The Longitudinal Study of the 2005 School Generation (Geres) is the ï¬rst survey of its kind successfully achieved and remain the only one in Brazil. It aimed to observe pupils’ achievements in mathematics and reading, and changes in individual performance and school characteristics over junior school years in ï¬ve cities: Rio de Janeiro, Belo Horizonte, Campinas, Campo Grande and Salvador. All pupils that were registered in the 1st grade of the selected schools made up the Geres sample for the ï¬rst wave. They were followed by ï¬ve waves, two in 2005 and one every year from 2006 to 2008. Also, the survey tracked additional pupils that joined the main grade currently in each wave in the selected schools.

Each city represented one stratum, and they were divided into three to four strata according to the schools’ administration system: state, municipal, private and exceptional schools. The survey had 17 strata in total, and they were called explicit strata. Each explicit stratum was divided by up to nine groups, according to the school size and socio-economic levels. These groups were called implicit strata by the survey report. The implicit stratification is discussed in the current work, and we assumed that random selection of schools for the first wave was made in each of them. Thus, they were ordinary strata (or explicit strata). The published weights include weights for the explicit and implicit strata at wave 1 only, for schools and pupils separately, though incomplete for pupils.

Additional pupils can be from the original population but moved from a non-sampled school to a sampled one. In this case, their selection probability could be computed if the initial sampling frame is available; however, the selection probability would slightly change for all sampled units. Other additional pupils were from different populations because in 2005 they were studying in grades above or below the first grade, and then they were moved to classes with original pupils in the selected schools. Thus, it is not possible to obtain their sampling weight according to the initial population. Either case, the additional units can have an estimation weight computed via Generalised Weight Share Method (GWSM), amply used in longitudinal household surveys, but it has never been used to estimate weights in schools’ surveys.

We estimated weights for all waves through GWSM and compared the point estimates of four different estimators for the proportion of repeaters in the fourth wave, given they were part of the original population. The estimator that consider the estimation weight computed with the GWSM is the one recommended because was the only one that considers the pupil’s mobility within and inter-schools, it also gave an estimation weight for all observed pupils, regardless they were part of the original population or not. The estimators based on the original sampling weights or the modified sampling weights do not reflect the mobility. We also estimated the variance of each estimator and investigated the conditions under the proposed estimators are unbiased through a small simulation.