# Weights and everything weighted

@amoeba and I had a lengthy (and hence not particularly productive, if the sheer length is any indication of the proximity to consensus) discussion of tag synonyms in the main "Tag synonyms candidates" thread, and I think both of us got lost in this, so let's take it up to a higher level of a separate thread.

Everything weighted includes the following tags:

At this stage, I quicked-and-dirtied wiki summaries for the first three, and they are mostly driven by my personal opinion. (I am a survey statistician, so the production and the use of survey weights is my main line of business; I also hold strong opinions on the proper use of terminology, so my approach is to make everything as clear as possible.) I have put a relatively strong language to avoid some of these confusing / ambiguous tags, and suggested to put something more specific to the problem at hand.

Basically, my take is that in "tidy" rectangular data sets, we can put weights:

• on observations/rows -- in which case they usually serve as the multipliers to the likelihood contributions / squared residuals in least squares problems. I am used to weights coming from probability sampling from finite populations, so they roughly represent the inverse probability of selection and response. Many other uses of weights, such as precision weights or frequency weights, as discussed in http://www.ats.ucla.edu/stat/stata/faq/weights.htm, are probably deprecated by now, with the modern software allowing all the analysis in a better shape than what all of these historic tricks been used for. The problem-specific weights also arise in robust procedures, where the weights are used to limit the influence of outlying observations.
• on variables/columns -- some literatures refer to regression coefficients as regression weights, for instance. And there are also weights in deep learning networks, and these weights are "learned" rather than "estimated". Also, weights on variables come up in principal component analysis / factor analysis (in which case my preferred language is that of "loadings").

There are also data sets auxiliary to the main data, such as those generated by computational Bayesian / Monte Carlo Markov chains. The importance sampling weight is the ratio of the "true" density of interest to the density of a convenient distribution to sample from.

Yet another concept of weights may arise in model averaging, where the weights are attached to models rather than neither observations nor variables. For these, may be a better home than .

Yet another use of weights is when the marketing folks try to aggregate ratings of a product from different users. I am not sure what to recommend here.

There is probably more than meets the eye.

As I have been going through these trying to clean up (I started with retagging to or where appropriate), I discovered a wild variety of ways to use the idea of weights... and the topics and problems that people tag with these (often out of confusion). So that one can be clarified. Also, can probably be cleaned and frozen/killed, as the one having fewest questions.

At this point, we are seeking a community input to:

• proper definition of weights as a concept;
• delineation of what to consider the weights on observations in rectangular data sets, and the best tag name for that;
• delineation of what to consider the weights on variables in rectangular data sets, and the best tag name for that;
• what the concept of weights may mean for irregular data sets;
• other uses of weights in statistics / machine learning / data science, and whether these should go under some general tag, or have their own tags developed.

Let me put some tentative ideas for up/down voting, but please feel free to express more on the topic. In particular, post your "case studies" of other uses of weights in statistics, with the specific posts that use weights in that way.

UPDATE: I am guilty of creating another tag, . I will send the questions about sampling design to , while the questions about analysis with survey data and survey weights will go to .

• As I said, I think [weighted-data] is a fine tag name for datasets with datapoint weights. – amoeba Aug 9 '16 at 23:00
• I think I speak for all CV users when I say that we've weighted a long time for this discussion. – Sycorax Aug 10 '16 at 2:10
• It's a pity that you never finished cleaning this up @StasK. I know this is a lot of work... Any chance of you getting back to it at some moment? Consider this a gentle nudge :-) – amoeba Feb 2 '17 at 12:04
• Well as soon as I get fired from the main paying job of working with weighted-data, @amoeba... Also, I should have put a bookend pointer to where I stopped. – StasK Feb 8 '17 at 17:48

## 7 Answers

Usage of "weights": regression coefficients

Regression coefficients are referred to as "regression weights" in some literatures. I personally find this confusing, and would like to steer the site users to the more traditional statistical literature that talks about coefficients.

• Upvote: questions that talk about regression coefficients as weights should have the weight-related tag(s) removed (possibly with an explanation to the OP why this is being done).
• Downvote: such questions should be left alone as is.
• Comment: please provide your considerations.
• +1 but are there any questions that talk about "regression weights" meaning "coefficients" and have weight-related tags? Is there many? Which tags are used? – amoeba Aug 9 '16 at 22:23

The tag

It is too generic, and should be killed.

