Logit has LPM, what does Multinomial Logit has? - SUR?

[teenug kaur]

Hi,

I am estimating an adoption model (0/1 binary response option), where for interpretability purposes, I am relying on linear probability model (LPM) instead of logit.

For the same setup, the choices can be coded to granular level, and I can estimate a multinomial logit model (because of the 4 different response options). What is the OLS version of multinomial logit? Should it be SUR?

Thank You!

G

[Clyde Schechter]

I don't think there is anything that is truly analogous to a linear probability model for a multinomial outcome. If somebody else knows of one, I'd be interested in hearing about it.

The reason -sureg- would not be adequate is that while mlogit jointly estimates things in a way that ensures that the sum of the predicted probabilities of each alternative outcome is always 1, -sureg- has no such similar feature--it just accounts for correlations among the errors. It might be possible with -sureg- to impose that summing to 1 as a constraint--I don't know, I have never tried it. -sureg- does support a -constraints()- option, though I don't know if it supports constraints applied to the outcome variables. If so, that might be reasonable to try.

[teenug kaur]

Thanks Clyde.

By that logic, even LPM is not adequate because it does not ensure predicted probabilities to stay within (0,1) range. I also think the issue of IIA, that exists for MNL, will be non-existent for SUR.

[Clyde Schechter]

There is one other issue. If you use SUR, you will have to omit one level of the outcome variable, otherwise the covariance matrix will be singular. (Kind of like the "dummy variable trap" in the dependent variables.)

As for LPM not ensuring predicted probabilities to stay within (0, 1), that is, indeed, a limitation that people often deal with by not using it when the predicted values are not predominantly going to be well away from 0 or 1. But LPMs do get used even in circumstances where they produce out of range values--I suppose it is a matter of accepting the limitations of the procedure. The same could be said about using SUR, I suppose.

[daniel klein]

The reason -sureg- would not be adequate is that while mlogit jointly estimates things in a way that ensures that the sum of the predicted probabilities of each alternative outcome is always 1, -sureg- has no such similar feature

True. But isn't that just the equivalent of the LPM not restricting the predicted values between 0 and 1?


Edit: Crossed with #3 and #4 above.

mvreg seems to be able to include all levels of the outcome.

[teenug kaur]

Thanks for your perspective Clyde. I appreciate it!

[Joro Kolev]

I think that Yes, any multinomial model can be represented as a system of equations. So there should be a way how to represent multinomial logit as some form of SUR. And the analogy will be loose just as the analogy between LPM and the logit is loose.

[Richard Williams]

It might be possible, but why do it? A much better approach for both logit and mlogit is, in my opinion, to use margins and adjusted predictions to make the results more intuitive and easy to understand.

https://www3.nd.edu/~rwilliam/xsoc73994/Margins05.pdf

Also, if someone could cite 10 articles using mlogit & SUR, that would be one thing, but if not I'm a bit leery of just making something up unless there is some major statistical advantage to doing so. If you do this, I think you'd need to demonstrate the statistical validity of it, not just say that it seems logical.

[daniel klein]

It might be possible, but why do it?

Well, you seem to be working on a command (predict_ldm) to get better predicted probabilities from the LPM together with Paul Allison. If we could apply that logic to mlogit, and if we could somehow replace a mlogit with a linear model for the purpose of multiple imputations via chained equations, that would speed things up and solve a lot of problems in terms of non-convergence issues that we often observe. That is probably a long way to go, and you would most definitely

need to demonstrate the statistical validity of it, not just say that it seems logical

but I am secretly hoping that you are heading in this direction.

[teenug kaur]

A much better approach for both logit and mlogit is, in my opinion, to use margins and adjusted predictions to make the results more intuitive and easy to understand

as daniel klein mentioned, I am having non-convergence issues, so I am relying on LPM. I feel stuck

[Richard Williams]

Some generic solutions for convergence problems are outlined at

https://www3.nd.edu/~rwilliam/xsoc73994/L02.pdf

The difficult option sometimes works miracles. Rescaling variables often helps too. And, of course, make sure your data are clean. I recently helped somebody with a variable that coded missing values as 99, and that was totally zapping the analysis,

In general, I would want to make sure my model and data are ok before I started searching for alternative approaches.

[Clyde Schechter]

I would add just one more thing to Richard Williams 's excellent advice about convergence issues. With -mlogit- I find that convergence issues are quite frequent if you have any outcome categories that are rare. So if you have such a category (or more than one) I would recommend either excluding those observations from the model, or merging that category with some other meaningfully-related category to produce a single category that is large enough for -mlogit- to handle gracefully.

[Richard Williams]

Related to what Clyde said, I often have people say that Long and Freese’s brant command gives an error. It is almost always because the ordinal dependent variable has a category or categories with very few cases, often six or less. Combining adjacent categories is often a good solution.

Again, my advice for many, many problems is to check out the basics before going higher tech. Convergence problems in particular often just need some tweaking of the current approach, not abandoning it.

If Teenug still can’t get his models to converge, he might show us his commands and output and we might be able to offer better advice.

[teenug kaur]

Thanks Clyde and Richard for your excellent advice. I will go mlogit route and attack non-convergence issues. I will come back after i tried mlogit. Thanks again!