Hello,
I am struggling to understand how R's lmer function handles missing data. I couldn't find an exact description in the documentation of the package. I also tried to play with some data, but still couldn't figure it out. Here is what I did:
I constructed a full data set with reaction times (RT) to words of 5-7 letters and fitted the following model to the data:
RT ~ Length + (1|Word).
The intercept and the estimates of the fitted model gave me the correct mean RTs in the various length conditions.
Then, I changed the RT value for a single observation (a 7-letter word) to NA, and refitted the model (using either na.action="na.omit", or "na.exclude"). The estimates for 5 and 6 letters were still correct, but for 7 letters (and also the grand mean, when trying sum coding) the result was a bit off. I tried to decipher how the estimate for 7 letters was calculated, but failed. It was not equal to the weighted mean over responses to the different 7-letter words, as I would have expected, but a slightly lower value.
Any idea how is the estimate calculated given some missing data?
Thanks,
Chen
Put simply it does listwise deletion to remove the row of values for when an observation is missing - that is imbalanced data result - maximum likelihood is then used to get estimates of the parameters of the model, these will be unbiased if the missingness is MAR or MCAR
see https://missingdata.lshtm.ac.uk/
If the data are Not Missing are Random you should expect to get biased estimates.
Depending on amount of missing data according to MCAR, you can implement varous imputation methods procedures to recover missing vector values.
Hope this helps,
Matt
Thank you for the suggestions. I understand from your answers that in cases of missing data the parameter estimates are not simply averages over raw data and it would be hard to calculate them "by hand". Is that correct?
(I thought that listwise deletion means that all responses for the particular item are excluded if one response is missing. I tried to exclude them manually, but I still couldn't replicate the estimate of the LMM.)
" the parameter estimates are not simply averages over raw data and it would be hard to calculate them "by hand". Is that correct? "
Yes that is in general correct - they are maximum likelihood estimates (and they have to be got by algorithmic that is iterative procedures). You should in my view concentrate on their properties and assumptions and not the mechanics of estimation; unless of course you are going to develop new algorithms etc
If you want to see an algorithm and more importantly for you the properties of an estimator have a look at this
Book Developing multilevel models for analysing contextuality, he...
I set out Goldstein's IGLS/RIGLS estimator for a 2 level-1 units in each of 2 level 2 units and consider precision weighting . This is not the estimator used in LME4 but in general you the results in well-behaved problems, when there is plenty of data available, should be the same. Increasingly when there is a lack of data, people are switching to Bayesian inspired MCMC estimation which is also covered in volume 1 and Volume 2.
So here is a dumb question probably. Do we need to account for NA's by including ANY code to handle them when we use lmer()?
I'm also interested in this question. You may refer to this article: https://www.theanalysisfactor.com/linear-mixed-models-for-missing-data-in-pre-post-studies/. It seems that linear mixed models will deal with the missing data through pairwise deletion (available case analyis (Pigott, 2001)), before the maximum likelihood is used. Kelvyn Jones
sorry but I have never used lme, but have a look at
https://stat.ethz.ch/pipermail/r-sig-mixed-models/2016q2/024636.html
Of course we are talking about the response/ outcome values being missing not the predictor variables.
Yes, we are talking about the "response/outcome values" being missing. This is quite common in real life experiments, say eye-tracking studies. To the best of my knowledge, many studies included all the participants irrespective of the number of sessions with valid data when fitting the lme models (see for example: Chapter Translation, Post-Editing and Directionality: A Study of Eff...
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In response to Kelvyn Jones' statement that R's lmer function applies listwise deletion, Jiajun Qian wrote:
"You may refer to this article: https://www.theanalysisfactor.com/linear-mixed-models-for-missing-data-in-pre-post-studies/. It seems that linear mixed models will deal with the missing data through pairwise deletion (available case analyis (Pigott, 2001)), before the maximum likelihood is used."
Jiajun Qian, bear in mind that if the software being used for repeated measures ANOVA requires a WIDE file format (e.g., SPSS does), then listwise deletion will result in an entire row (subject) being dropped if either of the paired scores (pre-post) is missing. But for multilevel modeling, a LONG file format is needed, which means there would be two rows of data for each subject with complete data, but only one row for those who are missing one of the scores. So from the point of view of a WIDE file format, yes, all available data would be used. But in the context of a LONG file, that would still be listwise deletion. I believe that is what Kelvyn meant.
HTH.
Bruce Weaver Thank you for the clarification. Indeed, when fitting LME models with R packages, listwise deletion or, simply put, the deletion of rows with missing response, is used.
I agree - I am thinking about long format. Sorry if there is any confusion.
Dear Chen Gafni
You may refer to this article;
http://christophe.genolini.free.fr/recherche/atelierATelecharger/atelier205_1_HJG.pdf
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