The estimated SE is a valid estimate of the SE of the mean for the subpopulation of cases that are always observed in repeated sampling. But the key issue here is whether the listwise-observed cases can be considered as a random sample of all the sampled cases, that is, the mechanism is MCAR. If not then the SE is not a good measure of precision, because it does not account for bias, whether or not it is a valid estimate of the SE in the above sense. Rod
Rod Little, [email protected] Richard D. Remington Distinguished University Professor of Biostatistics University of Michigan Department of Biostatistics M4071 SPH II, 1415 Washington Heights, Ann Arbor MI 48109 Survey Research Center, Room 4064 ISR, 426 Thompson St, Ann Arbor MI 48106 On Mon, May 8, 2023 at 5:30 PM Paul Von hippel <[email protected]> wrote: > 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$> >> >
