Cross-Level Invariance in Multilevel Factor Models

When modeling latent variables at multiple levels, it is important to consider the meaning of the latent variables at the different levels. If a higher-level common factor represents the aggregated version of a lower-level factor, the associated factor loadings will be equal across levels. However, many researchers do not consider cross-level invariance constraints in their research. Not applying these constraints when in fact they are appropriate leads to overparameterized models, and associated convergence and estimation problems. This simulation study used a two-level mediation model on common factors to show that when factor loadings are equal in the population, not applying cross-level invariance constraints leads to more estimation problems and smaller true positive rates. Some directions for future research on cross-level invariance in MLSEM are discussed.     

Testing measurement invariance of PISA 2015 mathematics,science, and ICT scales using the alignment method

This study investigates measurement invariance of the mathematics, science, and ICT scales across the 47 countries that participated in the PISA 2015 ICT Familiarity Questionnaire. Knowing whether the same constructs and measurements can be reliably compared across countries constitutes an important goal. The Alignment method is employed to test the measurement invariance of the three scales. The results show that mathematics and science scores are highly invariant and can be used to compare countries, whereas the ICT scale is mostly non-invariant and cannot be used to reliably compare ICT means across all participating countries. Implications and limitations are discussed.     

C_q(D)上扩展型广义块Pick矩阵的秩不变性

利用块Toeplitz向量方法,证明同一个矩阵值Carathéodory函数的扩展型广义块Pick矩阵的秩重合于具有秩不变性的块Toeplitz矩阵的秩,从而证明了该类型的广义块Pick矩阵的秩不变性.     

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.     

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.     

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.     

Testing Factorial Invariance of the Amotivation Inventory-Physical Education Across Gender for Urban Adolescents

Lack of motivation, or amotiation, is emerging as a critical issue in high school physical education. The Amotivation Inventory-Physical Education (Shen, Winger, Li, Sun, & Rukavina, 2010) was developed to measure the multidimensional nature of amotivation construct in physical education. This study was designed to examine the consistency of the metric properties of Amotivation Inventory-Physical Education scores by evaluating their factorial structure for invariance across gender in a sample of 985 urban inner-city high school adolescents. Latent mean invariance was also tested. Results revealed that constraining factor loadings and intercepts in sequential configural, metric, and scalar invariances had no meaningful impact on model fit. However, gender might play a role in the magnitude of factor scores. Findings suggest that the four-factor structure of the Amotivation Inventory-Physical Education is a satisfactory representation of motivational deficits for urban inner-city adolescents and provide significant validity evidence for the scale scores in urban high school settings.     

Factorial equivalence of social cognitive theory: educational levels × time differences

The study of social cognitive theory has involved a number of inquiries, notably one of which concerns the formation and development of self-efficacy beliefs. Social cognitive theory indicates that we form our self-efficacy beliefs from four major sources of information: enactive performance accomplishments, vicarious experiences, verbal persuasion and emotional and physiological states. We advance this tenet by exploring across four occasions, and the four sources of information in the context of elementary school learning. Two cohorts of participants, at level 2 (N?=?352 3rd–4th grade students) and level 3 (N?=?264 5th–6th grade students), answered a Likert’s-scale inventory that we developed and used in a previous study. We proposed and tested a number of a priori models using LISREL 8.80. Furthermore, factorial invariance analyses of the inventory were performed, a posteriori, to determine the stability/instability of the four sources of information.     

Assessing construct of DIBELS: Measurement invariance of DIBELS subscales,from kindergarten to the first grade

A challenge using the Dynamic Indicators of Basic Early Literacy Skills (DIBELS) in studying reading growth is that reading skills children exhibit change by age. In order to study growth using changing subscales, it is necessary to examine measurement invariance and measurement structure underlying the different subscales. The purpose of this paper is to examine the measurement structure of the DIBELS subscales, particular measurement invariance. The results indicate that the DIBELS subscales do not seem to have metric invariance but they do share a common factor over time, suggesting that the same construct of reading skills were measured but they manifested in the different fashion over time.