Exploratory and Confirmatory Factor Analysis of the School Level Environment Questionnaire (SLEQ)

The purpose of the present study was to validate an existing school environment instrument, the School Level Environment Questionnaire (SLEQ). The SLEQ consists of 56 items, with seven items in each of eight scales. One thousand, one hundred and six (1106) teachers in 59 elementary schools in a southwestern USA public school district completed the instrument. An exploratory factor analysis was undertaken for a random sample of half of the completed surveys. Using principal axis factoring with oblique rotation, this analysis suggested that 13 items should be dropped and that the remaining 43 items could best be represented by seven rather than eight factors. A confirmatory factor analysis was run with the other half of the original sample using structural equation modeling. Examination of the fit indices indicated that the model came close to fitting the data, with goodness-of-fit (GOF) coefficients just below recommended levels. A second model was then run with two of the seven factors, with their associated items removed. That left five factors with 35 items. Model fit was improved. A third model was tried, using the same five factors with 35 items but with correlated residuals between some of the items within a factor. This model seemed to fit the data well, with GOF coefficients in recommended ranges. These results led to a refined, more parsimonious version of the SLEQ that was then used in a larger study. Future research is needed to see if this model would fit other samples in different elementary schools and in secondary schools both in the USA and in other countries. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Systematic Evaluation and Comparison Between Exploratory Structural Equation Modeling and Bayesian Structural Equation Modeling

In this study, we contrast two competing approaches, not previously compared, that balance the rigor of CFA/SEM with the flexibility to fit realistically complex data. Exploratory SEM (ESEM) is claimed to provide an optimal compromise between EFA and CFA/SEM. Alternatively, a family of three Bayesian SEMs (BSEMs) replace fixed-zero estimates with informative, small-variance priors for different subsets of parameters: cross-loadings (CL), residual covariances (RC), or CLs and RCs (CLRC). In Study 1, using three simulation studies, results showed that (1) BSEM-CL performed more closely to ESEM; (2) BSEM-CLRC did not provide more accurate model estimation compared with BSEM-CL; (3) BSEM-RC provided unstable estimation; and (4) different specifications of targeted values in ESEM and informative priors in BSEM have significant impacts on model estimation. The real data analysis (Study 2) showed that the differences in estimation between different models were largely consistent with those in Study1 but somewhat smaller.     

Neglect the Structure of Multitrait-Multimethod Data at Your Peril: Implications for Associations With External Variables

In 1959, Campbell and Fiske introduced the use of multitrait–multimethod (MTMM) matrices in psychology, and for the past 4 decades confirmatory factor analysis (CFA) has commonly been used to analyze MTMM data. However, researchers do not always fit CFA models when MTMM data are available; when CFA modeling is used, multiple models are available that have attendant strengths and weaknesses. In this article, we used a Monte Carlo simulation to investigate the drawbacks of either using CFA models that fail to match the data-generating model or completely ignore the MTMM structure of data when the research goal is to uncover associations between trait constructs and external variables. We then used data from the National Institute of Child Health and Human Development Study of Early Child Care and Youth Development to illustrate the substantive implications of fitting models that partially or completely ignore MTMM data structures. Results from analyses of both simulated and empirical data show noticeable biases when the MTMM data structure is partially or completely neglected.     

Comparison of Frequentist and Bayesian Regularization in Structural Equation Modeling

Research in regularization, as applied to structural equation modeling (SEM), remains in its infancy. Specifically, very little work has compared regularization approaches across both frequentist and Bayesian estimation. The purpose of this study was to address just that, demonstrating both similarity and distinction across estimation frameworks, while specifically highlighting more recent developments in Bayesian regularization. This is accomplished through the use of two empirical examples that demonstrate both ridge and lasso approaches across both frequentist and Bayesian estimation, along with detail regarding software implementation. We conclude with a discussion of future research, advocating for increased evaluation and synthesis across both Bayesian and frequentist frameworks.     

