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I am a little bit rusty at this sort of thing, so I will not be offended if you tell me this is a stupid question. I am doing a logistic regression where my dependent variable is whether or not a person owns a particular product.

Among the variables in the model is an indicator of marital status, 1 for married, 0 for not married. This is reliable data taken directly from an application the client filled out, for example. In many cases, the data is missing (maybe the person never filled out an application) but there is a second data source which is somewhat accurate, but not completely so. Would it make sense to fill in the missing values - not with 0 or 1, but something in between? Like if they are probably married, based on the second data source, I give them 0.8 or else a 0.2 if they probably are not married.

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Do you have any measure on the degree of inaccuracy of your second file? – Placidia Jan 10 '13 at 19:09
I have not done it yet, but I could look at how frequently the two sources agree, when there is data from both. I just want to be sure that it is a reasonable thing to do. – Oliver Jan 10 '13 at 19:22
Welcome to our site! Your statement shows you can be rusty at something and still ask a good question. :-) I would suggest making your question a little more open-ended, though (and to that end I have attached the data-imputation tag): rather than asking our opinion of a particular procedure that comes to mind, why not ask for suggestions about how to deal with your missing data problem? That in turn suggests you might want to provide some additional information about the purpose of your analysis. – whuber Jan 10 '13 at 19:30

I have never seen this done, and I doubt other people have either. One usually gets informed answers on this site within a couple of hours of posting something. It's been a day, and no joy.

My thinking is this: if you want to tell the model that some values are more trustworthy than others, use weights. If you downweight values where you doubt the accuracy of the data, the model will basically accept a worse fit at that point -- which is what you want.

Example: suppose you have a very "married" set of covariates for someone coded "unmarried" in the dodgy data set. Without weights, the fitting algorithm could distort the parameter estimates in order to get some kind of fit. With weights, the algorithm need not try so hard. In effect, it lets you have bigger residuals when you don't trust the data.

If you want to go with your first idea of substituting data with probabilities, I would iterate: estimate probabilities that someone is married or not, then fit the model with my best guesses, then go back and adjust the estimates. This is an EM approach. So, I would not replace 0's and 1's with 0.8 and 0.2 in the fit. I would use 1 and 0 according as the probabilities were less than or greater than 0.5 - but then I would go back and adjust the probabilities on the basis of lack of fit at those points.

If you look at what happens in a logistic regression model, the math involved really expects that the data are going to be 0's or 1's. I think you want to stick with that. My advice boils down to using weights or estimating marital status from the rest of the data.

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Thanks Placidia. When I come back to this at the beginning of next week I will be pressed for time as well as stretching my brain cells back to my graduate level econometrics, so I want to keep this as simple (yet as accurate) as possible. I think after poking at the data I will either count the less trusted data the same as the good data or just not use it. In fact, as I sit here right now it is not obvious what sign would be on the coefficient for marital status. Maybe I will get lucky and it will be not significant. – Oliver Jan 11 '13 at 19:06
That's probably the safest way to go. – Placidia Jan 11 '13 at 22:17

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