1.6 What the book does not cover
The field of missing data research is vast. This book focuses on multiple imputation. The book does not attempt cover the enormous body of literature on alternative approaches to incomplete data. This section briefly reviews three of these approaches.
With the exception of McKnight et al. (2007 Chapter 4), books on missing data do not mention prevention. Yet, prevention of the missing data is the most direct attack on problems caused by the missing data. Prevention is fully in spirit with the quote of Orchard and Woodbury given on p. . There is a lot one could do to prevent missing data. The remainder of this section lists point-wise advice.
Minimize the use of intrusive measures, like blood samples. Visit the subject at home. Use incentives to stimulate response, and try to match up the interviewer and respondent on age and ethnicity. Adapt the mode of the study (telephone, face to face, web questionnaire, and so on) to the study population. Use a multi-mode design for different groups in your study. Quickly follow-up for people that do not respond, and where possible try to retrieve any missing data from other sources.
In experimental studies, try to minimize the treatment burden and intensity where possible. Prepare a well-thought-out flyer that explains the purpose and usefulness of your study. Try to organize data collection through an authority, e.g., the patient’s own doctor. Conduct a pilot study to detect and smooth out any problems.
Economize on the number of variables collected. Only collect the information that is absolutely essential to your study. Use short forms of measurement instruments where possible. Eliminate vague or ambivalent questionnaire items. Use an attractive layout of the instruments. Refrain from using blocks of items that force the respondent to stay on a particular page for a long time. Use computerized adaptive testing where feasible. Do not allow other studies to piggy-back on your data collection efforts.
Do not overdo it. Many Internet questionnaires are annoying because they force the respondent to answer. Do not force your respondent. The result will be an apparently complete dataset with mediocre data. Respect the wish of your respondent to skip items. The end result will be more informative.
Use double coding in the data entry, and chase up any differences between the versions. Devise nonresponse forms in which you try to find out why people they did not respond, or why they dropped out.
Last but not least, consult experts. Many academic centers have departments that specialize in research methodology. Sound expert advice may turn out to be extremely valuable for keeping your missing data rate under control.
Most of this advice can be found in books on research methodology and data quality. Good books are Shadish, Cook, and Campbell (2001), De Leeuw, Hox, and Dillman (2008), Dillman, Smyth, and Melani Christian (2008) and Groves et al. (2009).
1.6.2 Weighting procedures
Weighting is a method to reduce bias when the probability to be selected in the survey differs between respondents. In sample surveys, the responders are weighted by design weights, which are inversely proportional to their probability of being selected in the survey. If there are missing data, the complete cases are re-weighted according to design weights that are adjusted to counter any selection effects produced by nonresponse. The method is widely used in official statistics. Relevant pointers include Cochran (1977) and Särndal, Swensson, and Wretman (1992) and Bethlehem (2002).
The method is relatively simple in that only one set of weights is needed for all incomplete variables. On the other hand, it discards data by listwise deletion, and it cannot handle partial response. Expressions for the variance of regression weights or correlations tend to be complex, or do not exist. The weights are estimated from the data, but are generally treated as fixed. The implications for this are unclear (Little and Rubin 2002, 53).
There has been interest recently in improved weighting procedures that are “double robust” (Scharfstein, Rotnitzky, and Robins 1999; Bang and Robins 2005). This estimation method requires specification of three models: Model A is the scientifically interesting model, Model B is the response model for the outcome, and model C is the joint model for the predictors and the outcome. The dual robustness property states that: if either Model B or Model C is wrong (but not both), the estimates under Model A are still consistent. This seems like a useful property, but the issue is not free of controversy (Kang and Schafer 2007).
1.6.3 Likelihood-based approaches
Likelihood-based approaches define a model for the observed data. Since the model is specialized to the observed values, there is no need to impute missing data or to discard incomplete cases. The inferences are based on the likelihood or posterior distribution under the posited model. The parameters are estimated by maximum likelihood, the EM algorithm, the sweep operator, Newton–Raphson, Bayesian simulation and variants thereof. These methods are smart ways to skip over the missing data, and are known as direct likelihood, full information maximum likelihood (FIML), and more recently, pairwise likelihood estimation.
Likelihood-based methods are, in some sense, the “royal way” to treat missing data problems. The estimated parameters nicely summarize the available information under the assumed models for the complete data and the missing data. The model assumptions can be displayed and evaluated, and in many cases it is possible to estimate the standard error of the estimates.
Multiple imputation extends likelihood-based methods by adding an extra step in which imputed data values are drawn. An advantage of this is that it is generally easier to calculate the standard errors for a wider range of parameters. Moreover, the imputed values created by multiple imputation can be inspected and analyzed, which helps us to gauge the effect of the model assumptions on the inferences.
The likelihood-based approach receives an excellent treatment in the book by Little and Rubin (2002). A less technical account that should appeal to social scientists can be found in Enders (2010, chaps. 3–5). Molenberghs and Kenward (2007) provide a hands-on approach of likelihood-based methods geared toward clinical studies, including extensions to data that are MNAR. The pairwise likelihood method was introduced by Katsikatsou et al. (2012) and has been implemented in