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.     

Dyadic Curve-of-Factors Model: An Introduction and Illustration of a Model for Longitudinal Nonexchangeable Dyadic Data

The analysis of longitudinal data collected from nonexchangeable dyads presents a challenge for applied researchers for various reasons. This article introduces the dyadic curve-of-factors model (D–COFM), which extends the curve-of-factors model (COFM) proposed by McArdle (1988) for use with nonexchangeable dyadic data. The D–COFM overcomes problems with modeling composite scores across time and instead permits examination of the growth in latent constructs over time. The D–COFM also appropriately models the interdependency among nonexchangeable dyads. Different parameterizations of the D–COFM are illustrated and discussed using a real data set to aid applied researchers when analyzing dyadic longitudinal data.     

Variance and Invariance in Expert and Novice Triple Junipers

Abstract

The purpose of this study was to examine relative timing, relative distance, and effector independence characteristics of the triple jump. We videotaped expert and novice triple jumpers using standing and running starts. On some trials, the triple jumpers were required to take off from their nondominant leg. Gentner's (1987) interaction test was used to assess the proportional duration model in describing the timing of the component submovements. For both experts and novices, the proportional durations varied with the type of start. For experts, the relative timing of the jump components was independent of the take-off leg. The findings were mixed for the novices. Similar results were obtained when relative distance was examined. These results are discussed with respect to constructs related to variability in skilled performance.     

Student self-assessment practices: the role of gender,school level and goal orientation

The purpose of this study was to examine the effects of the key demographic variables of gender, school level and goal orientation on students’ self-assessment practices, including self-directed feedback seeking (SDFS) and self-reflection (SR). A total of 8843 Hong Kong students were surveyed, ranging from Primary 4 to Secondary 6. The results showed that female students demonstrated higher levels of self-assessment practices than male students, including both SDFS and SR. School level was also significantly associated with secondary students’ engagement in SR. Mastery goal orientation (MGO) was a significant and positive predictor of self-assessment practice including both SDFS and SR, while performance goal orientation (PGO) was a significantly negative predictor. Students with a higher level of MGO, or a lower level of PGO, were more likely to conduct self-assessment. The educational implications of the findings are discussed.     

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     

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.     

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.     

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.