For both the Malawi and Uganda, the entire sample of households from the latest round of the LSMSISA which had contact information served as the HFPS sample. In Malawi, the initial HFPS sample consisted of 2,337 households while for Uganda it consisted of 2,421 households. The crude contact and response rate was very high in Uganda where 93 percent (2,259) of sampled households were successfully interviewed. Malawi’s contact and response rates were slightly higher than Nigeria and Ethiopia with 74 percent (1,729) of sampled households being successfully interviewed.

# <mark>3.1.2 Sampling Weight and Bias Adjustments</mark>

Sampling weights were calculated in all four surveys following similar methods. The sampling weight for the most recent round of the LSMS-ISA survey served as the starting point in all four countries since these weights produce representative estimates from the full sample of households in those F2F surveys. These weights were then inflated through basic ratio adjustments at each stage of the selection and interview process from the frame to the interviewed sample (depicted in Figure 3.1). These ratio adjustments preserve the original sum of weights from the full sample of the LSMS-ISA survey. These naïve ratio adjustments do not take into account any nonrandom bias contained in the sample.

The ratio adjustments were then followed by the weighting adjustments to reduce bias in the interviewed sample relative to the F2F representative sample. The weighting adjustment implemented in each country serves to counteract both coverage and nonresponse bias simultaneously. However, the approaches taken at this stage vary in the four countries. For the Ethiopia, Malawi, and Uganda HFPS, the bias adjustment was conducted using a propensity model approach following Himelein (2014). The probability of household response was modeled using a logistic regression. The characteristics included in the logit response probability module are presented in Table 3.2 and were selected due to observed bias in the interviewed sample along these dimensions. Full results of the logit model are provided in Appendix Table 3.1. The predicted probability of response from the model parameters was obtained for each household the inverse of which was the basis for the bias adjustment factor. However, in order to prevent extreme weights due to the correction factor, the predicted probabilities were sorted into deciles and the mean inverse response probability within each decile taken as the final weight adjustment factor.

In Nigeria, the bias adjustment was performed using the calibration approach whereby the weights were adjusted (minimizing the distance between the original and calibrated weights) to achieve the same weighted estimates across selected characteristics in the GHS-Panel sample. Table 3.2 contains the list of characteristics that were used in the calibration model. These characteristics were selected for inclusion in the calibration due to observed bias in the interviewed sample across these dimensions. Adjusting the weights to match the same profile of characteristics obtained from the fully representative GHS-Panel sample will counteract the bias along these dimensions. However, one drawback to the calibration approach is that it can be difficult to consider a large set of characteristics and achieve convergence in the calibration model.

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