Measurement Invariance Testing with Many Groups: A Comparison of Five Approaches

With the increasing use of international survey data especially in cross-cultural and multinational studies, establishing measurement invariance (MI) across a large number of groups in a study is essential. Testing MI over many groups is methodologically challenging, however. We identified 5 methods for MI testing across many groups (multiple group confirmatory factor analysis, multilevel confirmatory factor analysis, multilevel factor mixture modeling, Bayesian approximate MI testing, and alignment optimization) and explicated the similarities and differences of these approaches in terms of their conceptual models and statistical procedures. A Monte Carlo study was conducted to investigate the efficacy of the 5 methods in detecting measurement noninvariance across many groups using various fit criteria. Generally, the 5 methods showed reasonable performance in identifying the level of invariance if an appropriate fit criterion was used (e.g., Bayesian information criteron with multilevel factor mixture modeling). Finally, general guidelines in selecting an appropriate method are provided.     

Investigating Factorial Invariance of Latent Variables Across Populations When Manifest Variables Are Missing Completely

Difficulties arise in multiple-group evaluations of factorial invariance if particular manifest variables are missing completely in certain groups. Ad hoc analytic alternatives can be used in such situations (e.g., deleting manifest variables), but some common approaches, such as multiple imputation, are not viable. At least 3 solutions to this problem are viable: analyzing differing sets of variables across groups, using pattern mixture approaches, and a new method using random number generation. The latter solution, proposed in this article, is to generate pseudo-random normal deviates for all observations for manifest variables that are missing completely in a given sample and then to specify multiple-group models in a way that respects the random nature of these values. An empirical example is presented in detail comparing the 3 approaches. The proposed solution can enable quantitative comparisons at the latent variable level between groups using programs that require the same number of manifest variables in each group.     

Investigating the Multidimensionality of Need Fulfillment: A Bifactor Exploratory Structural Equation Modeling Representation

This article assesses the multidimensionality of the Basic Psychological Need Satisfaction and Frustration Scale (BPNSFS) using bifactor exploratory structural equation modeling (bifactor ESEM). The first study relies on a sample of community adults (N = 2,301), and revealed the superiority of a bifactor ESEM representation, supporting the 6-factor structure of BPNSFS ratings, and the presence of a single continuum of need fulfillment relative to 2 distinct dimensions reflecting need satisfaction and frustration. These results were replicated in a second representative sample of the Hungarian adult population (N = 504), as well as across gender, and found no evidence of differential item functioning as a function of age. Relative to males, females presented higher levels of relatedness satisfaction and lower levels of competence satisfaction. Finally, autonomy frustration decreased with age, whereas competence satisfaction and frustration presented opposite curvilinear tendencies, showing that the fulfillment of this need increased sharply for younger participants, a tendency that became less pronounced with age.     

Investigating the theoretical structure of the DAS‐II core battery at school age using Bayesian structural equation modeling

Bayesian structural equation modeling (BSEM) was used to investigate the latent structure of the Differential Ability Scales—Second Edition core battery using the standardization sample normative data for ages 7–17. Results revealed plausibility of a three‐factor model, consistent with publisher theory, expressed as either a higher‐order (HO) or a bifactor (BF) model. The results also revealed an alternative structure with the best model fit, a two‐factor BF model with Matrices (MA) and Sequential and Quantitative Reasoning (SQ) loading on g only with no respective group factor loading. This was only the second study to use BSEM to investigate the structure of a commercial ability test and the first to use a large normative sample and the specification of both approximate zero cross‐loadings and correlated residual terms. It is believed that the results produced from the current study will advance the field's understanding of not only the factor structure of the DAS‐II core battery but also the potential utility of BSEM in psychometric investigations of intelligence test structures.     

Cross-National Validation of the What is Happening in this Class? (WIHIC) Questionnaire using Confirmatory Factor Analysis

Learning Environments Research - The What Is Happening In this Class? (WIHIC) questionnaire was validated cross-nationally using a sample of 3980 high school students from Australia, the UK and...     

