In the educational literature on peer effects, attention has been brought to the fact that the mechanisms creating peer effects are still to a large extent hidden in obscurity. The hypothesis in the study reported in this article was that the Frame Factor Theory (FFT) can be used to reveal such mechanisms. Using data from the Swedish TIMSS 2015 (N = 3761 students in 179 classes), a multilevel structural equation model (M-SEM) was specified in accordance with the FFT. As predicted, the SEM-model verified a strong relationship between class composition and a latent variable of limitations on instruction, a variable which in turn had a great impact on individual students' results in TIMSS 2015. The study hereby seems to reveal a fundamental mechanism of peer effects and provides evidence for the FFT.