一阶微分形式不变性在课堂教学中的妙用

通过举例说明使用一阶微分形式不变性对帮助学生理解凑微分积分法、多元复合函数求导、求多元复合函数的高阶偏导等内容,简化解题过程具有良好的作用     

一般洛伦兹变换的推导

本文根据相对性原理和间隔不变性,并借助Maple数学软件给出了一般洛伦兹变换的推导.     

Testing Factorial Invariance in Multilevel Data: A Monte Carlo Study

Testing factorial invariance has recently gained more attention in different social science disciplines. Nevertheless, when examining factorial invariance, it is generally assumed that the observations are independent of each other, which might not be always true. In this study, we examined the impact of testing factorial invariance in multilevel data, especially when the dependency issue is not taken into account. We considered a set of design factors, including number of clusters, cluster size, and intraclass correlation (ICC) at different levels. The simulation results showed that the test of factorial invariance became more liberal (or had inflated Type I error rate) in terms of rejecting the null hypothesis of invariance held between groups when the dependency was not considered in the analysis. Additionally, the magnitude of the inflation in the Type I error rate was a function of both ICC and cluster size. Implications of the findings and limitations are discussed.     

What are the Conditions Associated with Subscore Added Value Noninvariance? Implications for Improving Subscore Interpretation Fairness

Subscore added value analyses assume invariance across test taking populations; however, this assumption may be untenable in practice as differential subdomain relationships may be present among subgroups. The purpose of this simulation study was to understand the conditions associated with subscore added value noninvariance when manipulating: (a) subdomain test length, (b) differences in subgroup mean ability, and (c) subgroup differences in intersubdomain correlations. Results demonstrated that subscore added value was noninvariant for 24–100% of replications (depending on subdomain test length) when the subgroup difference in intersubdomain correlation was equal to .30. To examine if this condition was met in practice, applied invariance analyses of three operational testing programs were conducted. Across these datasets, noninvariant subscore added value was present for some subdomains across sex and ethnic subgroups. Overall, these results indicate that subscore added value noninvariance is largely driven by differential intersubdomain correlations among subgroups, which may be present in some operational testing programs.     

Revisiting the dimensionality of subjective task value: Towards clarification of competing perspectives

Expectancy-value researchers have described the components of subjective task value in multiple ways, leading to multiple competing structural representations of subjective task value data. The purpose of this study was to examine these competing multidimensional factor structures by comparing correlated factor, hierarchical, and bifactor representations of both confirmatory factor analysis and exploratory structural equation modeling (ESEM) models across three theoretical conceptualizations of subjective task value. Results indicate that, in an undergraduate life science learning context (n = 334), the best representation for subjective task value data was a bifactor ESEM model that allowed for the disentangling of general and specific variance of general subjective task value, specific value beliefs, and specific costs. Full measurement invariance of the retained structure across continuing generation and first-generation students was found, and no differential item functioning was found across gender. General subjective task value and specific opportunity cost significantly and positively predicted achievement and specific utility value significantly and negatively predicted achievement, providing support for the criterion-related validity of the general and specific factors for predicting achievement outcomes.     

Attitudes towards multiculturalism in Luxembourg: Measurement invariance and factor structure of the Multicultural Ideology Scale

In the present study, we examined the dimensionality and the measurement invariance of the Multicultural Ideology Scale (MCI), and mean differences across different cultural groups within the multilingual, multicultural context of Luxembourg. Luxembourg is a unique context to study attitudes towards diversity because 47.4 % of the citizens are non-nationals (i.e. economic migrants, sojourners, refugees) and minority and majority are increasingly difficult to define. Our sample included 1488 participants from diverse ethnic backgrounds who completed the survey in German, French or English. In contrast to previous findings, our analyses on responses to the MCI scale produced a two-dimensional structure, distinguishing between positive and negative attitudes towards multiculturalism. The factor structure was partially invariant across ethnocultural groups: Configural and metric invariance were established across natives and non-natives and different language versions. Scalar invariance was only established across gender groups. Natives and male participants reported the most negative attitudes towards multiculturalism. We discuss the importance of assessing measurement invariance and provide recommendations to improve the assessment of psychological multiculturalism.     

Reliability and Validity Evidence for Achievement Goal Models in High School Physical Education Settings

Although empirical research in academic areas provides support for both a 3-factor as well as a 4-factor achievement goal model, both models were proposed and tested with a collegiate sample. Little is known about the generalizability of either model with high school level samples. This study was designed to examine whether the 3-factor model (Mastery Goals, Performance-Approach Goals, and Performance-Avoidance Goals) or the 4-factor model (Mastery-Approach Goals, Mastery-Avoidance Goals, Performance-Approach Goals, and Performance-Avoidance Goals) is appropriate in high school physical education settings. The factorial validity of the models and internal consistency reliability were tested with confirmatory factor analysis, invariance testing, and tests of internal consistency across 2 samples. The results reveal that the items from the 4-factor achievement goal model can produce internally consistent and valid scores for high school students in physical education settings; the 4-factor model provides a better fit to the data than the 3-factor model. The multistep invariance analysis, however, reveals only metric invariance across 2 school samples.     

Development and validation of scales to measure environmental responsibility,character development,and attitudes toward school

This investigation examines the use of structural equation modeling (SEM) procedures to develop and validate scales to measure environmental responsibility, character development and leadership, and attitudes toward school for environmental education programs servicing middle school children. The scales represent outcomes commonly of interest to environmental education programs and also to after‐school and positive youth development activities. First, we developed the scales using confirmatory factor analysis (CFA) and then we used multi‐group longitudinal CFA to cross‐validate the model with data collected before participation in the environmental education program, immediately after the program, and three months later. The results support a three‐factor model, producing three scales that appear to be valid and reliable.     

教育技术学实验研究工具的跨时测量恒等检测

基于跨时测量恒等视角与知识图谱分析,文章对我国教育技术学较常探讨的变量"自我效能"量表进行了工具检测,并以四川省某小学三年级的197名学生为被试,前后测时间间隔为6个月。文章采用结构方程模型的跨时测量恒等检验程序,依序针对不同恒等程度的模型进行比较,结果发现:数学自我效能量表不符合完全的度量恒等,放宽两道题项的参数限制后可达到部分的纯量恒等,但仍不及严格恒等的要求;跨时测量恒等性的结果会影响配对样本t检验的结论。基于此,文章提出建议:为了提升实验的内在效度,较长时间的实验研究应纳入工具的跨时测量恒等性检验。     

量子场论中的时空特性分析

经典量子力学中粒子的基态场值,对应于量子场论中的真空期待值,场值的非零和零值,直接与背景空间的平坦性有关.当我们把坐标系建于运动的微观粒子之上时,坐标系的运动状态,又刚好与时空的平坦性相联系.匀速动的坐标系时空均匀而对称,加速运动的坐标系时空不均匀、不对称,有了这种联系,我们对量子场论中规范不变化的时空特征和真空对称性破缺机制就可做出合理的解释.