- in the new version of the questionnaire (i.e., “Given that the household has at least one component belonged to the original sample selected from a population, does the individual belong to the same population or are they new (newborn or immigrant)?”).

- - 7, using other stored variables and making some accurate assumptions. This variable should be directly asked in the We artificially created the individual multiplicity factor, vvnew version of the questionnaire (i.e., “Does the individual of the original sample change parish from 2009 to 2013 (years of the original samples?)”).

- - 7 8. - 9 10, using Based on the values of vv , we computed the household multiplicity factor vv other stored variables and making some accurate assumptions.

- - We artificially rebuilt the response indicator variable in each wave, vv4, for each individual selected in the original  and vv sample (not for the incorporated individuals), even if the individual did not respond We stored the inclusion probability, vv(i.e., in the current panel data, the weight is missing).

- We computed the GWSM weight that does not rely on the concept of the parent household, which can be a complex operation in practice.

- We computed the final weights using the standard calibration estimator and applied these for the cross-sectional and longitudinal estimates, creating a unique vector of sampling weights that simplifies the coherence of the individual and household estimates.

# 7. CONCLUSIONS

Given the complexity of the topics covered, we now retrace our main steps to provide a unified picture of the various results. In this paper, we explored the problem of enhancing the quality of cross-sectional and longitudinal estimates from surveys that are obtained by combining samples chosen at previous times with given rules to track panel members as they move away from the location of their initial survey interview.

We have seen that the issue is complicated and that action needs to be taken on several fronts, which refer to related but different scientific fields.

The first aspect is defining the quantities one wants to know, considering the nature of the population, which has both a cross-sectional and longitudinal aspects. That leads to appropriate consideration of the definition of the statistical units of interest over time and at the various points at which attention is focused for constructing cross-sectional and longitudinal estimates. While the solutions for simple statistical units (such as individuals) are relatively uncontroversial, for composite units (such as households), there are multiple possible solutions, and each solution has pros and cons in terms of being representative of what is happening in the reality of natural populations and of the observational ease of the phenomena of interest. We proposed the many-to-many approach for defining the continuity of a household over time, meaning that one household from an initial time may generate many families at the next time. Conversely, a household at the current time may be derived from several households from previous times. With that approach, there is a perfect correspondence between the longitudinal population of people and that of households. Moreover, the many-to-many approach includes the one-to-one continuity rule as a particular case.

Next, we considered the observational processes that make theoretically defined population quantities observable. We have seen that it is necessary to take into due consideration the timeline of repeated observations to avoid distortions that derive from considering the same 33