A. Katrin Arens

A bifactor exploratory structural equation modeling framework for the identification of distinct sources of construct-relevant psychometric multidimensionality

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.

Exploring sources of construct‐relevant multidimensionality in psychiatric measurement: A tutorial and illustration using the Composite Scale of Morningness

This paper illustrates a psychometric approach of broad relevance to psychiatric research instruments. Many instruments include indicators related to more than one source of true‐score variance due to the: (1) assessment of conceptually adjacent constructs; (2) the presence of a global construct underlying answers to items designed to assess multiple dimensions. Exploratory structural equation modelling (ESEM) is naturally suited to the investigation of the first source, whereas bifactor models are particularly suited to the investigation of the second source. When both sources are present, bifactor‐ESEM becomes the model of choice. To illustrate this framework, we use the responses of 1159 adults [655 female, 504 male, mean age (Mage) = 41.84] who completed the French Version of the Composite Scale of Morningness (CSM). We investigate the factor structure of the CSM, test the relations between CSM factors and body mass index, and verify the measurement invariance of the model across gender and age groups. Copyright

Examination of the Structure and Grade-Related Differentiation of Multidimensional Self-Concept Instruments for Children Using ESEM

This study is a substantive-methodological synergy in which exploratory structural equation modeling is applied to investigate the factor structure of multidimensional self-concept instruments. On the basis of a sample of German students (N = 1958) who completed the Self-Description Questionnaire I and the Self-Perception Profile for Children, the results supported the superiority of exploratory structural equation modeling compared with confirmatory factor analyses for both instruments. Exploratory structural equation modeling resulted in lower factor correlations and substantively meaningful cross-loadings. The authors also proposed and contrasted 3 mechanisms for testing grade-related differences in the differentiation of self-concept facets and found no evidence of increased differentiation between Grades 3 to 6.

Breaking the double-edged sword of effort/trying hard: Developmental equilibrium and longitudinal relations among effort, achievement, and academic self-concept.

Ever since the classic research of Nicholls (1976) and others, effort has been recognized as a double-edged sword: while it might enhance achievement, it undermines academic self-concept (ASC). However, there has not been a thorough evaluation of the longitudinal reciprocal effects of effort, ASC, and achievement, in the context of modern self-concept theory and statistical methodology. Nor have there been developmental equilibrium tests of whether these effects are consistent across the potentially volatile early-to-middle adolescence. Hence, focusing on mathematics, we evaluate reciprocal effects models (REMs) over the first 4 years of secondary school (grades 5-8), relating effort, achievement (test scores and school grades), ASC, and ASC × Effort interactions for a representative sample of 3,144 German students (Mage = 11.75 years at Wave 1). ASC, effort, and achievement were positively correlated at each wave, and there was a clear pattern of positive reciprocal positive effects among ASC, test scores, and school grades-each contributing to the other, after controlling for the prior effects of all others. There was an asymmetrical pattern of effects for effort that is consistent with the double-edged sword premise: prior school grades had positive effects on subsequent effort, but prior effort had nonsignificant or negative effects on subsequent grades and ASC. However, on the basis of a synergistic application of new theory and methodology, we predicted and found a significant ASC × Effort interaction, such that prior effort had more positive effects on subsequent ASC and school grades when prior ASC was high-thus providing a key to breaking the double-edged sword. (PsycINFO Database Record

Relationship between self-esteem and academic self-concept for German elementary and secondary school students

This study aims to investigate the construct of global self-esteem and its relationship with academic self-concept within a sample of German students attending grades 3–6 (N = 1958), considering the domain specificity and competence–affect separation of academic self-concept. Confirmatory factor analyses found global self-esteem to be similarly related to domain-specific (math and verbal) and general measures of academic self-concept. Self-perceived competence and affect were similarly related to global self-esteem. There was some evidence that the mean level of global self-esteem was higher for fourth grade students (before transition) than for 5th graders (after transition), and the lowest for 6th grade students. The relationship between global self-esteem and academic self-concept was found to be invariant across grade levels although descriptive results indicated a weaker relationship after transition.

Age and Gender Differences in the Relation between Self-Concept Facets and Self-Esteem.

This study tested whether the gender intensification hypothesis applies to relations between multiple domain-specific self-concept facets and self-esteem. This hypothesis predicts gender-stereotypic differences in these relations and assumes they intensify with age. Furthermore, knowledge about gender-related or age-related differences in self-concept–self-esteem relations might provide valuable knowledge for designing effective self-esteem enhancement interventions. We investigated grade and gender differences in the relations between domain-specific self-concept facets and self-esteem within a sample of 1958 German students in Grades 3 to 6. Results indicated no difference in the self-concept–self-esteem relations between the subsamples of third and fourth graders and fifth and sixth graders or between boys and girls. These relations also did not differ between boys and girls in the subsamples of third and fourth graders and fifth and sixth graders. These results suggest self-concept-self-esteem relations to be invariant across grade levels and gender and thus did not support the gender intensification hypothesis.

