Bayesian approaches for estimating multilevel latent variable models can be beneficial in small samples. Prior distributions can be used to overcome small sample problems, for example, when priors that increase the accuracy of estimation are chosen. This article discusses two different but not mutually exclusive approaches for specifying priors. Both approaches aim at stabilizing estimators in such a way that the Mean Squared Error of the estimator of the between-group slope will be small. In the first approach, the MSE is (...) decreased by specifying a slightly informative prior for the group-level variance of the predictor variable, whereas in the second approach, the decrease is achieved directly by using a slightly informative prior for the slope. Mathematical and graphical inspections suggest that both approaches can be effective for reducing the MSE in small samples, thus rendering them attractive in these situations. The article also discusses how these approaches can be implemented in Mplus. (shrink)

Argumentation is considered crucial in numerous disciplines in schools and universities because it constitutes an important proficiency in peoples' daily and professional lives. However, it is unclear whether argumentation is understood and practiced in comparable ways across disciplines. This study consequently examined empirically how students perceive argumentation in science and language lessons. Specifically, we investigated students' beliefs about the relevance of discourse and the role of facts. Data from 3,258 high school students from 85 German secondary schools were analyzed with (...) multigroup multilevel structural equation modeling in order to disentangle whether or not differences in argumentation across disciplines exist and the extent to which variation in students' beliefs can be explained by gender and school track. Results showed that students perceived the role of facts as highly relevant for science lessons, whereas discursive characteristics were considered significantly less important. In turn, discourse played a central role in language lessons, which was believed to require less knowledge of facts. These differences were independent of students' gender. In contrast, school track predicted the differences in beliefs significantly. Our findings lend evidence on the existence of disciplinary school cultures in argumentation that may be the result of differences in teachers' school-track-specific classroom practice and education. Implications in terms of a teacher's role in establishing norms for scientific argumentation as well as the impact of students' beliefs on their learning outcomes are discussed. (shrink)