1.3 Weighting Design
Considering that we want to extrapolate from the interviews conducted to the respective target population, it is necessary to weigh each interviewer appropriately according to their representation in the target population. For this purpose, in each wave of the study we provide weights that allow to adjust for differences in demographic attributes of the ELSOC sample relative to the target population.
Below we describe the process of elaboration of weights^ [These weights can be understood as “cross-sectional weights” since we ignored the problems derived from their longitudinal nature.] in order to achieve correspondence between the sample and the target population. Such weighting corresponds to the inverse of its probability of selection or inclusion in the sample. In this case, the probability of selection of individual \(i\) from household \(j\) belonging to block \(l\) of stratum \(k\), \(P_{ijlk}\) is given by:
\[P_{iklk} = \pi_i|_{jlk}\pi_j|_{lk}\pi_{lk}\] Where:
- \(\pi_i|_{jkl}\) is the probability of selecting an individual \(i\) in the sample given the selection of the household where they live and the block location.
- \(\pi_j|_{lk}\) is the probability of selecting a household \(j\) in the sample given the selection of block \(l\) (containing household \(j\)).
- \(\pi_lk\) is the probability of selecting block \(l\) of stratum \(k\) in the sample.
The design or theoretical weight \(w_{ijlk}\) is defined as the inverse of the selection probability:
\[P_{ijlk}=\frac{1}{w_{ijlk}}\]
The value of the aforementioned probabilities is:
\[\pi_{lk} = n_k\frac{M_{kl}}{M_k}\]
\[\pi_{j|lk} = \frac{m_{lk}}{M'_k}\]
\[\pi_{i|jlk} = \frac{1}{N_{jlk}}\]
Where we have that \(n_k\) is the number of blocks to select from stratum \(k\), \(_lk\) is the number of households in block \(l\) of stratum \(k\), \(M_k\) is the total number of households in stratum \(k\), \(m_{lk}\) is the number of households to survey within block \(l\), \(M'_k\) is the updated number of households in block \(l\) post-registration, \(N_{jlk}\) is the number of persons in the target population living in household \(j\) in block \(l\) of stratum \(k\).
Based on the above, weights adjust based on the base probabilities, with non-response adjustment, with adjustment to the number of cases3 and to the number of cases and sex variable4.