NEO instruments are widely used to assess Big Five personality factors, but confirmatory factor analyses (CFAs) conducted at the item level do not support their a priori structure due, in part, to the overly restrictive CFA assumptions. We demonstrate that exploratory structural equation modeling (ESEM), an integration of CFA and exploratory factor analysis (EFA), overcomes these problems with responses (N = 3,390) to the 60-item NEO-Five-Factor Inventory: (a) ESEM fits the data better and results in substantially more differentiated (less correlated) factors than does CFA; (b) tests of gender invariance with the 13-model ESEM taxonomy of full measurement invariance of factor loadings, factor variances-covariances, item uniquenesses, correlated uniquenesses, item intercepts, differential item functioning, and latent means show that women score higher on all NEO Big Five factors; (c) longitudinal analyses support measurement invariance over time and the maturity principle (decreases in Neuroticism and increases in Agreeableness, Openness, and Conscientiousness). Using ESEM, we addressed substantively important questions with broad applicability to personality research that could not be appropriately addressed with the traditional approaches of either EFA or CFA.

Classroom context and climate are inherently classroom-level (L2) constructs, but applied researchers sometimes—inappropriately—represent them by student-level (L1) responses in single-level models rather than more appropriate multilevel models. Here we focus on important conceptual issues (distinctions between climate and contextual variables; use of classroom L2 rather than student-level L1 measures) and more appropriate multilevel models. To illustrate these issues, we consider the effects of two L2 classroom climate variables and one L2 classroom contextual variable on two L1 student-level outcomes for 2261 students in 128 classes. Through this example, we illustrate how to apply evolving doubly latent multilevel models to (a) evaluate the factor structure of L1 and L2 constructs based on multiple indicators of classroom climate and context measures, (b) control measurement error at L1 and L2, (c) control sampling error in the aggregation of L1 responses to form L2 constructs (the average of student-level responses to form classroom-level constructs), and (d) provide guidelines for appropriate analysis of classroom climate as an L2 construct. [Supplementary materials are available for this article. Go to the publisher's online edition of Educational Psychologist for the following free supplemental resources: Substantive basis of the present investigation and more detailed description of the methodology.]

This article is a methodological-substantive synergy. Methodologically, we demonstrate latent-variable contextual models that integrate structural equation models (with multiple indicators) and multilevel models. These models simultaneously control for and unconfound measurement error due to sampling of items at the individual (L1) and group (L2) levels and sampling error due the sampling of persons in the aggregation of L1 characteristics to form L2 constructs. We consider a set of models that are latent or manifest in relation to sampling items (measurement error) and sampling of persons (sampling error) and discuss when different models might be most useful. We demonstrate the flexibility of these 4 core models by extending them to include random slopes, latent (single-level or cross-level) interactions, and latent quadratic effects. Substantively we use these models to test the big-fish-little-pond effect (BFLPE), showing that individual student levels of academic self-concept (L1-ASC) are positively associated with individual level achievement (L1-ACH) and negatively associated with school-average achievement (L2-ACH)—a finding with important policy implications for the way schools are structured. Extending tests of the BFLPE in new directions, we show that the nonlinear effects of the L1-ACH (a latent quadratic effect) and the interaction between gender and L1-ACH (an L1 × L1 latent interaction) are not significant. Although random-slope models show no significant school-to-school variation in relations between L1-ACH and L1-ASC, the negative effects of L2-ACH (the BFLPE) do vary somewhat with individual L1-ACH. We conclude with implications for diverse applications of the set of latent contextual models, including recommendations about their implementation, effect size estimates (and confidence intervals) appropriate to multilevel models, and directions for further research in contextual effect analysis.

This substantive-methodological synergy applies evolving approaches to factor analysis to substantively important developmental issues of how five-factor-approach (FFA) personality measures vary with gender, age, and their interaction. Confirmatory factor analyses (CFAs) conducted at the item level often do not support a priori FFA structures, due in part to the overly restrictive assumptions of CFA models. Here we demonstrate that exploratory structural equation modeling (ESEM), an integration of CFA and exploratory factor analysis, overcomes these problems with the 15-item Big Five Inventory administered as part of the nationally representative British Household Panel Study (N = 14,021; age: 15-99 years, Mage = 47.1). ESEM fitted the data substantially better and resulted in much more differentiated (less correlated) factors than did CFA. Methodologically, we extended ESEM (introducing ESEM-within-CFA models and a hybrid of multiple groups and multiple indicators multiple causes models), evaluating full measurement invariance and latent mean differences over age, gender, and their interaction. Substantively the results showed that women had higher latent scores for all Big Five factors except for Openness and that these gender differences were consistent over the entire life span. Substantial nonlinear age effects led to the rejection of the plaster hypothesis and the maturity principle but did support a newly proposed la dolce vita effect in old age. In later years, individuals become happier (more agreeable and less neurotic), more self-content and self-centered (less extroverted and open), more laid back and satisfied with what they have (less conscientious, open, outgoing and extroverted), and less preoccupied with productivity.

The present investigation has a dual focus: to evaluate problematic practice in the use of item parcels and to suggest exploratory structural equation models (ESEMs) as a viable alternative to the traditional independent clusters confirmatory factor analysis (ICM-CFA) model (with no cross-loadings, subsidiary factors, or correlated uniquenesses). Typically, it is ill-advised to (a) use item parcels when ICM-CFA models do not fit the data, and (b) retain ICM-CFA models when items cross-load on multiple factors. However, the combined use of (a) and (b) is widespread and often provides such misleadingly good fit indexes that applied researchers might believe that misspecification problems are resolved--that 2 wrongs really do make a right. Taking a pragmatist perspective, in 4 studies we demonstrate with responses to the Rosenberg Self-Esteem Inventory (Rosenberg, 1965), Big Five personality factors, and simulated data that even small cross-loadings seriously distort relations among ICM-CFA constructs or even decisions on the number of factors; although obvious in item-level analyses, this is camouflaged by the use of parcels. ESEMs provide a viable alternative to ICM-CFAs and a test for the appropriateness of parcels. The use of parcels with an ICM-CFA model is most justifiable when the fit of both ICM-CFA and ESEM models is acceptable and equally good, and when substantively important interpretations are similar. However, if the ESEM model fits the data better than the ICM-CFA model, then the use of parcels with an ICM-CFA model typically is ill-advised--particularly in studies that are also interested in scale development, latent means, and measurement invariance.