广州澳门两地青少年价值观的比较研究

以920名广州青少年及665名澳门青少年为被试,通过探索性因素分析和验证性因素分析,编制青少年价值观问卷,并考察两地青少年价值观的特点及其影响因素。结果表明：（1）青少年价值观问卷由社会观、人际观、家庭观、成就观、理想观、尊严观、生活观,及爱情观等八个因素组成;（2）问卷具有较好的信度和效度;（3）家庭观、成就观是两地青少年的主导价值观,但两地青少年在某些价值观维度的得分上存在差异;（4）两地青少年在“影响价值观形成的因素”的看法上存在一定的差异,但都将“家庭的影响”和“个人生活经历的变化”视为最重要的影响因素。     

The Model Size Effect in SEM: Inflated Goodness-of-Fit Statistics Are Due to the Size of the Covariance Matrix

The size of a model has been shown to critically affect the goodness of approximation of the model fit statistic T to the asymptotic chi-square distribution in finite samples. It is not clear, however, whether this “model size effect” is a function of the number of manifest variables, the number of free parameters, or both. It is demonstrated by means of 2 Monte Carlo computer simulation studies that neither the number of free parameters to be estimated nor the model degrees of freedom systematically affect the T statistic when the number of manifest variables is held constant. Increasing the number of manifest variables, however, is associated with a severe bias. These results imply that model fit drastically depends on the size of the covariance matrix and that future studies involving goodness-of-fit statistics should always consider the number of manifest variables, but can safely neglect the influence of particular model specifications.     

Emphasis on emotions in student learning: Analyzing relationships between overexcitabilities and the learning approach using Bayesian MIMIC modeling

The aim of this study is to investigate interrelationships between overexcitability and learning patterns from the perspective of personality development according to Dabrowski’s theory of positive disintegration. To this end, Bayesian structural equation modeling (BSEM) is applied which allows for the simultaneous inclusion in the measurement model of all, approximate zero cross-loadings and residual covariances based on zero-mean, small-variance priors, and represents substantive theory better. Our BSEM analysis with a sample of 516 students in higher education yields positive results regarding the validity of the model, in contrast to a frequentist approach to validation, and reveals that overexcitability – the degree and nature of which is characteristic of the potential for advanced personality development, according to Dabrowski’s theory – is substantially related to the way in which information is processed, as well as to the regulation strategies that are used for this purpose and to study motivation. Overexcitability is able to explain variations in learning patterns to varying degrees, ranging from weakly (3.3% for reproduction-directed learning for the female group) to rather strongly (46.1% for meaning-directed learning for males), with intellectual overexcitability representing the strongest indicator of deep learning. This study further argues for the relevance of including emotion dynamics – taking into account their multilevelness – in the study of the learning process.     

Cultural,social, and economic capital constructs in international assessments: an evaluation using exploratory structural equation modeling

The article employs exploratory structural equation modeling (ESEM) to evaluate constructs of economic, cultural, and social capital in international large-scale assessment (LSA) data from the Progress in International Reading Literacy Study (PIRLS) 2006 and the Programme for International Student Assessment (PISA) 2009. ESEM integrates the theory-generating approach of exploratory factor analysis (EFA) and theory-testing approach of confirmatory factor analysis (CFA). It relaxes the zero-loading restriction in CFA, allowing items to load on different factors simultaneously, and it provides measurement invariance tests across countries not available in EFA. A main criticism of international LSA studies is the extended use of indicators poorly grounded in theory, like socioeconomic status, that prevent the study of mechanisms underlying associations with student outcomes. This article contributes to addressing this criticism by providing statistical criteria to evaluate the fit of well-defined sociological constructs with the empirical data.     

Evaluation of Structural Relationships in Autoregressive Cross-Lagged Models Under Longitudinal Approximate Invariance:A Bayesian Analysis

To infer longitudinal relationships among latent factors, traditional analyses assume that the measurement model is invariant across measurement occasions. Alternative to placing cross-occasion equality constraints on parameters, approximate measurement invariance (MI) can be analyzed by specifying informative priors on parameter differences between occasions. This study evaluated the estimation of structural coefficients in multiple-indicator autoregressive cross-lagged models under various conditions of approximate MI using Bayesian structural equation modeling. Design factors included factor structures, conditions of non-invariance, sizes of structural coefficients, and sample sizes. Models were analyzed using two sets of small-variance priors on select model parameters. Results showed that autoregressive coefficient estimates were more accurate for the mixed pattern than the decreasing pattern of non-invariance. When a model included cross-loadings, an interaction was found between the cross-lagged estimates and the non-invariance conditions. Implications of findings and future research directions are discussed.     

