A Comparison of Factor Rotation Methods for Dichotomous Data

Exploratory factor analysis (EFA) is frequently used in the social sciences and is a common component in many validity studies. A core aspect of EFA is the determination of which observed indicator variables are associated with which latent factors through the use of factor loadings. Loadings are initially extracted using an algorithm, such as maximum likelihood or weighted least squares, and then transformed - or rotated - to make them more interpretable. There are a number of rotational techniques available to the researcher making use of EFA. Prior work has discussed the advantages of a number of these criteria from a theoretical perspective, but few previous studies compare their performance across a broad range of conditions. This simulation study compared eight factor rotation criteria in terms of how well they were able to group dichotomous indicator variables correctly on the same factor, order the indicators by the magnitude of the factor loadings (identifying those indicators that were most strongly associated with the factors) and estimate the inter-factor correlations. Results reveal a mixed pattern of performance among the various rotations with the orthogonal Equamax consistently near the top in terms of correctly grouping and ordering indicator variables, and the orthogonal Facparsim performing well with more observed indicators. Advice regarding possible rotations to use for researchers conducting EFA with dichotomous indicators is provided

Regularization Methods for Fitting Linear Models with Small Sample Sizes: Fitting the Lasso Estimator using R

Researchers and data analysts are sometimes faced with the problem of very small samples, where the number of variables approaches or exceeds the overall sample size; i.e. high dimensional data. In such cases, standard statistical models such as regression or analysis of variance cannot be used, either because the resulting parameter estimates exhibit very high variance and can therefore not be trusted, or because the statistical algorithm cannot converge on parameter estimates at all. There exist an alternative set of model estimation procedures, known collectively as regularization methods, which can be used in such circumstances, and which have been shown through simulation research to yield accurate parameter estimates. The purpose of this paper is to describe, for those unfamiliar with them, the most popular of these regularization methods, the lasso, and to demonstrate its use on an actual high dimensional dataset involving adults with autism, using the R software language. Results of analyses involving relating measures of executive functioning with a full scale intelligence test score are presented, and implications of using these models are discussed. Accessed 4,969 times on https://pareonline.net from May 08, 2016 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right

Using Exploratory Factor Analysis for Locating Invariant Referents in Factor Invariance Studies

Model identification in multi-group confirmatory factor analysis (MCFA) requires an equality constraint of referent variables across groups. Invariance assumption violations make it difficult to locate parameters that actually differ. Suggested procedures for locating invariant referents are cumbersome, complex, and provide imperfect results. Exploratory factor analysis (EFA) may be an alternative because of its ease of use, yet empirical evaluation of its effectiveness is lacking. EFAs accuracy for distinguishing invariant from non-invariant referents was examined

Comparing Factor Loadings in Exploratory Factor Analysis: A New Randomization Test

Factorial invariance testing requires a referent loading to be constrained equal across groups. This study introduces a randomization test for comparing group exploratory factor analysis loadings so as to identify an invariant referent. Results show that it maintains the Type I error rate while providing adequate power under most conditions

Parameter Estimation with Mixture Item Response Theory Models: A Monte Carlo Comparison of Maximum Likelihood and Bayesian Methods

The Mixture Item Response Theory (MixIRT) can be used to identify latent classes of examinees in data as well as to estimate item parameters such as difficulty and discrimination for each of the groups. Parameter estimation via maximum likelihood (MLE) and Bayesian estimation based on the Markov Chain Monte Carlo (MCMC) are compared for classification accuracy and parameter estimation bias for difficulty and discrimination. Standard error magnitude and coverage rates were compared across number of items, number of latent groups, group size ratio, total sample size and underlying item response model. Results show that MCMC provides more accurate group membership recovery across conditions and more accurate parameter estimates for smaller samples and fewer items. MLE produces narrower confidence intervals than MCMC and more accurate parameter estimates for larger samples and more items. Implications of these results for research and practice are discussed

A Mixture IRT Analysis of Risky Youth Behavior

The study reported in this manuscript used a mixture item response model with data from the Youth Risk Behavior Survey 2009 (N = 16,410) to identify subtypes of adolescents at-risk for engaging in unhealthy behaviors, and to find individual survey items that were most effective at identifying such students within each subtype. The goal of the manuscript is twofold: (1) To demonstrate the utility of the mixture item response theory model for identifying subgroups in the population and for highlighting the use of group specific item response parameters and (2) To identify typologies of adolescents based on their propensity for engaging in sexually and substance use risky behaviors. Results indicate that four classes of youth exist in the population, with differences in risky sexual behaviors and substance use. The first group had a greater propensity to engage in risky sexual behavior, while group 2 was more likely to smoke tobacco and drink alcohol. Group 3 was the most likely to use other substances, such as marijuana, methamphetamine, and other mind altering drugs, and group 4 had the lowest propensity for engaging in any of the sexual or substance use behaviors included in the survey. Finally, individual items were identified for each group that can be most effective at identifying individuals at greatest risk. Further proposed directions of research and the contribution of this analysis to the existing literature are discussed

