Daniel A. Sass

Testing Measurement Invariance and Comparing Latent Factor Means Within a Confirmatory Factor Analysis Framework

Researchers commonly compare means and other statistics across groups with little concern for whether the measure possesses strong factorial invariance (i.e., equal factor loadings and intercepts/thresholds). When this assumption is violated, inaccurate inferences associated with statistical and practical significance can occur. This manuscript emphasizes the importance of testing for measurement invariance (MI) and provides guidance when conducting these tests. Topics discussed are potential causes of noninvariant items, the difference between measurement bias and invariance, remedies for noninvariant measures, and considerations associated with model estimation. Using a sample of 491 teachers, a demonstration is also provided that evaluates whether a newly constructed behavior and instructional management scale is invariant across elementary and middle school teachers. Analyses revealed that the results differ slightly based on the estimation method utilized although these differences did not greatly influence the latent factor mean difference conclusions. Additional implications and considerations related to invariance testing are discussed.

A Comparative Investigation of Rotation Criteria Within Exploratory Factor Analysis

Exploratory factor analysis (EFA) is a commonly used statistical technique for examining the relationships between variables (e.g., items) and the factors (e.g., latent traits) they depict. There are several decisions that must be made when using EFA, with one of the more important being choice of the rotation criterion. This selection can be arduous given the numerous rotation criteria available and the lack of research/literature that compares their function and utility. Historically, researchers have chosen rotation criteria based on whether or not factors are correlated and have failed to consider other important aspects of their data. This study reviews several rotation criteria, demonstrates how they may perform with different factor pattern structures, and highlights for researchers subtle but important differences between each rotation criterion. The choice of rotation criterion is critical to ensure researchers make informed decisions as to when different rotation criteria may or may not be appropriate. The results suggest that depending on the rotation criterion selected and the complexity of the factor pattern matrix, the interpretation of the interfactor correlations and factor pattern loadings can vary substantially. Implications and future directions are discussed.

Rotation Criteria and Hypothesis Testing for Exploratory Factor Analysis: Implications for Factor Pattern Loadings and Interfactor Correlations

Exploratory factor analysis (EFA) has long been used in the social sciences to depict the relationships between variables/items and latent traits. Researchers face many choices when using EFA, including the choice of rotation criterion, which can be difficult given that few research articles have discussed and/or demonstrated their differences. The goal of the current study is to help fill this gap by reviewing and demonstrating the utility of several rotation criteria. Furthermore, this article discusses and demonstrates the importance of using factor pattern loading standard errors for hypothesis testing. The choice of a rotation criterion and the use of standard errors in evaluating factor loadings are essential so researchers can make informed decisions concerning the factor structure. This study demonstrates that depending on the rotation criterion selected, and the complexity of the factor pattern matrix, the interfactor correlations and factor pattern loadings can vary substantially. It is also illustrated that the magnitude of the factor loading standard errors can result in different factor structures. Implications and future directions are discussed.

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.

Predicting teacher retention using stress and support variables

Purpose – Teacher attrition is a significant international concern facing administrators. Although a considerable amount of literature exists related to the causes of job dissatisfaction and teachers leaving the profession, relatively few theoretical models test the complex interrelationships between these variables. The goal of this paper is to partially fill this gap.Design/methodology/approach – Using a sample of 479 certified teachers who taught either at elementary (55.3 percent), middle (33.0 percent), or high (10.6 percent) school levels, three competing theoretical models with variables related to teacher stress or support were tested using structural equation modeling to predict job dissatisfaction and eventual intention to quit.Findings – The most parsimonious model revealed that student stressors completely mediated the relationship between teacher efficacy related to student engagement and job dissatisfaction, with social support superiors and student stressors being best predictors of job dis...

Undergraduate Engineering Students' Beliefs, Coping Strategies, and Academic Performance: An Evaluation of Theoretical Models.

Research has identified factors associated with academic success by evaluating relations among psychological and academic variables, although few studies have examined theoretical models to understand the complex links. This study used structural equation modeling to investigate whether the relation between test anxiety and final course grades was mediated by personal control, self-efficacy, goal orientation, coping strategies, and self-regulation. Participants were 297 undergraduate students taking an algebra course designed for engineering students. Results indicated that the proposed theoretical model was supported by the data, although a modified model produced a better fit. Other competing models were also tested. Collectively, analyses revealed that the psychological variables played important roles in predicting students’ grades, as all the structural coefficients and R 2 statistics were statistically and practically significant. Findings suggest value in the development and testing of additional models that contribute to the expansion of intervention programs to enhance academic outcomes among students.

