

Nonword recall and phonemic discrimination in four‐ to six‐year‐old children

Previous research has established that the degree of ‘wordlikeness’ of nonwords affects young children's nonword repetition performance. Experiment 1 examined the possibility that output processes are responsible for the wordlikeness effect by using a probed recall procedure. Wordlikeness was defined in terms of phonological neighbourhood density, although this measure was found to be related to the traditional measure of wordlikeness involving adult ratings. A significant effect of number of phonological neighbours/wordlikeness was observed in favour of nonwords with many neighbours. In Experiments 2 and 3 the wordlikeness effect was qualified by a significant interaction with nonword repetition ability. Children with poorer repetition ability were affected by number of neighbours/wordlikeness, while children with better repetition ability were not. Children with poorer repetition ability were significantly poorer than the better repeaters with nonwords with few neighbours. The results were interpreted in terms of theories of phonological development that suggest progressive segmentation of lexical representations. In Experiment 4 the relationship of children's nonword repetition ability to phonemic discrimination ability was investigated. The results demonstrated that children with better nonword repetition ability had superior phonemic discrimination performance than children with poorer nonword repetition ability.     

A Simulation Investigation of the Performance of Invariance Assessment Using Equivalence Testing Procedures

Factorial invariance assessment is central in the development of educational and psychological assessments. Establishing invariance of factor structures is key for building a strong score and inference validity argument and assists in establishing the fairness of score use. Fit indices and guidelines for judging a lack of invariance is an ongoing line of research. In this study, the authors examined the performance of the root mean squared error of approximation equivalence testing approach described by Yuan and Chan in the context of measurement invariance assessment. This investigation was completed through a simulation study in which several factors were varied, including sample size, type of invariance tested, and magnitude and percent of a lack of invariance. The findings generally support the use of equivalence testing for situations in which the indicator variables were normally distributed, particularly for total sample sizes of 200 or more.