Math self-concept, grades, and achievement test scores: Long-term reciprocal effects across five waves and three achievement tracks.

This study examines reciprocal effects between self-concept and achievement by considering a long time span covering grades 5 through 9. Extending previous research on the reciprocal effects model (REM), this study tests (1) the assumption of developmental equilibrium as time-invariant cross-lagged paths from self-concept to achievement and from achievement to self-concept, (2) the generalizability of reciprocal relations when using school grades and standardized achievement test scores as achievement indicators, and (3) the invariance of findings across secondary school achievement tracks. Math self-concept, school grades in math, and math achievement test scores were measured once each school year with a representative sample of 3,425 German students. Students’ gender, IQ, and socioeconomic status (SES) were controlled in all analyses. The findings supported the assumption of developmental equilibrium for reciprocal effects between self-concept and achievement across time. The pattern of results was found to be invariant across students attending different achievement tracks and could be replicated when using school grades and achievement test scores in separate and in combined models. The findings of this study thus underscore the generalizability and robustness of the REM.

Native Language Self-Concept and Reading Self-Concept: Same or Different?.

In assessing verbal academic self-concept with preadolescents, researchers have used scales for students’ self-concepts in reading and in their native language interchangeably. The authors conducted 3 studies with German students to test whether reading and German (i.e., native language) self-concepts can be treated as the same or different constructs. Compared with other facets of academic self-concept, reading self-concept was more highly related to reading test scores (Study 1) and German self-concept to German grades (Study 2). In Study 3, reading and general school self-concepts demonstrated similar relations to German grades. The findings of the 3 studies, albeit indirect, supported the specificity matching principle and caution researchers against applying reading and native language self-concept scales uncritically to infer verbal self-concept.

An integrated model of academic self-concept development: Academic self-concept, grades, test scores, and tracking over 6 years.

Our newly proposed integrated academic self-concept model integrates 3 major theories of academic self-concept formation and developmental perspectives into a unified conceptual and methodological framework. Relations among math self-concept (MSC), school grades, test scores, and school-level contextual effects over 6 years, from the end of primary school through the first 5 years of secondary school (a representative sample of 3,370 German students, 42 secondary schools, 50% male, M age at grade 5 = 11.75) support the (1) internal/external frame of reference model: Math school grades had positive effects on MSC, but the effects of German grades were negative; (2) reciprocal effects (longitudinal panel) model: MSC was predictive of and predicted by math test scores and school grades; (3) big-fish-little-pond effect: The effects on MSC were negative for school-average achievement based on 4 indicators (primary school grades in math and German, school-track prior to the start of secondary school, math test scores in the first year of secondary school). Results for all 3 theoretical models were consistent across the 5 secondary school years: This supports the prediction of developmental equilibrium. This integration highlights the robustness of support over the potentially volatile early to middle adolescent period; the interconnectedness and complementarity of 3 ASC models; their counterbalancing strengths and weaknesses; and new theoretical, developmental, and substantive implications at their intersections.

The murky distinction between self-concept and self-efficacy: beware of lurking jingle-jangle fallacies

This study extends the classic constructive dialogue/debate between self-concept and self-efficacy researchers (Marsh, Roche, Pajares, & Miller, 1997) regarding the distinctions between these 2 constructs. The study is a substantive-methodological synergy, bringing together new substantive, theoretical, and statistical models and developing new tests of the classic jingle-jangle fallacy. We demonstrate that in a representative sample of 3,350 students from math classes in 43 German schools, generalized math self-efficacy and math outcome expectancies were indistinguishable from math self-concept, but were distinct from test-related and functional measures of self-efficacy. This is consistent with the jingle-jangle fallacies that are proposed. On the basis of pretest variables, we demonstrate negative frame-of-reference effects in social (big-fish-little-pond effect) and dimensional (internal/external frame-of-reference effect) comparisons for three self-concept-like constructs in each of the first 4 years of secondary school. In contrast, none of the frame-of-reference effects were significantly negative for either of the two self-efficacy-like constructs in any of the 4 years of testing. After controlling for pretest variables, each of the 3 self-concept-like constructs (math self-concept, outcome expectancy, and generalized math self-efficacy) in each of the 4 years of secondary school was more strongly related to posttest outcomes (school grades, test scores, future aspirations) than were the corresponding 2 self-efficacy-like factors. Extending discussion by Marsh et al. (1997), we clarify distinctions between self-efficacy and self-concept; the role of evaluation, worthiness, and outcome expectancy in self-efficacy measures; and complications in generalized and global measures of self-efficacy.