Examining the Relationship Between Teacher Performance Ratings and District Under the Ohio Teacher Evaluation System

The soundness of the Ohio Teacher Evaluation System (OTES) depends heavily on evaluators’ uniform interpretation of the qualitative Teacher Performance rubric. This study investigates the relationship between teachers’ district of employment, and the Teacher Performance ratings they receive under OTES. For Ohio districts that implemented OTES in 2012-2013, 2013-2014, and 2014-2015, the proportion of various Teacher Performance ratings and Student Growth Measures ratings are examined and compared to statewide proportions, using descriptive data and a log-linear model. Findings speak to the importance of a continued or renewed emphasis on fostering uniform interpretation and implementation of teacher evaluation rubrics and systems

The Association Between the Long-Term Change in Directly Measured Cardiorespiratory Fitness and Mortality Risk

Introduction: There is a strong inverse association between cardiorespiratory fitness (CRF) and mortality outcomes. This relationship has predominantly been assessed cross-sectionally, however low CRF is a modifiable risk factor, thus assessing this association using a single baseline measure may be sub-optimal. Purpose: To examine the association of the long-term change in CRF, measured using cardiopulmonary exercise testing (CPX) with all-cause and disease-specific mortality. Methods: Participants included 833 apparently healthy men and women (42.9±10.8 years) who underwent two maximal CPXs, the second CPX being ≥ 1 year following the baseline assessment. Participants were followed for 17.7 ± 11.8 years for allcause, cardiovascular disease (CVD), and cancer mortality. Cox-proportional hazard models were performed to determine the association between the change in CRF, computed as visit 1 (V1) peak oxygen consumption (VO2peak (ml·kg-1·min-1)) – visit 2 (V2) VO2peak, and mortality outcomes. Results: During follow-up, 172 participants died. Overall, the change in CPX-derived CRF was inversely related to all-cause, CVD, and cancer mortality (p\u3c0.05). Each 1 ml·kg-1·min-1 increase was associated with a 10.8, 14.7, and 15.9% reductions in allcause, CVD, and cancer mortality, respectively. The inverse relationship between CRF and all-cause mortality remained significant (p\u3c0.05) when men and women were examined independently, after adjusting for years since first CPX, baseline VO2peak, and age. Conclusion: Long-term changes in CRF were inversely related to mortality outcomes, and mortality was better predicted by CRF measured at subsequent examination than baseline CRF. These findings support the recent American Heart Association scientific statement advocating CRF as a clinical vital sign that should be assessed routinely in clinical practice, as well as support regular participation in physical activity to maintain adequate CRF levels across the lifespan

Charter School Funding: Inequity Persists

In 2005, the Thomas B. Fordham Institute, with the support of the Walton Family Foundation and the Bill and Melinda Gates Foundation, published a report showing that charter schools were greatly underfunded compared to traditional district schools in the 2002-03 school year. This report uses FY 2006-07 data, the most recent available when this project began, to describe the state of charter funding, and to see if it has changed since the last report. It includes all of the original 17 states and Washington D.C., as well as seven new states. The new edition also improves our method of analyzing state-level disparities to provide a better estimate of how much funding charter schools receive compared to how much funding district schools would have received to educate the same students

Profiles of Temperament and Perfectionism in High Ability College Students

Different physical, mental, and motivational outcomes for perfectionistic strivings and perfectionistic concerns indicate that individuals have different experiences of perfectionism. Although research has focused on parenting practices as a factor related to these differences, little research has examined the impact of temperamental differences on perfectionism. In the current study, 434 high ability undergraduate students completed perfectionism, adult temperament, and personality measures. Latent class analysis that examined the patterns among the relationships between self-oriented perfectionism, socially prescribed perfectionism, and four dimensions of adult temperament (negative affect, effortful control, extraversion, orienting sensitivity) revealed three distinct subgroups. Although the largest subgroup demonstrated patterns consistent with prior research on perfectionism (e.g., perfectionism associated with negative affect), two other subgroups revealed separate patterns that were inconsistent with prior research (e.g., one subgroup had negative relationships between negative affect and both types of perfectionism). Our results demonstrate that temperament may play an important role in explaining the heterogeneity among perfectionists