线性拟合法和非线性拟合法在化学动力学数据计算中的应用

分别用线性拟合法和非线性拟合法对实际反应体系力学动力淡数据进行计算，求出相应的反应级数和反应活化能等动力学参数。编制了For程序，实现了自动化处理。     

正交多项式拟合法

对曲线拟合中的正交多项式拟合法作了研究;介绍了正交多项式的概念,给出了正交多项式拟合法及相应的程序实现;本论文的研究,对从事计算科学的工作者在做数据拟合时具有指导意义     

拟合法在证明极限问题中的应用

本文通过具体实例介绍如何应用拟合法解决数学分析中某些特殊极限的证明问题。     

对用ε-N定义明数列极限的方法技巧的讨论

用ε-N证明数列极限，思路基本有两种，一种是对Xn-A进行简化，放大，由繁到简；另一种思路是将A变复杂，利用拟合法，同时结合等价无穷小替换的思想。     

MATLAB在光学实验中的应用

利用MATLAB强大便捷的科学计算功能，引入多项式拟合法处理牛顿环实验数据，提高了实验的测量精度，拓展了测量范围；基于MATLAB的科学可视化功能对光学实验现象进行计算机模拟，在实验教学中应用效果明显。     

GPS水准拟合方法比较

主要介绍GPS水准拟合中的多项式拟合法和Shepard曲面拟合法的基本原理。以我国某地区(52 km×100km)的实测高程异常数据和GPS/水准数据为例,对多项式拟合模型的选取和Shepard曲面拟合法中拟合参数的确定等进行了讨论。     

关于水位改正数学模型的分析

针对水位改正中观测粗差和观测时间对海底地形成果质量的影响，就如何合理的使用目前水位改正中常见的多项式拟合法、样条函数法两种数学模型加以数值分析，并将三角多项式拟合法引入水位改正中。通过3组实验数据的计算结果证明：如果不消除原始水位观测数据中存在的粗差值，则无论采用何种水位改正数学模型均不能满足作业规范要求的精度，同时建议可有条件的把水位观测的时间间隔放宽到1h。     

He-Ne激光光束远场发散角的测量研究

对He-Ne激光光束远场发散角进行了实验测量研究,分别采用刀口法、拟合法和CCD摄像法.刀口法测量实验装置简单,但是实验测量数据量较大;拟合法可以克服刀口法中可能出现的测量误差,提高测量的精度;CCD摄像法实验简单数据量小,但是衰减片的使用则有可能引起光斑的畸变,也会影响实验结果.     

EXCEL在计算方法中的应用

数学拟合问题和插值问题相类似,在插值问题中,要求f(x)=∮(x)在插值结点Xi上,满足f(xi)=∮(xi),要求所求曲线通过所有点(xi,yi),但一般实验中给出的数据总是有观测误差。而数据拟合法不要求曲线通过所有的点(xi,yi),而是根据数据之间的相互关系用其他方法给出它们之间合适的数学公式,画出一条近似曲线,以反映给定曲线的一般趋势。该曲线用EXCEL来实现更简单。     

用换元法优化根式问题的求解

在二次根式的求值问题中,有时会遇到一些较为复杂的情况,此时不妨试作一些代换,常可简化结构,便于问题的解决.一、常数代换     

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.     

试论大学物理实验数据处理法的选取

本文论述了大学物理实验的种类和层面及实验中数据处理的几种方法;重点论述了最小二乘法和线性拟合的原理,并分别用图解法、差分法和用线性拟合法对大学物理实验普朗克常数测定的实例数据进行处理,而后进行比较,提出了应根据实验目的而优选大学物理实验数据处理法.     

Use the Correlation Coefficient to Summarize Regression Performance?

The correlation coefficient is commonly used to indicate the quality of fit in regression. This practice is questionable.     

The Poor Fit of Model Fit for Selecting Number of Factors in Exploratory Factor Analysis for Scale Evaluation

Model fit indices are being increasingly recommended and used to select the number of factors in an exploratory factor analysis. Growing evidence suggests that the recommended cutoff values for common model fit indices are not appropriate for use in an exploratory factor analysis context. A particularly prominent problem in scale evaluation is the ubiquity of correlated residuals and imperfect model specification. Our research focuses on a scale evaluation context and the performance of four standard model fit indices: root mean square error of approximate (RMSEA), standardized root mean square residual (SRMR), comparative fit index (CFI), and Tucker–Lewis index (TLI), and two equivalence test-based model fit indices: RMSEAt and CFIt. We use Monte Carlo simulation to generate and analyze data based on a substantive example using the positive and negative affective schedule (N = 1,000). We systematically vary the number and magnitude of correlated residuals as well as nonspecific misspecification, to evaluate the impact on model fit indices in fitting a two-factor exploratory factor analysis. Our results show that all fit indices, except SRMR, are overly sensitive to correlated residuals and nonspecific error, resulting in solutions that are overfactored. SRMR performed well, consistently selecting the correct number of factors; however, previous research suggests it does not perform well with categorical data. In general, we do not recommend using model fit indices to select number of factors in a scale evaluation framework.     

