of _Ai_ and _Sh_ precisely. Using the actual areas, rather than the areas of the circles with radius _rh_ , addresses the issue of lower probabilities of selection for households near the boundary of the study area (see Barrett 1964 for a discussion of “edge effect bias”). (It is also possible to conceptualize the sampling technique used in this study as a form of indirect sampling. Such an approach would also lead to appropriate probabilities of selection and weights (Lavallée 2007). We have chosen not to take such an approach here because of the difficulty of dividing the study area into slices of land which lead to selection of unique sets of households. See Roesch et. al. (1993) for such an approach in the context of RGCS.) Although 125 circles were selected, only 102 were visited by interviewing teams, as discussed below. For the _ch_ values, we use the number of visited circles rather than the number of selected circles, under the assumption that the circles within a stratum that the teams did not visit are missing at random. The initial weight for each household is then the reciprocal of its overall probability of −1 selection: w1i = πi .

We make one adjustment to this weight, for the unobserved portions of the selected circles. The fieldwork protocol stipulated that interviewer teams should systematically observe the entire circle, however, this was not always possible due to the challenges discussed above (and possibly also due to low effort by the interviewing teams, which is discussed in more detail below). We calculate an alternative set of weights that adjusts for the portion of each circle that was not observed. The GIS technique of Viewshed analysis uses the tracks recorded by the GPS devices as the interviewers traveled within the circle, along with an altitude map, to determine what the interviewers were able to observe, that is, the area that was in their line of sight as they travelled around the circle. Figure 5 in the appendix shows an example of a map produced by the Viewshed analysis. The white tracks are the paths taken by the interviewing team members in circle 134 and the land within the circle that they could observe from those paths. We see that although the interviewers walked only a small portion of the circle, they were able to observe the majority of the area, 72.4 percent in this case. Across all of the visited circles, the observed coverage percentages range from 14.1 to 99.0, with a mean of 84.0.

The multiplicative weight adjustment is the reciprocal of the percent observed in each circle. If we believe that there are households within the unobserved portions of the selected circles, and that these households are similar to those interviewed in the observed portion, then the adjusted weight is appropriate and improves estimates. If, alternatively, we believe that the areas that were not observed were missed because they could not possibly contain any livestock, due, for example, to flood water or vegetation too thick to traverse, the adjustment to the weights is not necessary. We use both the unadjusted and the adjusted weights in the results section. No further adjustment to the weights for household nonresponse was made as the field teams did not report any issues with participation. Household surveys in rural areas of the developing world, and in particular Ethiopia, have historically had high response rates.

The weights require one further caveat. The probabilities of selection on which the weights are based are accurate only if the people and livestock that the survey aims to capture do not move during the study period. If a man and his camels are selectable in more than one circle over the data collection period, then they have more than one probability of selection, which greatly complicates the weighting. To minimize this complication, we constrained the data collection period to one month. We also asked three questions in the survey regarding the past and future movements of the respondents. The first item asks whether the respondent had traveled during the dry season with his livestock outside of the area where the interview took place, the second asks if the livestock had traveled separately outside the area where they were currently, and finally if the respondent planned to travel outside of the current area during the dry season. In approximately six percent of the cases, the respondent had travelled with 8