Does Convergence Really Matter?
For many data sets, especially for non mandatory surveys, missing data are a common problem. Deleting units that are not completely observed and using only the remaining units is a popular, easy to implement approach in this case. This can possibly introduce severe bias if the strong assumption of a missing pattern that is completely at random (MCAR) is not fulfilled (see for example Rubin (1987)). Imputing the missing values can overcome this problem. However, ad hoc methods like, e.g., mean imputation can destroy the correlation between the variables. Furthermore, imputing missing values only once (single imputation) generally doesn’t account for the fact that the imputed values are only estimates for the true values. After the imputation process, they are treated like truly observed values leading to an underestimation of the variance in the data and by this to p values that are too significant.
The remainder of the paper is organized as follows. Section 2 recapitulates multiple imputation as a means of treating missing data problems. Section 3 introduces the two different methods to generate draws from the posterior distribution of (Ymis|Yobs) and describes the conditions necessary for compatible conditional distributions. Section 4 extends the simulation study from Van Buren et al. (2006) using different means for the bivariate normal distribution. The paper concludes with some final remarks.
KeywordsJoint Distribution Multiple Imputation Gibbs Sampler Joint Modeling Complete Case Analysis
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