Missing Data

Abstract

It is very common for data to be missing and this introduces a risk of bias if inferences are drawn from incomplete samples. However, we are not usually interested in the missing data themselves but in the population characteristics to whose estimation those values were intended to contribute. Learning something about the data that are missing is thus only the first step on the way to inference. One approach is to use a direct method, such as maximum likelihood but the price to be paid is usually much greater complexity in the estimation process. Methods such as the E-M algorithm sometimes make this easier by requiring us to solve a much simpler problem many times as the estimates converge to the desired values. Sometimes it is actually advantageous to introduce hypothetical variables. Which are then treated as unobserved and an example is provided concerning a mixture of exponential distributions. A different kind of approach is to impute values to replace those that are missing. This yields a complete sample which can then be analysed in the usual way. Imputed values can be derived from the conditional distribution of the missing values given those that are observed. This possibility depends upon being able to say something about why some sample members are missing and this may be done by specifying a probabilistic loss mechanism.