Variance formulae for composite estimators in rotation designs - ARCHIVED

In many government surveys, respondents are interviewed a set number of times during the life of the survey, a practice referred to as a rotation design or repeated sampling. Often composite estimation - where data from the current and earlier periods of time are combined - is used to measure the level of a characteristic of interest. As other authors have observed, composite estimation can be used in a rotation design to decrease the variance of estimators of change in level. In this paper, simple expressions are derived for the variance of a general class of composite estimators for level, change in level, and average level over time. Considered first are “one-level” rotation designs, where only the current month is referenced in the interview. Results are developed for any sampling pattern of m interviews over a period of M months. Subsequently, “multi-level” plans are addressed. In each month one of p different groups is interviewed. Respondents then answer questions referring to the previous p months. Results from the several sections apply to a wide range of government surveys.