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There are frequent questions on CV about how to deal with structural zeros. Most recently, this question asked about how to use a variable for "spouse's education" when many people have no spouses. I've seen at least two similar questions recently.

Do we have a tag for this? If not, I think we should create one.

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    $\begingroup$ You don't really need to ask, @Peter, you have the privilege. Just make the tag and add it to the threads. If you do make it, please at least add a tag wiki excerpt to define it & guide its usage. $\endgroup$ Commented May 18 at 12:17
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    $\begingroup$ @gung-ReinstateMonica I was just wondering if there is some tag that I am missing that would cover this. $\endgroup$
    – Peter Flom
    Commented May 18 at 12:19
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    $\begingroup$ I agree with @gung-ReinstateMonica, Peter, if you think it's needed, go ahead and make one. As of whether any related tag exists, I haven't noticed any. $\endgroup$ Commented May 18 at 12:24
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    $\begingroup$ OK, I added the tag and some very brief description. $\endgroup$
    – Peter Flom
    Commented May 18 at 12:30
  • $\begingroup$ Didn't know that the correct term for this is "structural-zeros" but I think these threads are relevant? How do you deal with "nested" variables in a regression model?, 80% of missing data in a single variable. $\endgroup$
    – dipetkov
    Commented May 19 at 15:20
  • $\begingroup$ I do think there is another tag for this, nested-data $\endgroup$ Commented May 19 at 15:27
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    $\begingroup$ @kjetilbhalvorsen That tag is much broader, but related. If people think it's a synonym, that can vote on my tag, but I think it's different enough. $\endgroup$
    – Peter Flom
    Commented May 19 at 16:17
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    $\begingroup$ Hm. Is it only me that thinks "structural zero" is not a very good description of "spouse's education if no spouse exists"? That sounds like a textbook case of "not applicable", not "structural zero". Similarly, if no measurement was recorded because the sensor was broken/the store was closed/the data was lost, I would not call that a "structural zero", but "N/A" or "missing data". Of course the issue often is that a zero is recorded (but per this, shouldn't have been) and needs to be distinguished from bona fide zeros. Thoughts? $\endgroup$ Commented May 20 at 9:37
  • $\begingroup$ @StephanKolassa I thought this kind of "not applicable" was a structural 0? Can a non-existent spouse have any education? $\endgroup$
    – Peter Flom
    Commented May 20 at 10:16
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    $\begingroup$ I just don't think it makes sense to put any number in that field. Would zero be a useful input into any kind of model, whether as IV or DV? If at all, better to put -9999, which at least has a slightly better chance of being correctly interpreted as missing. "What color is your shirt?" "Red, because I'm not wearing a shirt." $\endgroup$ Commented May 20 at 13:13
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    $\begingroup$ @StephanKolassa, I would say that whether the right thing to do in that situation is put a 0 or treat it as missing data is a different issue than whether that situation exists & people ask questions about it. "Structural zero" is ultimately a name for the situation. It isn't hard for me to imagine that people come across this situation and just stick a 0 in there. I think it is OK to have a tag for this. If you have a better name, we could make [sz] a synonym (assuming askers will be familiar with / using sz). $\endgroup$ Commented May 20 at 15:58
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    $\begingroup$ I agree that there should be a tag for this and also think that we should come up with a name that doesn't use the word "zero" since the issue here is about non-applicable responses, and we don't want people to get confused and think that we're actually talking about (e.g. below) zero-inflation or other stats stuff that involves zero. $\endgroup$ Commented May 20 at 20:39
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    $\begingroup$ I will look through the nested-data and how it is used, but I have only ever seen it used for the cases you speak about here ... $\endgroup$ Commented May 21 at 2:08

3 Answers 3

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I am not aware of another tag. If it turns out there is one, we can always have them merged afterwards. I would say that you should just make the tag, since you've earned the privilege and you have a good reason. When you make the tag, be sure to add it to at least a second thread, or it will disappear automatically after 30 days. Also, please be sure to at least create a tag wiki excerpt to define it and provide some brief usage guidance, or a full wiki, if you're feeling ambitious.

