The approach proposed in this paper can be applied to other countries across the Europe and Central Asia (ECA) region and beyond. The method can help survey implementation in countries where a reliable national sampling frame is unavailable which often causes the World Bank, UN, and other international organizations to face critical challenges in preparing socioeconomic surveys. In those countries, the National Statistical Offices (NSOs) are often unwilling to share their census sampling frame with international organizations although the sample frame might be available. Even if the census sampling frame is available, census EAs are often large and cover large population areas which require substantial resources and time to conduct the household listing. The resource and time-efficient approach we propose thus can save a significant amount of budget, which could be invested in other areas, in all sampling stages.

# **5 Discussion**

The national sampling frame based on pre-EAs provides several benefits that the existing and accessible potential sampling frames cannot offer. However, it could also introduce some practical challenges and methodological limitations. This section thus now discusses the additional benefits and potential concerns and proposes alternative solutions that have been previously tested to resolve some of those challenges in other developing countries where pre-EAs have been employed, such as Somalia (Qader et al., 2021) and the Democratic Republic of the Congo (Qader et al., 2023).

**Population Estimates as a Measure of EA Size:** The main challenge of using the proposed national sampling frame for household surveys is that the size of the pre-EA is measured by population estimates, which can differ from the actual population and thus introduce bias in the probability of EAs being selected in the first stage of the two-stage design.

Although it has been made clear that this study does not address the validation of the gridded population estimates, it is important to provide some clarity to understand the limitations of the data. The automatic creation of a national sampling frame requires granular information about the population to ensure that the output sampling units are manageable. This level of granularity does not exist in the existing census data in Armenia. Instead, gridded population data is leveraged. In developing countries, several gridded population datasets with various spatial resolutions are accessible, including Gridded Population of the World (GPWv4) (CIESIN, 2016), WorldPop (Bondarenko et al., 2020), High-Resolution Settlement Layer (HRSL) (Facebook and CIESIN, 2016), Demobase Population datasets (Azar et al., 2013), Global Human Settlement Population Grid (GHS-POP) (JRC, 2015), Global Rural-Urban Mapping Project (GRUMP) (CIESIN, 2011) and LandScan (Dobson et al., 2000). The quality of the input data model, which includes census data, satellitederived covariates, and statistical model selection, is primarily responsible for the accuracy and quality of the gridded population data. The WorldPop-constrained gridded population data for Armenia in 2020 has been used to create the national sampling frame. It was WorldPop’s most recent gridded population available. It implies that there may be notable differences between the population’s size and distribution in 2020 and today. Since the user can update the national sampling frame’s population based on their desired population such as population registry, this should not be a major concern.

This paper established an accessible and usable urban and rural classification in Armenia for the first time, and it fits within the concept of a national sampling frame. The output might not reflect the reality, despite a significant correlation between the aggregated population estimates from the census and gridded population estimates for urban and rural areas, as discussed in Section 5. It is primarily because the GHSL SMOD divides the world into urban and rural classes using gridded populations and built-up areas developed using various data sources. The algorithms used to generate the input data for both datasets and the date of the satellite imagery from which the covariates are extracted introduce certain biases. The severity of bias 24