The influence of personality factors,value appraisals,and control appraisals on cognitive test anxiety

Cognitive test anxiety is a considerable barrier to academic success. The control value theory of achievement emotions suggests emotions within academic situations—including test‐anxious responses—follow from control and value appraisals. Furthermore, the control value theory suggests a multitude of individual‐level factors that influence appraisals. However, few investigations have explored the interactive influence of enduring personality traits and control and value appraisals on the experience of cognitive test anxiety. The current study was designed to explore the relationship among openness to experience, neuroticism, conscientiousness, control and value appraisals, and cognitive test anxiety. Participants (N = 481) completed the Big Five Inventory, the Motivated Strategies for Learning Questionnaire, and the Cognitive Test Anxiety Scale‐Short Form. Using exploratory structural equation modeling, we demonstrated that value and control appraisals were important predictors of cognitive test anxiety. Furthermore, results indicated that openness to experience was a positive predictor of value appraisals. Finally, results indicated that higher levels of control appraisals were associated with higher levels of conscientiousness and openness to experience and lower levels of neuroticism. These findings have important implications for our understanding of the determinants of cognitive test anxiety and have implications for efforts designed to identify test‐anxious students.     

A Comparison of Method Effects in Two Confirmatory Factor Models for Structurally Different Methods

It is well known that measurement error in observable variables induces bias in estimates in standard regression analysis and that structural equation models are a typical solution to this problem. Often, multiple indicator equations are subsumed as part of the structural equation model, allowing for consistent estimation of the relevant regression parameters. In many instances, however, embedding the measurement model into structural equation models is not possible because the model would not be identified. To correct for measurement error one has no other recourse than to provide the exact values of the variances of the measurement error terms of the model, although in practice such variances cannot be ascertained exactly, but only estimated from an independent study. The usual approach so far has been to treat the estimated values of error variances as if they were known exact population values in the subsequent structural equation modeling (SEM) analysis. In this article we show that fixing measurement error variance estimates as if they were true values can make the reported standard errors of the structural parameters of the model smaller than they should be. Inferences about the parameters of interest will be incorrect if the estimated nature of the variances is not taken into account. For general SEM, we derive an explicit expression that provides the terms to be added to the standard errors provided by the standard SEM software that treats the estimated variances as exact population values. Interestingly, we find there is a differential impact of the corrections to be added to the standard errors depending on which parameter of the model is estimated. The theoretical results are illustrated with simulations and also with empirical data on a typical SEM model.     

Growth Curve Modeling to Studying Change: A Comparison of Approaches Using Longitudinal Dyadic Data With Distinguishable Dyads

Although methodology articles have increasingly emphasized the need to analyze data from two members of a dyad simultaneously, the most popular method in substantive applications is to examine dyad members separately. This might be due to the underappreciation of the extra information simultaneous modeling strategies can provide. Therefore, the goal of this study was to compare multiple growth curve modeling approaches for longitudinal dyadic data (LDD) in both structural equation modeling and multilevel modeling frameworks. Models separately assessing change over time for distinguishable dyad members are compared to simultaneous models fitted to LDD from both dyad members. Furthermore, we compared the simultaneous default versus dependent approaches (whether dyad pairs’ Level 1 [or unique] residuals are allowed to covary and differ in variance). Results indicated that estimates of variance and covariance components led to conflicting results. We recommend the simultaneous dependent approach for inferring differences in change over time within a dyad.     

Estimating Latent Variable Interactions with the Unconstrained Approach: A Comparison of Methods to Form Product Indicators for Large,Unequal Numbers of Items

This Monte Carlo simulation study investigated methods of forming product indicators for the unconstrained approach for latent variable interaction estimation when the exogenous factors are measured by large and unequal numbers of indicators. Product indicators were created based on multiplying parcels of the larger scale by indicators of the smaller scale, multiplying the three most reliable indicators of each scale matched by reliability, and matching items by reliability to create as many product indicators as the number of indicators of the smallest scale. The unconstrained approach was compared with the latent moderated structural equations (LMS) approach. All methods considered provided unbiased parameter estimates. Unbiased standard errors were obtained in all conditions with the LMS approach and when the sample size was large with the unconstrained approach. Power levels to test the latent interaction and Type I error rates were similar for all methods but slightly better for the LMS approach.