Missing-Data Patterns and Mechanisms Sample Clauses

Missing-Data Patterns and Mechanisms. Missing-data patterns define the type of missingness depending on values observed and missing in the data set. Missing-data mechanisms capture the relationship between the missingness of values of certain variables and values of all variables in the data set. Let Z = (zij) be an n × p data matrix with i-th row a p-vector observation of variables (Z1, ..., Zp) for subject i. In the presence of missing data, we further let R = (rij) be the matrix of binary missing-data indicators of the same dimension as the data set Z, with rij = 1 if zij is observed and rij = 0 otherwise. If the missing values only occur on one variable but a set of the rest variables is fully observed, we call it a univariate missing-data pattern. Some methods are restricted to univariate missing-data patterns since such patterns are simple and the methods are easy to illustrate. A data set has a monotone missing-data pattern if its variables could be arranged so that if Zj is missing for a subject, then Zj+1, ..., Zp are missing as well. The monotone missing-data pattern often arises in longitudinal studies that suffer from subjects’ dropouts. A more common missing-data pattern is the general pattern. A data set has a general missing-data pattern when any set of variables may be missing for any subjects. Figure 1.1 illustrates the three missing-data patterns.