Let me try again, more concretely. When you use listwise deletion, you get point estimates -- e.g., for means, regression coefficients, etc. There is some work on the conditions under which listwise deleted estimates are consistent estimates of the corresponding population parameters.
When you use listwise deletion, you also get standard error estimates, which are meant to estimate the true standard deviation of the listwise deleted point estimates across repeated samples (with values deleted from each sample by the same missing data mechanism). My question: How well, and under what assumptions, do the standard error estimates obtained using listwise deletion estimate the true standard deviation of the listwise deleted point estimates? I agree that the MCAR condition is sufficient for listwise deletion to produce standard errors that are valid in this sense, but I suspect that weaker conditions will do. Many thanks if you know of relevant studies of this question. Best, Paul On Mon, May 8, 2023 at 4:15 PM Patrick Malone <[email protected]> wrote: > Hi, Paul. > > I'm still not entirely clear. By: > > the true standard errors of the listwise deleted point estimates? > > Do you mean the (unobservable) SE of a statistic *for the cases that were > deleted* listwise? > > Again, I don't think you can apply "consistency" to an SE, because SE is a > characteristic of the sample and dependent on N. There is no corresponding > population parameter. > > But if you want the SE of the complete-case mean (or other statistic) to > be the best estimate of the hypothetical SE of the statistic for the > omitted cases ("unbiased," not "consistent") then I think my two conditions > are still the answer. > > If you want a consistent estimator of the *SD* of a variable in the > omitted cases, which *is* an estimate of a population value, that would > be a different scenario. I think MCAR would be the answer to > the basic question. > > If you're also interested in *precision *of your estimate of the SD from > omitted cases, you'd want to consider the SE of the *variance *estimate, > which scales inversely with the square root of N (probably the N of the > smaller of the retained and discarded subsamples). > > Pat > " > > On Mon, May 8, 2023 at 3:43 PM Paul Von hippel <[email protected]> > wrote: > >> Sorry, as Patrick pointed out my question wasn't clear. Let me rephrase >> it: >> >> What is known about the properties of standard error estimates obtained >> using listwise deletion. When are they consistent estimates of the true >> standard errors of the listwise deleted point estimates? >> >> >> On Mon, May 8, 2023 at 2:15 PM Paul Von hippel <[email protected]> >> wrote: >> >>> Hi, all. What is known about the properties of standard error estimates >>> obtained using listwise deletion. When are they consistent estimates of the >>> listwise deleted point estimates? >>> >>> -- >>> >>> >>> Thanks! >>> Paul von Hippel >>> Professor, Associate Dean for Research >>> LBJ School of Public Affairs >>> University of Texas, Austin >>> >>> >>> > > -- > He/him/his > > This message is from an external sender. Learn more about why this > matters. > <https://urldefense.com/v3/__https://ut.service-now.com/sp?id=kb_article&number=KB0011401__;!!Dq0X2DkFhyF93HkjWTBQKhk!TwrQYTO4NQ0FaQC_2YIvH3NNqNtbtTcW4lDLcsEnj5bb7pT55dQltp40hgZ1VH8JrwSafgm4gtf8ZNlAn77I6wQFy8aZfbJC5Kd0L6VcqQ$ > > >
