members in panel surveys. See Rendtel and Harms (2009) for a discussion of several different methods of weight correction.

Therefore, for any given household with new members, there are two ways that a household can become part of the survey: either by being selected initially for round 1 (and during the subsequent rounds of subselection), or by receiving a member that came from a household that was selected for round 1 (and during the subsequent rounds of sub-selection). In order to properly account for the household’s current probability of selection, it would be necessary to calculate the exact probability of selection for each new member brought into the household, and adjust the weights accordingly. This adjustment is necessary since households receiving members have higher probabilities of selection (and therefore necessarily lower weights) because the household could have been selected into the survey in multiple ways. The precise calculation, however, would be impossible in all but the rarest of circumstances.<sup>8</sup> Since it is not possible to compute round 1 probabilities of selection for every member of each sample household in a subsequent round, simplifying assumptions are necessary to continue with the weight calculations. The first simplifying assumption is that the new members to the survey arrived together from one other household. This would be the situation in most common cases, for example, a man and woman marrying and setting up a new household, or an older relative moving in with adult children. In certain cases, however, arriving members come from more than one household. Therefore, assuming only two source households slightly underestimates the probability of selection (and therefore over-estimates the weights) for those cases where members actually came from more than two households. However, as long as the incidence of these cases is believed to be relatively rare, any resulting bias should be negligible.

The second necessary simplifying assumption is that the arriving members have the same probability of selection, on average, as those original members living in the household to which they come. This would not be true on a case-by-case basis but would be true in the aggregate. With these simplifying assumptions, the household probability of selection is increased by a factor of 2 for all households that have new members arriving from other households, whether the receiving household is a parent or splitoff, and regardless of if they have been selected for tracking. (Note that children born since the previous round of data collection was completed are not taken as new members from this perspective because they could not have been selected in round 1.) This takes into account the fact that they could have been selected in two ways, and assumes that the probability of selection is equal.

A limitation of the panel methodology used in the LSMS-ISA surveys is that the represented round 2 population is not completely representative, as it does not include those solely from outside the original universe of selection who formed households. In this case, it would not include households completely formed by those leaving an institutionalized population, or immigrants from outside the study country. Inclusion of such households would necessitate refreshing the sample with new households. However, in cases where this type of in-migration into the household population is relatively rare, the represented population is close enough to the actual population to permit the desired estimates.

# _5) Pooling_

> 8 One example of a rare circumstance where the exact calculation would be possible would be if two (or more) eligible members of existing separate panel households merged into a single household, for example if the children of two panel households in the same village married and established a new household.  In this case the probability of selection for both the husband and wife would be known, and the exact probability could be calculated.

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