Intelligence as a Potential Moderator in the Internal/external Frame of Reference Model: An Exploratory analysis/Intelligenz Als Potentieller Moderator Des I/E-Modells - eine Explorative Untersuchung

1. IntroductionAbility self-concept (ASC) is one of the key theoretical constructs in educational psycholog)'' (Marsh, Xu, & Martin, 2012), which can be explained by its relation to several educational outcomes, among them academic achievement (e.g., Steinmayr & Spinath, 2009a). The internal/external frame of reference (I/E) model by Marsh (1986) is currently one of the most prominent models serving to explain the emergence of ASC (Brunner, Liidtke, & Trautwein, 2008). It posits that ASCs are formed by using both an internal and an external frame of reference. On the one hand, students conduct social comparisons, that is, they compare their own accomplishments with those of their classmates (external frame of reference). On the other hand, students evaluate their achievements in any particular subject in relation to their achievements in other subjects (internal/dimensional frame of reference). The validity of the model is well demonstrated and was shown for several nationalities (e.g., Marsh & Hau, 2004). However, the spectrum of the reported postulated associations between the different variables of the model varies widely. A recent meta-analysis demonstrated that this variability could not be accounted for by sampling error alone and identified several moderators (Moller, Pohlmann, Koller, & Marsh, 2009). However, this meta-analysis did not take into account any cognitive or motivational characteristics as potential moderators. This might be due to the fact that so far hardly any research on such potential moderators has been conducted. The aim of the present study is to investigate the moderating influence of intelligence on the dimensional comparisons as postulated by the I/E model.l. l The I/E modelThe I/E model was developed by Herbert Marsh to explain the paradoxical finding that domain-specific academic self-concepts in math and verbal domains do not or only weakly correlate despite the well-known fact that mathematical and verbal abilities are medium to highly correlated (e.g., Marsh, 1986). Based on the latter finding, one would assume that the domain-specific self-concepts also positively correlate with each other as domain-specific self-concepts are highly correlated with achievement in the corresponding domain. The I/E model explains the low or non-existent correlations between mathematical and verbal self-concepts by assuming two comparison processes that are involved in the formation of domainspecific self-concepts. First, students are believed to be engaged in social comparison processes. Within an external frame of reference, they compare their own domain-specific ability with the corresponding ability of other students. The social comparison process leads to a positive correlation between students' performance in one domain and the corresponding self-concept. This is usually indicated by means of the correlation between performance measures (grades, standardized achievement measures, etc.) and ASCs. Moller et al. (2009) report an average correlation of r - . 43 (r = .35) between math achievement and math self-concept (verbal achievement and verbal self-concept). When the authors analyzed the association within the I/E model path-analytically, they found an average path coefficient from math achievement (verbal achievement) to math self-concept (verbal self-concept) of β - . 61 (β - .49). Second, the I/E model postulates dimensional comparisons. Dimensional comparisons refer to an internal frame of reference and depict such comparison processes in which students compare their ability in two domains (Moller & Marsh, 2013). For example, if a person performs better in English than in math this dimensional comparison process will result in a negative evaluation of one's mathematical ability independent from the actual performance level this person has in math relative to others. Thus, the I/E model postulates a negative effect from students' performance in one domain to students' ASC in the other domain. …