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CFAs of multidimensional constructs often fail to meet standards of good measurement (e.g., goodness-of-fit, measurement invariance, and well-differentiated factors). Exploratory structural equation modeling (ESEM) represents a compromise between exploratory factor analysis' (EFA) flexibility, and CFA/SEM's rigor and parsimony, but lacks parsimony (particularly in large models) and might confound constructs that need to be kept separate. In Set-ESEM, two or more a priori sets of constructs are modeled within a single model such that cross-loadings are permissible within the same set of factors (as in Full-ESEM) but are constrained to be zero for factors in different sets (as in CFA). The different sets can reflect the same set of constructs on multiple occasions, and/or different constructs measured within the same wave. Hence, Set-ESEM that represents a middle-ground between the flexibility of traditional-ESEM (hereafter referred to as Full-ESEM) and the rigor and parsimony of CFA/SEM. Thus, the purposes of this article are to provide an overview tutorial on Set-ESEM, juxtapose it with Full-ESEM, and to illustrate its application with simulated data and diverse "real" data applications with accessible, heuristic explanations of best practice.

Self-esteem and body image are central to coping successfully with the developmental challenges of adolescence. However, the current knowledge surrounding self-esteem and body image is fraught with controversy. This study attempts to clarify some of them by addressing three questions: (1) Are the intraindividual developmental trajectories of self-esteem and body image stable across adolescence? (2) What is the direction of the relations between body image and self-esteem over time? (3) What is the role of gender, ethnicity, and pubertal development on those trajectories? This study relies on Autoregressive Latent Trajectory analyses based on data from a 4-year, 6-wave, prospective longitudinal study of 1,001 adolescents. Self-esteem and body image levels remained high and stable over time, although body image levels also tended to increase slightly. The results show that levels of self-esteem were positively influenced by levels of body image. However, these effects remained small and most of the observed associations were cross-sectional. Finally, the effects of pubertal development on body image and self-esteem levels were mostly limited to non-Caucasian females who appeared to benefit from more advanced pubertal development. Conversely, Caucasian females presented the lowest self-esteem and body image levels of all, although for them more advanced pubertal development levels were associated with a slight rise in body image over time.

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.

Bong (1998) extended the internal/external frame of reference (I/E) model by attempting to operationalize the internal and external comparison processes that are central to the model and expanding the range of academic self-concept domains. Bong concluded that the "I/E model failed to receive clear support" (p. 102) in relation to predictions that she derived from her extension of the original model. Our critical evaluation and reanalysis, however, reveals problems in the operationalization of the internal and external comparisons, the rationale for post hoc confirmatory factor analysis models and, thus, the original conclusions. Our reanalysis, however, provide strong support for the original I/E model, some support for the separation of the internal and external comparison processes, and good support for a new extension to incorporate a wider range of academic domains. In particular, for these largely Hispanic-American students, Spanish achievement and self-concept were very distinct from achievements and self-concepts in all other school subjects. Accomplishments in Spanish provided one basis for evaluating accomplishments in other school subjects. In contrast, achievements and self-concepts in these other school subjects could be explained in terms of higher-order Verbal achievement and self-concept factors and higher-order Math achievement and self-concept factors.

External assessor ratings of the quality of the research team and of the proposed research were evaluated for proposals submitted to the highly competitive Australian Research Council large grants program. The structure of the responses by multiple assessors was evaluated using a series of nested models that are variations of the traditional congeneric, tau-equivalent, and parallel measurement models. The estimated reliability based on four independent assessors was modest but comparable to other peer review research: .494 for proposal ratings, .634 for researcher ratings, and .704 for a total assessment. Mean ratings (averaged over multiple assessors) of the proposal and the research team were highly correlated (r = .85), suggesting a lack of differentiation and a substantial method/halo effect in ratings by the same assessor. Confirmatory factor analysis models supported this suggestion, representing this method effect as correlated uniquenesses. Tests of whether proposal and researcher ratings reflected one or two latent variables, based on the internal structure of the assessment ratings and relations with external criteria (academic rank, prior funding, and publications), supported a one-factor solution.

We evaluated whether "more is ever too much" for the number of indicators (p) per factor (p/f) in confirmatory factor analysis by varying sample size (N = 50-1000) and p/f (2-12 items per factor) in 35,000 Monte Carlo solutions. For all N's, solution behavior steadily improved (more proper solutions, more accurate parameter estimates, greater reliability) with increasing p/f. There was a compensatory relation between N and p/f: large p/f compensated for small N and large N compensated for small p/f, but large-N and large-p/f was best. A bias in the behavior of the χ(2) was also demonstrated where apparent goodness of fit declined with increasing p/f ratios even though approximating models were "true". Fit was similar for proper and improper solutions, as were parameter estimates form improper solutions not involving offending estimates. We also used the 12-p/f data to construct 2, 3, 4, or 6 parcels of items (e.g., two parcels of 6 items per factor, three parcels of 4 items per factor, etc.), but the 12-indicator (nonparceled) solutions were somewhat better behaved. At least for conditions in our simulation study, traditional "rules" implying fewer indicators should be used for smaller N may be inappropriate and researchers should consider using more indicators per factor that is evident in current practice.

The purposes of the present investigation are to demonstrate extensions of the confirmatory factor analysis approach (CFA) to multitrait-multimethod (MTMM) data and to evaluate self-other agreement on multiple dimensions of self-concept. Two studies evaluated the ability of significant others to infer multiple dimensions of self-concept of university students in Australia (n = 151) and in Canada (n = 941). In both studies self-other agreement on the 13 Self Description Questionnaire 111 (SDQIII) factors was higher than reported in previous research. Traditional and CFA approaches to MTMM data demonstrated convergent and discriminant validity. An extension of the CFA-MTMM approach examined within-group invariance of responses by self and others and between group invariance across Australian and Canadian responses. Between-group invariance tests support the total invariance of CFA-MTMM solutions across Australian and Canadian responses. The imposition of invariance constraints produced substantially more parsimonious models and apparently offers one practical remedy to problems of ill-defined solutions that have plagued the CFA approach to MTMM data.

