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Academic self-concept (ASC) is comprised of individual perceptions of one- own academic ability. In a cross-sectional quasi-representative sample of 3,779 German elementary school children in grades 1 to 4, we investigated (a) the structure of ASC, (b) ASC profile formation, an aspect of differentiation that is reflected in lower correlations between domain-specific ASCs with increasing grade level, (c) the impact of (internal) dimensional comparisons of one- own ability in different school subjects for profile formation of ASC, and (d) the role played by differences in school grades between subjects for these dimensional comparisons. The nested Marsh/Shavelson model, with general ASC at the apex and math, writing, and reading ASC as specific factors nested under general ASC fitted the data at all grade levels. A first-order factor model with math, writing, reading, and general ASCs as correlated factors provided a good fit, too. ASC profile formation became apparent during the first two to three years of school. Dimensional comparisons across subjects contributed to ASC profile formation. School grades enhanced these comparisons, especially when achievement profiles were uneven. In part, findings depended on the assumed structural model of ASCs. Implications for further research are discussed with special regard to factors influencing and moderating dimensional comparisons.
This paper mainly studies two topics: linear complementarity problems for modeling electricity market equilibria and optimization under uncertainty. We consider both perfectly competitive and Nash–Cournot models of electricity markets and study their robustifications using strict robustness and the -approach. For three out of the four combinations of economic competition and robustification, we derive algorithmically tractable convex optimization counterparts that have a clear-cut economic interpretation. In the case of perfect competition, this result corresponds to the two classic welfare theorems, which also apply in both considered robust cases that again yield convex robustified problems. Using the mentioned counterparts, we can also prove the existence and, in some cases, uniqueness of robust equilibria. Surprisingly, it turns out that there is no such economic sensible counterpart for the case of -robustifications of Nash–Cournot models. Thus, an analog of the welfare theorems does not hold in this case. Finally, we provide a computational case study that illustrates the different effects of the combination of economic competition and uncertainty modeling.
