Can Stan do mixed membership?

[Christopher Grainger]

I've been looking to implement a mixed membership model (e.g. students across multiple schools or firms operating in multiple countries) and I'm wondering if it's possible to estimate weighted variance components models with Stan. There do not appear to be any implementations in the existing examples. Has anyone done this before? Is it possible? With Level 2 predictors?

[Bob Carpenter]

On Jun 19, 2014, at 2:05 PM, Christopher Grainger <cigra...@gmail.com> wrote:

> I've been looking to implement a mixed membership model (e.g. students across multiple schools or firms operating in multiple countries) and I'm wondering if it's possible to estimate weighted variance components models with Stan. There do not appear to be any implementations in the existing examples. Has anyone done this before? Is it possible? With Level 2 predictors?

I don't know what any of these are:

* mixed membership model

* weighted variance components models

* level 2 predictors


If you can write down the joint density of data and parameters
and all the parameters are continuous, then you can probably fit
in Stan.

Are there examples in BUGS or JAGS? If so, they're usually
pretty easy to translate (unless you have to marginalize discrete
parameters).

For what it's worth, we're going to be spending a lot of
time over the next two or three years working on a range
of education models. So we're quite interested in
coverage here if we can understand the models.

- Bob

[Christopher Grainger]

Thanks for the response Bob. I guess I'm using terminology used by the folks at Bristol. The paper that has what I'm interested in is here: http://webarchive.nationalarchives.gov.uk/20130401151715/http://www.education.gov.uk/publications/eorderingdownload/rr791.pdf

Mixed membership model is a multilevel model in which units belong to multiple groups of the same type. For example, a firm might operate in multiple countries with known weights (summing to 1).

Weighted variance components model is just the terminology the Bristol guys are using for a multilevel model in which the random group effect is weighted by the known weights mentioned above.

Level 2 predictors are just group-level predictors.

I haven't seen this implemented in BUGS or JAGS. It seems that they use MLwiN.

[Richard McElreath]

I think I did a model like this in Stan a few months ago, so it's definitely possible. I say "I think", because the Bristol documentation style is very black-box, in my experience, so I don't know if what I did is what they mean by mixed/multiple membership. 

The example I think of often is grant review committees, in which the decision for a grant proposal depends upon features of multiple raters. So predicting overall rating of a proposal requires accounting for features of each individual rater, combined through some (possibly non-additive) function. This seems like the case where outcome for a firm depends upon features of different nations it operates in. 

The only trick I think is to set up a regular varying intercepts model, and then combine the varying intercepts to construct each prediction. Sounds like the firm example is just an additive combination with known weights, so should be possible to set up a weighted average of varying intercepts on nations in the linear predictor for the outcome.

Does this sound like the right interpretation?

[Bob Carpenter]

On Jun 20, 2014, at 5:20 PM, Richard McElreath <rmcel...@gmail.com> wrote:

> I think I did a model like this in Stan a few months ago, so it's definitely possible. I say "I think", because the Bristol documentation style is very black-box, in my experience, so I don't know if what I did is what they mean by mixed/multiple membership.
>

> The only trick I think is to set up a regular varying intercepts model, and then combine the varying intercepts to construct each prediction. Sounds like the firm example is just an additive combination with known weights, so should be possible to set up a weighted average of varying intercepts on nations in the linear predictor for the outcome.
>
> Does this sound like the right interpretation?

That would indeed be straightforward to code in Stan.
And it should fit well.

> The example I think of often is grant review committees, in which the decision for a grant proposal depends upon features of multiple raters. So predicting overall rating of a proposal requires accounting for features of each individual rater, combined through some (possibly non-additive) function. This seems like the case where outcome for a firm depends upon features of different nations it operates in.

I don't see how this is related, but I've built lots of
these rating models over the past few years.
I formulated them a la Dawid and Skene (1979)
as measurement error models --- there's a latent true rating
and then each rater has a response based on the true rating
and perhaps other features of the item. The responses can
be categorical, ordinal, or even continuous. They've gotten
very popular with the ease of collecting crowdsourced data.
Marc Girolami and collaborators had a cool paper with GP priors
for ordinal data; Uebersax and Grove had a neat latent continuous
ordinal model in the early 90s.

- Bob

>
> On Friday, June 20, 2014 12:42:29 AM UTC-7, Christopher Grainger wrote:
> Thanks for the response Bob. I guess I'm using terminology used by the folks at Bristol. The paper that has what I'm interested in is here: http://webarchive.nationalarchives.gov.uk/20130401151715/http://www.education.gov.uk/publications/eorderingdownload/rr791.pdf
>
> Mixed membership model is a multilevel model in which units belong to multiple groups of the same type. For example, a firm might operate in multiple countries with known weights (summing to 1).
>
> Weighted variance components model is just the terminology the Bristol guys are using for a multilevel model in which the random group effect is weighted by the known weights mentioned above.
>
> Level 2 predictors are just group-level predictors.
>
> I haven't seen this implemented in BUGS or JAGS. It seems that they use MLwiN.
>
> On Thursday, June 19, 2014 9:35:40 PM UTC+1, Bob Carpenter wrote:
> On Jun 19, 2014, at 2:05 PM, Christopher Grainger <cigra...@gmail.com> wrote:
>
> > I've been looking to implement a mixed membership model (e.g. students across multiple schools or firms operating in multiple countries) and I'm wondering if it's possible to estimate weighted variance components models with Stan. There do not appear to be any implementations in the existing examples. Has anyone done this before? Is it possible? With Level 2 predictors?
>
> I don't know what any of these are:
>
> * mixed membership model
>
> * weighted variance components models
>
> * level 2 predictors
>
>
> If you can write down the joint density of data and parameters
> and all the parameters are continuous, then you can probably fit
> in Stan.
>
> Are there examples in BUGS or JAGS? If so, they're usually
> pretty easy to translate (unless you have to marginalize discrete
> parameters).
>
> For what it's worth, we're going to be spending a lot of
> time over the next two or three years working on a range
> of education models. So we're quite interested in
> coverage here if we can understand the models.
>
> - Bob
>

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