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  • $\begingroup$ gung - Reinstate Monica, there is a zero-inflation tag, which appears (to me) to be what Peter Flom is referring to by "structural zeros".` $\endgroup$
    – Alexis
    Commented May 19 at 22:52
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    $\begingroup$ @Alexis, his example is a 0 for spouse's education when the respondent is unmarried. That's different from zero inflation in a count model. $\endgroup$ Commented May 20 at 11:20
  • $\begingroup$ 1/2 ZIPs are one example of zero-inflated models. Two-stage hurdle models also permit modeling of zero-inflation even if the second stage is a continuous variable. See, for example, Cragg, J. G. (1971). Some Statistical Models for Limited Dependent Variables with Application to the Demand for Durable Goods. Econometrica, 39(5), 829–844. $\endgroup$
    – Alexis
    Commented May 20 at 14:43
  • $\begingroup$ 2/2 Cragg gives an example of modeling distance of a residential move where the first stage models whether or not someone moves to account for inflated distances of zero. $\endgroup$
    – Alexis
    Commented May 20 at 14:47
  • $\begingroup$ "his example is a 0 for spouse's education when the respondent is unmarried. That's different from zero inflation in a count model." Why wouldn't (1) model whether someone has a spouse or not (i.e. model structural zeros), then (2) model spouse's educational attainment fit the bill here? $\endgroup$
    – Alexis
    Commented May 20 at 16:02
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    $\begingroup$ @Alexis, the issue is broader than that. FTR, I am familiar w/ hurdle models. I acknowledge that they would be one option when you want to model spouse's education as the outcome. I don't see how to use a hurdle model when spouse's education is one of the covariates someone wants to include. I think there can be other cases as well. $\endgroup$ Commented May 20 at 16:08
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    $\begingroup$ Claro. Hmm... is this a differentiation between the phenomena and the model for it a la your, Achim Zeileis' answers? $\endgroup$
    – Alexis
    Commented May 20 at 16:12
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    $\begingroup$ Also: Ah ha! Just registered the right-hand variable situation for spouse's education. $\endgroup$
    – Alexis
    Commented May 20 at 16:13
  • $\begingroup$ That's very big of you, @Alexis. $\endgroup$ Commented May 22 at 2:31
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There is an existing tag for nested-data with a fairly popular generic question/answer here. I'm not sure if this covers all instances of "structural zeros" or if there could be other contexts where those would occurs outside of nested data. If you feel that a structural-zero tag would be a useful supplement (that is not covered by the existing nested-data tag) then feel free to create it and see if it becomes useful.

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  • $\begingroup$ I think nested data is a much broader topic, but ... let's see what happens. $\endgroup$
    – Peter Flom
    Commented May 21 at 10:56
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We have a tag for zero-inflation which appears to by synonymous for what you term "structural zeros". There is currently a blurb for the zero-inflation tag reading (Wikipedia link for zero-inflated models added here):

Excessive 0's in a variable compared to a specified reference distribution. Regression approaches include zero-inflated models and hurdle (2-part) models. For count data, zero-inflated and hurdle models based on Poisson or negative binomial distributions are common (ZIP/ZINB and HP/HNB).

However, there is no deeper information under the "learn-more" link. Perhaps you can edit the tag to add!

**Edit: ** @gung - Reinstate Monica's comment about, e.g., a variable for spouse's education when one has no spouse as a right-hand variable clarifies for me why zero-inflation does not capture the issue.

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    $\begingroup$ No, zero-inflation is very different and doesn't necessarily involve any kind of nesting, nor is the 0 necessarily "structural". Structural zero, at least to my understanding, involves something that can't happen, dud to the answer to another question. Zero inflation is a variable where there are more 0's than would be expected under a particular distribution (usually Poisson, but also negative binomial and even Normal) $\endgroup$
    – Peter Flom
    Commented May 20 at 10:19
  • $\begingroup$ @PeterFlom I disagree, and encourage you to read the Cragg article introducing hurdle models: The distribution of how far you moved your residence in a given period (continuous variable) depends first on whether you are in the class of people who are moving (zero inflation, discrete distribution). Count models like ZIP and ZINB provide one example of what I think you are referring to as structural zeros, but not the only ones. But perhaps you can help me understand the distinction you are drawing. $\endgroup$
    – Alexis
    Commented May 20 at 14:49
  • $\begingroup$ @PeterFlom In other words "there are more 0's than would be expected under a particular distribution" seems to be a distinction without a difference: For example, in your example of "spouse's education" there is a prior probability that someone marries/is in the class of people with a spouse. $\endgroup$
    – Alexis
    Commented May 20 at 14:55
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    $\begingroup$ No. In one case, it is impossible to give an answer. In the other, the answer is 0 too often. They don't really have anything to do with each other. $\endgroup$
    – Peter Flom
    Commented May 20 at 17:37
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    $\begingroup$ @PeterFlom gung's comment about using, e.g., spouse's education as a right-hand variable helped clarify for me. :) You point about $0 \ne \varnothing$ is taken with respect to coding.. $\endgroup$
    – Alexis
    Commented May 20 at 17:52

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