Hello, I am trying to fit a multivariate linear regression (Y = alpha + beta1 * X1 + beta2 * X2) wherein my 2 input variables (X1, X2) are correlated. I have uncertainties for all the variables (Y, X1, X2). I am using the following code to estimate the values for the intercept and the slopes: wit…

Hi, a couple of previous threads that might help: Errors-in-variables model in PyMC3 - #2 by chartl Dealing with multivariate x, errors in both x and y, and posterior predictive for y

Hi, Thanks for the links. However, neither thread talks about correlated input variables. That’s the main part I would like to tackle. How can one incorporate the uncertainties with this MvNormal construct? obs = pm.MvNormal("obs", μ, chol=chol, observed=observed_df) The observed argument here …

Is this a possible solution? The changes w.r.t. the above block of code are in the section immediately above the declaration of the likelihood. with pm.Model() as model: # Priors for unknown model parameters alpha = pm.Normal("alpha", mu=0, sigma=10) beta1 = pm.Normal("beta1", mu=0, si…

Aha, I see. Then more questions, sorry: Do you want to estimate the covariance of X1 and X2? Do you think the errors in X1 and X2 might also covary and you and want to estimate that too? Cheers, Jon

Thanks for the follow up. I just wanted to estimate the covariance of X1 and X2. However, I will be interested in knowing how to do the latter as well.

Hi again, Does anyone have any ideas on how to do this?

I think you’ll want your two betas to be MvNormals instead of Normals. There you can then specify a prior for the correlation between the two.

Multivariate Linear Regression with correlated input variables

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jonsedar May 5, 2021, 9:20am 2

Hi, a couple of previous threads that might help:

Errors-in-variables model in PyMC3 - #2 by chartl
Dealing with multivariate x, errors in both x and y, and posterior predictive for y

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Multivariate Linear Regression with correlated input variables

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