The big-fish-little-pond effect on academic self-concept: a comparison of GAPIM and a latent-manifest contextual model (SRA)

The goal of this paper was to compare two methods for the analysis of group composition effects using the classical big-fish-little-pond effect (BFLPE) as an example. The BFLPE (Marsh, 1987) is a well-known and frequently investigated group composition effect in educational research (e.g. Seaton, Marsh, & Craven, 2009; Wang, 2013). According to this effect, students compare their own academic abilities with those of their school- or classmates and the information obtained then forms a reference that shapes students’ academic self-concept. As a result, being in a group with high achievers often has detrimental influence on students’ academic self-concept. Such negative comparative peer group influences are evident over and above the positive association between individual achievement and academic self-concept. Participants were 598 adolescents (Mage = 12.20; SDage = 0.80; 48% girls) from 40 classes (grade 6) with a sampling ratio close to 100%. Academic self-concept was measured using a 4-item scale developed by Venetz, Zurbriggen, and Eckhart (2014). Academic achievement was the average score on standardized math and German achievement tests (Machievement = -.005; SDachievement = .81; range -2.41 to +1.67). The data were analyzed using two methods: (1) a latent-manifest contextual model within a multilevel SEM framework (Marsh et al., 2009) and (2) the Group Actor-Partner Interdependence Model (GAPIM; Garcia, Meagher, & Kenny, 2014; Kenny & Garcia, 2012). In the latent-manifest contextual model, a latent group-mean centered variable for academic achievement at the individual level (L1) and the observed mean on academic achievement at the classroom level (L2) were used to predict a latent measure of academic self-concept (using the 4-item scale) at both levels (see Figure 1). In the GAPIM, four (manifest) group composition effects were calculated and used as individual level (L1) predictors to predict a latent measure of academic self-concept at Level 1 in a multilevel SEM framework. Both methods supported the BFLPE, but results differed slightly. In the GAPIM approach, the contrast model was the best fitting model, where both main effects are constrained to be equal but with opposite signs (see Table 1). Adolescents’ academic self-concept was positively predicted by their own academic achievement, but negatively by the average academic achievement of all others in the group (i.e., a BFLPE). In the latent-manifest contextual model (see Figure 1), results were similar. However, estimates and standard errors were slightly larger than in the GAPIM. Simulation studies by Lüdtke et al. (2008) showed that this may occur when using a multilevel latent approach to correct for sampling error as this may result in a positive bias and larger root-mean-square error of contextual effects when the sampling ratio is large (i.e., when most or all participants of a group are sampled) and when the number of participants per group and the number of groups are low, a situation typical in adolescent peer relationships research. The analyses showed that both methods have advantages and disadvantages, depending on the nature of the data. Benefits and drawbacks of the GAPIM in comparison to a latent MSEM approach will be discussed.