The Efficiency of Missing at Random Planned Missing Designs

Planned Missing Designs (PMDs) allow for different sets or patterns of variables to be collected from sample units. While the typical motivation for PMDs is to manage respondent burden, they can also reduce data collection costs and provide flexibility in meeting reliability requirements for key survey outputs. Almost all PMD applications involve data being Missing Completely At Random (MCAR). That is, the pattern of variables to be collected from a sample unit is determined prior to collecting any variables from the unit. Here we generalise this approach by considering designing PMDs that allow data to be Missing At Random (MAR). That is, the set of variables collected from a unit is allowed to depend upon the value of some of the variables collected from the unit. At the design stage no data have been observed and so we consider the expected information function associated with maximum likelihood estimation for any specified PMD. We show how the missing information principle can be used to determine the loss of information arising from the use of a PMD. This paper considers the multinomial distribution in detail and conducts an empirical evaluation to illustrate potential efficiency gains associated with MCAR and MAR PMDs.