Exploratory factor analysis (EFA) and confirmatory factor analysis (CFA), path analysis, and structural equation modeling (SEM) have long histories in clinical research. Although CFA has largely superseded EFA, CFAs of multidimensional constructs typically fail to meet standards of good measurement: goodness of fit, measurement invariance, lack of differential item functioning, and well-differentiated factors in support of discriminant validity. Part of the problem is undue reliance on overly restrictive CFAs in which each item loads on only one factor. Exploratory SEM (ESEM), an overarching integration of the best aspects of CFA/SEM and traditional EFA, provides confirmatory tests of a priori factor structures, relations between latent factors and multigroup/multioccasion tests of full (mean structure) measurement invariance. It incorporates all combinations of CFA factors, ESEM factors, covariates, grouping/multiple-indicator multiple-cause (MIMIC) variables, latent growth, and complex structures that typically have required CFA/SEM. ESEM has broad applicability to clinical studies that are not appropriately addressed either by traditional EFA or CFA/SEM.

In this investigation, we used a classic latent profile analysis (LPA), a person-centered approach, to identify groups of students who had similar profiles for multiple dimensions of academic self-concept (ASC) and related these LPA groups to a diverse set of correlates. Consistent with a priori predictions, we identified 5 LPA groups representing a combination of profile level (high vs. low overall ASC) and profile shape (math vs. verbal self-concepts) that complemented results based on a traditional variable-centered approach. Whereas LPA groups were substantially and logically related to the set of 10 correlates, much of the predictive power of individual ASC factors was lost in the formation of groups and the inclusion of the correlates into the LPA distorted the nature of the groups. LPA issues examined include distinctions between quantitative (level) and qualitative (shape) differences in LPA profiles, goodness of fit and the determination of the number of LPA groups, appropriateness of correlates as covariates or auxiliary variables, and alternative approaches to present and interpret the results.

This study is a methodological-substantive synergy, demonstrating the power and flexibility of exploratory structural equation modeling (ESEM) methods that integrate confirmatory and exploratory factor analyses (CFA and EFA), as applied to substantively important questions based on multidimentional students' evaluations of university teaching (SETs). For these data, there is a well established ESEM structure but typical CFA models do not fit the data and substantially inflate correlations among the nine SET factors (median rs = .34 for ESEM, .72 for CFA) in a way that undermines discriminant validity and usefulness as diagnostic feedback. A 13-model taxonomy of ESEM measurement invariance is proposed, showing complete invariance (factor loadings, factor correlations, item uniquenesses, item intercepts, latent means) over multiple groups based on the SETs collected in the first and second halves of a 13-year period. Fully latent ESEM growth models that unconfounded measurement error from communality showed almost no linear or quadratic effects over this 13-year period. Latent multiple indicators multiple causes models showed that relations with background variables (workload/difficulty, class size, prior subject interest, expected grades) were small in size and varied systematically for different ESEM SET factors, supporting their discriminant validity and a construct validity interpretation of the relations. A new approach to higher order ESEM was demonstrated, but was not fully appropriate for these data. Based on ESEM methodology, substantively important questions were addressed that could not be appropriately addressed with a traditional CFA approach.

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.

This study illustrates an overarching psychometric approach of broad relevance to investigations of 2 sources of construct-relevant psychometric multidimensionality present in many complex multidimensional instruments routinely used in psychological and educational research. These 2 sources of construct-relevant psychometric multidimensionality are related to (a) the fallible nature of indicators as perfect indicators of a single construct, and (b) the hierarchical nature of the constructs being assessed. The first source is identified by comparing confirmatory factor analytic (CFA) and exploratory structural equation modeling (ESEM) solutions. The second source is identified by comparing first-order, hierarchical, and bifactor measurement models. To provide an applied illustration of the substantive relevance of this framework, we first apply these models to a sample of German children (N = 1,957) who completed the Self-Description Questionnaire (SDQ–I). Then, in a second study using a simulated data set, we provide a more pedagogical illustration of the proposed framework and the broad range of possible applications of bifactor ESEM models.

Despite the increased popularity of person-centered analyses, no comprehensive approach exists to guide the systematic investigation of the similarity (or generalizability) of latent profiles, their predictors, and their outcomes across subgroups of participants or time points. We propose a six-step process to assess configural (number of profiles), structural (within-profile means), dispersion (within-profile variability), distributional (size of the profiles), predictive (relations between predictors and profile membership), and explanatory (relations between profile membership and outcomes) similarity. We then apply this approach to data on organizational commitment mindsets collected in North America (n = 492) and France (n = 476). This approach provides a rigorous method to systematically and quantitatively assess the extent to which a latent profile solution generalizes across diverse samples, such as in the cross-national comparison in our illustrative example, or the extent to which interventions or naturalistic changes may impact the nature of a latent profile solution. This approach also helps to identify the nature of any differences that might be present, thus providing richer interpretations of observed differences and ideas for future research.