Need suggestions on setting up a peculiar sampling design using svyset

[Deepan Pitchairaj]

I have understood the basics of svyset in Stata, but I am slightly confused about how to apply it to my sampling design.

Sampling design

A State population is divided into Rural and Urban populations.

Within the Urban population, Million-Plus (MP) cities are carved out, and the remaining urban population is treated as Non-Million Plus (NMP) urban.

• Urban MP cities form a separate domain.
  From this domain, 50% of the cities are selected. If only one MP city exists in a state, it is selected with certainty.
• Urban NMP and Rural populations exclude MP cities completely and are stratified into five strata.
  From each stratum, one district (PSU) or more is selected .depends on the requirement considering the size of the state.

Thus, the State population can be written as:

State Population = Rural ∪ Urban
State Population = Rural ∪ Urban NMP ∪ Urban MP

Problem


Using svyset, it is straightforward to specify stratification and PSUs and obtain State-level estimates when all PSUs come from strata (i.e., Rural and Urban NMP).

However, MP cities cannot naturally be treated as a stratum, since:

• They are not districts/counties instead it is present under a district
• They are carved out from the Urban population before stratification (5 strata)
• Their selection mechanism differs from the rest of the sample

At the same time, MP cities are part of the Urban population and must contribute to State-level estimates.

Question


How should MP cities be handled in svyset so that:

1. Their contribution is correctly reflected in State-level estimates, and
2. Design-based inference remains valid,

Given that MP cities are neither standard strata, since stratification is based on the poverty index.
MP cities are not districts, where multiple cities, towns, and villages together form a district.

This information is crucial for obtaining overall State-level estimates and for calibration, especially since I only have population information on:

• Percentage of Rural, Urban NMP, and Urban MP, and
• Gender ratios for Urban and Rural populations (but not separately for NMP and MP).

Any guidance or suggestions would be greatly appreciated.