• Upvote: agree, this is too ambiguous; this needs to be cleaned, and further use is discouraged/limited
• Downvote: keep it generic
• Comment: please provide your considerations
• +1 Definitely too generic and unclear. – amoeba Aug 9 '16 at 22:24

Usage of "weights": in neural networks

There is simply no way we can possibly make neural network people to stop saying "weights". This is a huge field, and model coefficients are always called weights there.

This does not seem to be a big problem for our tags: there are only 6 questions tagged with and together. We can easily remove [weights] from all these threads.

Upvote if you agree.

• To prevent confusion in the future, we can think of creating a [neural-network-weight] tag and mapping it to [neural-networks] as a synonym. Upvote this comment if you think it's a good idea. – amoeba Aug 9 '16 at 22:58

Usage of "weights": in meta-analysis

You ask about other uses. In the thread there are occasional posts about alternatives to the standard inverse-variance weighted method.

======edited ===========

There seem to be three with tag, two with and one with out of ~450. The last one seems justifiable as the OP wanted to meta-analyse data from survey samples but the other five seem tautologous to me.

• Upvote: delete tags on the five
• Downvote: leave it
• Comment otherwise

Assuming I can work out how to (and have enough rep) I am happy to do the deletion if it gets voted for.

• This is a good point, but is there a specific recommendation here that we are up/downvoting for? – Silverfish Aug 11 '16 at 20:46
• +1. You have over 2k rep so you should be able to directly edit any post, including adding or removing tags. – amoeba Aug 12 '16 at 20:19
• I have now done this. I left one of the weighted regression ones as I was not sure whether that was in fact more relevant than meta-analysis – mdewey Aug 19 '16 at 12:16

The tag

It needs to be refined. @StasK's inclination is to limit it to computational Monte Carlo where it means the ratio of the target to sampling density; a lot of other uses actually mean unequal probability sampling in complex surveys, and these should be tagged instead. There is also a small minority of questions where the tag is used for what may be a better fit.

• Upvote: limit this to a technical use
• Downvote: keep it generic
• Comment: please provide your considerations
• Can you give us some idea about how many of the ~150 threads tagged with [weithed-sampling] fall into which category? There is only one single question that I get when I search for [weighted-sampling] monte carlo. If so, do we need this Monte Carlo related tag at all? – amoeba Aug 9 '16 at 23:04
• About a third of these can be rerouted to survey-sampling. Many just don't seem to fit anything reasonable... may be weighted-data until a better resolution is found. – StasK Aug 10 '16 at 12:51
• Most questions are abandoned -- there are many unanswered requests for clarification that have been dead for a few months. – StasK Aug 10 '16 at 13:16
• I am presently not sure we need a tag for that. I mean, we have a [monte-carlo] tag already. And [importance-sampling]. Perhaps it is enough? – amoeba Aug 10 '16 at 15:21
• Should be enough, I agree. I am trying to clean up that tag at the moment. I am back in time to early 2016 at this point. – StasK Aug 10 '16 at 15:28
• You are doing great job. – amoeba Aug 10 '16 at 15:32

Usage of "weights": in surveys

Weights are used in analysis of complex survey data. The initial motivation comes from Horwitz-Thompson estimator, in which the weights are the inverse probabilities of selection. In most modern survey data sets, weights also account for multiple ways to reach the observation unit (e.g., through both landline and cell phones in phone surveys), nonresponse, and calibration/generalized regression estimation intended to improve precision.

• Upvote: questions that primarily deal with this use of weights should be (re)tagged .
• Downvote: such questions should be left alone as is.
• Comment: please provide your considerations.

The tag

This tag is used when people are unsure what to do.

• Upvote: make it a synonym / fold into
• Downvote: keep it generic
• Comment: please provide your considerations
• [weighted-mean] seems to be exactly equivalent to [mean] + [weighted-data], but it might still make sense to keep it as a separate tag, given that it has been used 100+ times. – amoeba Aug 9 '16 at 21:57
• Disagree on strict equivalence. Sometimes, weighted-mean refers to some ingenious methods, such as rolling averages in time series. That does not fit my preferred definition of weighted-data where there is one and only one weight attached to an observation. – StasK Aug 9 '16 at 22:00
• Hmm, so you yourself are against the suggestion expressed in this answer of yours? That's confusing. – amoeba Aug 9 '16 at 22:05
• I have been trying too hard on this, apparently. May be this suggestion is too strong, in the first place, so feel free to downvote. There may be another way to manage that tag, too. – StasK Aug 9 '16 at 22:37