The general model typically used in the confirmatory factor analysis (CFA) approach to multitrait-multimethod (MTMM) data is plagued with methodological problems and frequently results in improper or unstable solutions. Here we reanalyze data from a previously published study, demonstrating that this model may lead to inappropriate interpretations even when it does converge to a proper solution, and describe safeguards against this occurrence. The results support the correlated uniqueness model, diagnostic tests of the validity of CFA-MTMM solutions, the inclusion of external validity criteria in the MTMM design as described by Marsh (1988; 1989; Marsh & Bailey, 19911, and the application of factorial invariance to test the stability of CFA-MTMM solutions. More generally, we demonstrate the flexibility of the CFA-MTMM approach for testing a variety of construct validity issues.

Masculinity (M) and femininity (F) were related to multiple dimensions of self-concept in responses from 962 high school students. Androgyny theory predicts that both M and F will contribute positively and uniquely to self-concept, but previous research, typically relying on undifferentiated self-concept measures, has found the unique contribution of F to be nil. In contrast the present investigation found that M and F each contributed positively and uniquely to the prediction of well differentiated facets of self-concept. Consistent with a new model to explain MF/self-concept relations, the differentiated additive model, the relative contribution of M and F varied substantially depending on the area of self-concept; F contributed more positively to the self-concept facets for which girls had higher self-concepts than boys, and in some areas the contribution of F was more positive than the contribution of M. Contrary to predictions for interactive androgyny models and the sex-typed model, M-by-F interactions were not significant, and the effects of M, F and M-by-F did not depend on gender. The social desirability of MF items, whether they were negatively or positively valued, was more highly correlated with the self-concept responses than whether the items were M or F.

The purpose of this study is to examine the factor structure of responses to the masculinity/femininity (MF) scale of the Comrey Personality Scales for males (N = 366) and females (N = 384). The study also illustrates the use of confirmatory factor analysis for testing hierarchical factor structures and factorial invariance. The MF scale consists of M and F items designed to measure five distinguishable components of MF. Neither a one-factor solution with a single bipolar MF factor, nor a two-factor solution with separate M and F factors, was able to fit the data. However, a five-factor solution derived from the design of the MF scale provided an adequate fit, and the relationships among the five first-order factors could be explained by a single higher-order, bipolar MF factor. Contrary to the findings and proposals from androgyny research, when separate masculinity and femininity constructs were defined, the correlation between the constructs was nearly - 1.0. The findings argue that MF is a multifaceted, hierarchical construct instead of either a single bipolar MF construct, or separate M and F factors.

The factorial invariance of responses by preadolescent males and females to a multidimensional self-concept instrument was examined for responses to the Self Description Questionnaire (SDQ). Sets of responses by 500 males and by 500 females were each randomly divided in half to form four groups (M1, M2, Fl, and F2). The factorial invariance of an a priori structure demonstrated the replicability of the structure across cross-validation groups (M1 and M2, F1 and F2) and the generality of the structure across sex (M1 and Fl, M2 and F2). Additional a posteriori structures that better fit the data were derived on the basis of the initial analyses, but the estimated values of the new parameters were not invariant across cross-validation groups or across sex. This suggests that some of the improved fit was illusory and due to capitalizing on chance. However, factor loadings and factor correlations were invariant across sex for a priori and a posteriori structures. Hence the results support the replicability of SDQ factor structure across cross-validation samples and its generality across responses by preadolescent males and females.

Students' Prior Subject Interest in a course showed similar correlations with student ratings of instructional effectiveness in two university settings (N = 1102 classes). Correlations between Prior Subject Interest and different dimensions of instructional effectiveness varied from approximately zero to .44. Though these correlations were not high, Prior Subject Interest predicted student ratings better than any of 15 other student/course/instructor characteristics considered (e.g., Expected Grade, Class Size, Workload/Difficulty, Teacher Rank). Instructor self-evaluations of their own teaching effectiveness (N = 329 classes) were also positively correlated with both their own and their students' perceptions of Prior Subject Interest; the dimensions that were most highly correlated -- particularly Learning/Value -- were the same as observed with student ratings. Since both student and instructor self evaluations were similarly related to Prior Subject Interest, it appears that this variable actually affects instructional effectiveness in a way that is accurately reflected in the student ratings.

Rotter (1966, 1975) concluded that responses to his Internal-External (I-E) scale were unidimensional, or at least that one general factor explained most of the variance in the total score. The purpose of the present investigation is to examine the factorial structure of the original Rotter scale. A review of 20 published factor analyses indicated that the scale is not unidimensional, that not even two or three factors may be able to adequately explain responses to the scale, and that six distinguishable factors have been identified. Confirmatory factor analyses indicated that a five-factor model provided an adequate fit to data from the present investigation, but that alternative models with fewer factors or a simpler structure did not fit the data as well. However, a single higher-order factor was able to explain much of the variance in the lower-order factors and also provided a reasonable fit to the data. Hence, while there is strong evidence against the unidimensionality of the Rotter scale, the findings suggest that the first-order factors do define a single higher-order construct that may represent the generalized IE construct that Rotter originally hypothesized. Nevertheless, the continued reliance of locus of control research on the Rotter scale and on global measures of the construct may be counterproductive.