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  1. Why is it that in repeated measures ANOVA if one measurement is missing, the entire case gets dropped?

    • If found the following explanation but don't really get what it means:

      The problem is that repeated measures ANOVA treats each measurement as a separate variable. Because it uses listwise deletion, if one measurement is missing, the entire case gets dropped.

  2. Why is this not that case for linear mixed models?

    • In my understanding one doesn't need complete cases here because the variance estimation procedure for the random effects accounts for sampling variance (and in doing so, for the number of measurements) through shrinkage.
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This is not an inherent feature of the methods, but rather a specific choice of a software. However, there are reasons that are to do with the methods.

While everyone knows that listwise deletion is nearly always inappropriate (unless the incredibly strong condition of missingness completely at random are fulfilled), it is easy to implement.

With random effects models, an implicit imputation assuming missingness at random occurs essentially automatically if you set up the data correctly (one record per observation not per observational unit - e.g. one record per patient per visit rather than on record per patient containing all the visits as separate variables), which is why a lot of software for random effects models does not apply listwise deletion (usually unless model covariates are missing) and does this implicit imputation instead.

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    $\begingroup$ Thanks for this explanation. But what exactly is the problem with missing data in rmANOVAs (i.e. why can't the results be calculated and cases have to be dropped in order to make the method work)? $\endgroup$ – statmerkur Oct 14 '17 at 17:55
  • $\begingroup$ As far as I am aware rmANOVA does not have an automatically in-built imputation like a random effects model, so whoever developed the software you used decided that the best/easiest thing to do would be to apply listwise deletion. They could easily have decided instead to do a multiple imputation e.g. using the multivariate normal MCMC approach instead. $\endgroup$ – Björn Oct 15 '17 at 6:26
  • $\begingroup$ I understand that it would be possible to do multiple imputation. My question ist about why rmANOVA doesn't work on datasets with missing data points (s. updated question) $\endgroup$ – statmerkur Oct 15 '17 at 12:00
  • $\begingroup$ In answer to the first comment - try computing means or variances with a missing value and still including that case. $\endgroup$ – mdewey Oct 15 '17 at 12:28
  • $\begingroup$ @mdewey this doesn't answer the question why rmANOVA doesn't work with missing data data $\endgroup$ – statmerkur Nov 22 '17 at 15:45

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