Advanced methods for missing data

and Graham (2002); and Schlomer, Bauman, and Card (2010). A comprehensive approach usually includes the following steps:

1Identify the missing data.

2Examine the causes of the missing data.

3Delete the cases containing missing data, or replace (impute) the missing values with reasonable alternative data values.

Unfortunately, identifying missing data is usually the only unambiguous step. Learning why data are missing depends on your understanding of the processes that generated the data. Deciding how to treat missing values will depend on your estimation of which procedures will produce the most reliable and accurate results.

A classification system for missing data

Statisticians typically classify missing data into one of three types. These types are usually described in probabilistic terms, but the underlying ideas are straightforward. We’ll use the measurement of dreaming in the sleep study (where 12 animals have missing values) to illustrate each type in turn:

■Missing completely at random—If the presence of missing data on a variable is unrelated to any other observed or unobserved variable, then the data are missing completely at random (MCAR). If there’s no systematic reason why dream sleep is missing for these 12 animals, the data are said to be MCAR. Note that if every variable with missing data is MCAR, you can consider the complete cases to be a simple random sample from the larger dataset.

■Missing at random—If the presence of missing data on a variable is related to other observed variables but not to its own unobserved value, the data are missing at random (MAR). For example, if animals with smaller body weights are more likely to have missing values for dream sleep (perhaps because it’s harder to observe smaller animals), and the “missingness” is unrelated to an animal’s time spent dreaming, the data are considered MAR. In this case, the presence or absence of dream sleep data is random, once you control for body weight.

■Not missing at random—If the missing data for a variable are neither MCAR nor MAR, the data are not missing at random (NMAR). For example, if animals that spend less time dreaming are also more likely to have a missing dream value (perhaps because it’s harder to measure shorter events), the data are considered NMAR.

Most approaches to missing data assume that the data are either MCAR or MAR. In this case, you can ignore the mechanism producing the missing data and (after replacing or deleting the missing data) model the relationships of interest directly.

Data that are NMAR can be difficult to analyze properly. When data are NMAR, you have to model the mechanisms that produced the missing values, as well as the relationships of interest. (Current approaches to analyzing NMAR data include the use of selection models and pattern mixtures. The analysis of NMAR data can be complex and is beyond the scope of this book.)

Figure 18.1 Methods for handling incomplete data, along with the R packages that support them

There are many methods for dealing with missing data—and no guarantee that they’ll produce the same results. Figure 18.1 describes an array of methods used for handling incomplete data and the R packages that support them.

A complete review of missing-data methodologies would require a book in itself. In this chapter, we’ll review methods for exploring missing-values patterns and focus on the three most popular methods for dealing with incomplete data (a rational approach, listwise deletion, and multiple imputation). We’ll end the chapter with a brief discussion of other methods, including those that are useful in special circumstances.

18.2 Identifying missing values

To begin, let’s review the material introduced in section 4.5, and expand on it. R represents missing values using the symbol NA (not available) and impossible values using the symbol NaN (not a number). In addition, the symbols Inf and -Inf represent positive infinity and negative infinity, respectively. The functions is.na(), is.nan(), and is.infinite() can be used to identify missing, impossible, and infinite values, respectively. Each returns either TRUE or FALSE. Examples are given in table 18.1.

Table 18.1 Examples of return values for the is.na(), is.nan(), and is.infinite() functions