Is it possible to use poststratification when some observations have missing values on the variables used as strata?

Question

This is a theoretical question, so I don't have data to share.

Let's say I know the percentage of men and women in my population of interest, as well as the distribution of occupations and age categories.

I conduct a survey on a sample from this population, to know their opinion about various topics. I suspect the sample might be biased, so I want to give weights to respondents to correct for that. I plan to use poststratification and the information I know about the population.

However, some survey respondents did not give information about their gender, occupation, and/or age. So for some of them, we might have no information at all, and for others we might have partial information.

Is poststratification still possible, without discarding people who did not answer questions about their gender, occupation, or age? If it's possible, how to compute their weights? And how reliable is it, in a "best case" scenario?

Thanks.

Answer 1

You are understating the problem when you ask whether poststratification is still possible "without discarding people who did not answer..."? Discarding them does not solve the problem. Suppose your sample has 47% responding "man", 48% responding "woman" and 5% not responding on gender. If you simply delete the 5% and poststratify you will be matching a population total for men to a sample total for "men and responded", which isn't the same variable.

There isn't an ideal solution. Whatever you do will involve some model for how the non-responders split, so decide that and do the post-stratification. If the item non-response for your stratification questions is less than the unit non-response you will probably still improve your estimates. It might also be worth doing a sensitivity analysis to see how your conclusions change for different ways of dividing up the non-responders