Most of the nonresponse literature has been emphasized at the element level, that is, the nonrespondent is the ultimate unit in the sampling process. However, it is frequently found in survey practice nonresponse at earlier stages of the sampling process, especially on surveys of institutions, such as schools or establishments. One possible alternative when such event occurs is to substitute the nonresponding unit. Although such procedure has been extensively criticized in survey sampling literature, it is largely used in practice, especially in school-based surveys. Moreover, there are different ways such substitution can be implemented and it is not yet clear which one performs better. This study aims to evaluate the impact on the survey estimates under the presence of nonresponse at the primary selection unit level of a two-stage cluster sampling and the properties of such estimates when various forms of substitution are used. A simulation study is conducted to evaluate under which scenarios these substitution procedures are justified compared to other alternative strategies, such as sample size inflation and weighting.
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