I have data from a between-subject experiment (Repeated measures, two conditions). Condition A has 15 participants while condition B is with 19. The difference is due to missing data.

My aim is to use this data to compare the frequentist( lme4) approach to the Bayesian approach (brms).

What can I do about the difference in sample size between A & B?

  • $\begingroup$ It might be informative to remove the missing data from both groups and regress them together as a single data set. There is a possibility that something interesting could be found from this, and such a test is certainly easy to perform.. $\endgroup$ – James Phillips Aug 31 '19 at 11:08
  • $\begingroup$ @JamesPhillips Why & how to combine two different datasets(two conditions) into a single data set to compare the difference between the two conditions? $\endgroup$ – amarykya_ishtmella Sep 1 '19 at 13:48
  • $\begingroup$ I was discussing this portion of your question: "The difference is due to missing data". $\endgroup$ – James Phillips Sep 1 '19 at 13:59

Both the frequentist and Bayesian approaches are likelihood-based approaches in this case. And likelihood-based approaches give you valid results under both the missing completely at random and missing at random missing data mechanisms. This is under the proviso that the model is correctly/flexibly specified. This includes also the variance-covariance structure for the repeated measurements. That is, you should model the correlations in the repeated measurements adequately.

In both approaches you can/should work with all available data. You should not do a complete cases analysis (i.e., only consider the 15 subjects who provide all measurements) because this will be less efficient and also be valid only under missing completely at random.

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  • $\begingroup$ For bayesian I was not skeptical about including all data. But for doing ANOVA, isn't different sample sizes a problem considering the difference between the conditions w.r.t the data is around 20%. $\endgroup$ – amarykya_ishtmella Sep 1 '19 at 14:02
  • $\begingroup$ Package lme4 does not do ANOVA. It fits mixed-effects models using maximum likelihood or restricted maximum likelihood (the latter being only applicable for continuous outcomes and normal error terms). $\endgroup$ – Dimitris Rizopoulos Sep 1 '19 at 18:05

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