Estimation of covariance over variables in a regression model

#1

In Full information maximum likelihood estimation (FIML) of a regression with missing data one jointly estimates

  • the regression model parameters and
  • the covariance between variables involved in the regression plus some auxiliary variables.

Can this be done in brms?

Example:
I want to estimate the effect of E on O.
There is missingness in E, which depends on M. M is also a mediator between E and O.

To obtain an unbiased estimates for the effect of E I would like to estimate jointly the regression model O ~ E, while also imputing the missing data in O and estimating the covariances between O, E, and M.

Thanks in advance, Guido

PS: I can do this directly in Stan, but I am looking for a solution for people who don’t want to write a Stan program.

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#2

I don’t think you can do exactly what you are speaking about, but the vignette on missing values shows approaches that work with brms: 1) using linear predictor for missing data and 2) multiple imputation. For what it’s worth a linear predictor for missing values is probably very close to estimating covariance, maybe even identical if only one predictor contains missing data, but I didn’t check the math.

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