An NCME Instructional Module on Item‐Fit Statistics for Item Response Theory Models

Drawing valid inferences from item response theory (IRT) models is contingent upon a good fit of the data to the model. Violations of model‐data fit have numerous consequences, limiting the usefulness and applicability of the model. This instructional module provides an overview of methods used for evaluating the fit of IRT models. Upon completing this module, the reader will have an understanding of traditional and Bayesian approaches for evaluating model‐data fit of IRT models, the relative advantages of each approach, and the software available to implement each method.     

Examination of the Weighted Root Mean Square Residual: Evidence for Trustworthiness?

This study examined the performance of the weighted root mean square residual (WRMR) through a simulation study using confirmatory factor analysis with ordinal data. Values and cut scores for the WRMR were examined, along with a comparison of its performance relative to commonly cited fit indexes. The findings showed that WRMR illustrated worse fit when sample size increased or model misspecification increased. Lower (i.e., better) values of WRMR were observed when nonnormal data were present, there were lower loadings, and when few categories were analyzed. WRMR generally illustrated expected patterns of relations to other well-known fit indexes. In general, a cutoff value of 1.0 appeared to work adequately under the tested conditions and the WRMR values of “good fit” were generally in agreement with other indexes. Users are cautioned that when the fitted model is misspeficifed, the index might provide misleading results under situations where extremely large sample sizes are used.     

Exploring the Impact of Rater Effects on Person Fit in Rater-Mediated Assessments

Researchers have documented the impact of rater effects, or raters’ tendencies to give different ratings than would be expected given examinee achievement levels, in performance assessments. However, the degree to which rater effects influence person fit, or the reasonableness of test-takers’ achievement estimates given their response patterns, has not been investigated. In rater-mediated assessments, person fit reflects the reasonableness of rater judgments of individual test-takers’ achievement over components of the assessment. This study illustrates an approach to visualizing and evaluating person fit in assessments that involve rater judgment using rater-mediated person response functions (rm-PRFs). The rm-PRF approach allows analysts to consider the impact of rater effects on person fit in order to identify individual test-takers for whom the assessment results may not have a straightforward interpretation. A simulation study is used to evaluate the impact of rater effects on person fit. Results indicate that rater effects can compromise the interpretation and use of performance assessment results for individual test-takers. Recommendations are presented that call researchers and practitioners to supplement routine psychometric analyses for performance assessments (e.g., rater reliability checks) with rm-PRFs to identify students whose ratings may have compromised interpretations as a result of rater effects, person misfit, or both.     

New Ways to Evaluate Goodness of Fit: A Note on Using Equivalence Testing to Assess Structural Equation Models

Structural equation models are typically evaluated on the basis of goodness-of-fit indexes. Despite their popularity, agreeing what value these indexes should attain to confidently decide between the acceptance and rejection of a model has been greatly debated. A recently proposed approach by means of equivalence testing has been recommended as a superior way to evaluate the goodness of fit of models. The approach has also been proposed as providing a necessary vehicle that can be used to advance the inferential nature of structural equation modeling as a confirmatory tool. The purpose of this article is to introduce readers to key ideas in equivalence testing and illustrate its use for conducting model–data fit assessments. Two confirmatory factor analysis models in which a priori specified latent variable models with known structure and tested against data are used as examples. It is advocated that whenever the goodness of fit of a model is to be assessed researchers should always examine the resulting values obtained via the equivalence testing approach.     

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.     

Assessing the Sensitivity of Weighted Least Squares Model Fit Indexes to Local Dependence in Item Response Theory Models

Given the relationships of item response theory (IRT) models to confirmatory factor analysis (CFA) models, IRT model misspecifications might be detectable through model fit indexes commonly used in categorical CFA. The purpose of this study is to investigate the sensitivity of weighted least squares with adjusted means and variance (WLSMV)-based root mean square error of approximation, comparative fit index, and Tucker–Lewis Index model fit indexes to IRT models that are misspecified due to local dependence (LD). It was found that WLSMV-based fit indexes have some functional relationships to parameter estimate bias in 2-parameter logistic models caused by violations of LD. Continued exploration into these functional relationships and development of LD-detection methods based on such relationships could hold much promise for providing IRT practitioners with global information on violations of local independence.