Pass posterior of model1 in as prior for model2 ?

[Derek Powell]

I'm wondering if it's possible to do as the subject says: Is there a way to take the posterior distributions for model parameters from one model and use them as the prior distribution for those parameters in another model? The context in which I'm doing this is that model1 is a component of model2, but there are new variables measured in model2 not represented in the data used to estimate model1.

I can think of two approaches:

1. I could approximate those posterior distributions using an accepted stan distribution and pass them in as the prior argument. The downside here is approximation--if the posterior isn't actually normal, student, beta, gamma, etc.

2. I could put all the data together and impute the missing values in the model1 data using mice or using brms (following the missing vignette). However, there are a fair number of missing data so I'm worried that will clog up my formula syntax (using the 1 pass approach), result in much longer estimating times (using mult imputation), and/or possibly bias estimates in some way?

Any thoughts on best practice here?

[Paul Buerkner]

Hi Derek,

there is no canonical approach.

1) This would at least ignore most of the correlation between parameters and would thus be a poor approximation in most cases.

2) This would be the better approach I guess, although the drawbacks you mention stand of you.

Talking about bias is a difficult topic. Missing value imputation, if done correctly, will reduce bias induced by data non missing completely at random, but this depends on whether you have observered the necessary variables and included them in the model / imputation.

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[Derek Powell]

Thanks Paul! I hadn't thought about correlations among parameters but that's now obviously a huge strike against option 1. I guess I will have to play around with imputation. In my case, I have one set of complete data measured at two time points and another set of data measured at just one of the time points. So I think the missing values can be fairly straightforwardly imputed from the other timepoint.

On Tuesday, April 17, 2018 at 12:13:39 AM UTC-7, Paul Buerkner wrote:

Hi Derek,

there is no canonical approach.

1) This would at least ignore most of the correlation between parameters and would thus be a poor approximation in most cases.

2) This would be the better approach I guess, although the drawbacks you mention stand of you.

Talking about bias is a difficult topic. Missing value imputation, if done correctly, will reduce bias induced by data non missing completely at random, but this depends on whether you have observered the necessary variables and included them in the model / imputation.

2018-04-16 20:50 GMT+02:00 Derek Powell <derek...@gmail.com>:

I'm wondering if it's possible to do as the subject says: Is there a way to take the posterior distributions for model parameters from one model and use them as the prior distribution for those parameters in another model? The context in which I'm doing this is that model1 is a component of model2, but there are new variables measured in model2 not represented in the data used to estimate model1.

I can think of two approaches:

1. I could approximate those posterior distributions using an accepted stan distribution and pass them in as the prior argument. The downside here is approximation--if the posterior isn't actually normal, student, beta, gamma, etc.

2. I could put all the data together and impute the missing values in the model1 data using mice or using brms (following the missing vignette). However, there are a fair number of missing data so I'm worried that will clog up my formula syntax (using the 1 pass approach), result in much longer estimating times (using mult imputation), and/or possibly bias estimates in some way?

Any thoughts on best practice here?

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