Incomplete Data

In the previous chapters we assumed that the observational units are selected by a sampling design, usually simple random, and that the values of the relevant variables are recorded with precision for each selected unit. A sound principle in conducting studies is to ensure good representation of the relevant population by a planned (deliberate) design, a controlled sampling mechanism, and to collect all the data as planned. This chapter describes methods applicable when the data collection exercise is imperfect-when, contrary to the plan, some data are not collected or the sampling and data recording processes depart from the protocol in some other way. At the outset, we consider a sampling design with good representation and collection of the values of a set of variables from each selected unit. Later we expand the scope of the methods by defining ideal sampling and measurement processes that were not intended to be implemented, but for which the analysis would have been simple and manageable. We adapt the analysis to this less congenial setting. Further exploitation of this idea, entailing ingenuity in what is declared as ‘missing’ from the ideal dataset, substantially widens the horizon of problems that can be analysed efficiently and with integrity. Chapters 6 and 7 present two such applications of methods for incomplete data.