Importance of sampling weights in multilevel modeling of international large-scale assessment data

Multilevel modeling is an important tool for analyzing large-scale assessment data. However, the standard multilevel modeling will typically give biased results for such complex survey data. This bias can be eliminated by introducing design weights which must be used carefully as they can affect the results. The aim of this paper is to examine different approaches and to give recommendations concerning handling design weights in multilevel models when analyzing large-scale assessments such as TIMSS (The Trends in International Mathematics and Science Study). To achieve the goal of the paper, we examined real data from two countries and included a simulation study. The analyses in the empirical study showed that using no weights or only level 1 weights sometimes could lead to misleading conclusions. The simulation study only showed small differences in estimation of the weighted and unweighted models when informative design weights were used. The use of unscaled or not rescaled weights however caused significant differences in some parameter estimates.