Healthy & Ready to Learn: Examining the Efficacy of an Early Approach to Obesity Prevention and School Readiness

The collision of the childhood obesity epidemic with pressure to achieve high academic standards is of serious concern in the United States. Growing numbers of low-income, minority children face double jeopardy as alarming obesity rates further widen existing achievement gaps. Health and education disparities persist when children enter kindergarten lacking fundamental school readiness skills and are also at risk of obesity. The goal of this study was to address serious gaps in research by examining the efficacy of an innovative program, Healthy & Ready to Learn, an early approach to obesity prevention and promotion of school readiness. The study targeted low-income, predominantly Latino preschoolers who are particularly at risk of health and educational disparities. The pretest–posttest, quasi-experimental study involved 405 children, ages 3 to 5 years, enrolled in four matched Head Start centers. To ensure rigorous assessment, the study used a battery of objective and validated instruments as direct measures of child outcomes. Using multilevel modeling, several linear growth models were conducted with participants growth at Level-1 (i.e., time) and subject-level variables at Level-2 (i.e., treatment, gender, age, & body mass index classification) for each outcome variable of interest. Results revealed statistically significant improvements in growth (i.e., height), gross motor skills, physical activity levels, and receptive language development when comparing the treatment and control conditions. These promising results suggest that the Healthy & Ready to Learn program has potential as an early approach to improve childrens health and, simultaneously, enhance their trajectory toward better academic performance.

Testing measurement and structural invariance: Implications for practice

As part of their research activities, researchers in all areas of education develop measuring instruments, design and conduct experiments and surveys, and analyze data resulting from these activities. Educational research has a strong tradition of employing state-of-the-art statistical and psychometric (psychological measurement) techniques. Commonly referred to as quantitative methods, these techniques cover a range of statistical tests and tools. Quantitative research is essentially about collecting numerical data to explain a particular phenomenon of interest. Over the years, many methods and models have been developed to address the increasingly complex issues that educational researchers seek to address. This handbook serves to act as a reference for educational researchers and practitioners who desire to acquire knowledge and skills in quantitative methods for data analysis or to obtain deeper insights from published works. Written by experienced researchers and educators, each chapter in this handbook covers a methodological topic with attention paid to the theory, procedures, and the challenges on the use of that particular methodology. It is hoped that readers will come away from each chapter with a greater understanding of the methodology being addressed as well as an understanding of the directions for future developments within that methodological area.

Estimating Non-Normal Latent Trait Distributions within Item Response Theory Using True and Estimated Item Parameters

Item response theory (IRT) procedures have been used extensively to study normal latent trait distributions and have been shown to perform well; however, less is known concerning the performance of IRT with non-normal latent trait distributions. This study investigated the degree of latent trait estimation error under normal and non-normal conditions using four latent trait estimation procedures and also evaluated whether the test composition, in terms of item difficulty level, reduces estimation error. Most importantly, both true and estimated item parameters were examined to disentangle the effects of latent trait estimation error from item parameter estimation error. Results revealed that non-normal latent trait distributions produced a considerably larger degree of latent trait estimation error than normal data. Estimated item parameters tended to have comparable precision to true item parameters, thus suggesting that increased latent trait estimation error results from latent trait estimation rather than item parameter estimation.

Impact of Diabetes Disclosure on Perceptions of Eating and Self-Care Behaviors:

PURPOSE This study investigated whether disclosure of diabetes and gender influenced perceptions of eating and self-care behaviors. METHODS A vignette was developed in which a hypothetical friend engaged in diabetes self-care behaviors during a meal. Respondents (231 young adults) read vignettes that varied according to a 2 x 2 design (male vs female, preventative disclosure vs nondisclosure of diabetes). Participants answered 12 questions, which resulted in 2 factors: concern for friend and encourage professional help. RESULTS Significantly higher scores resulted on the concern for friend and encourage professional help factors when diabetes was not disclosed. Female characters also received significantly higher scores on the concern for friend factor. CONCLUSIONS Individuals with diabetes who choose to disclose their illness may prevent negative or incorrect perceptions related to self-care and eating behaviors, and may have a decreased likelihood that a true eating disorder would be identified by others.