F-f-f-fake data

Tiago Fragoso writes:
Suppose I fit a two stage regression model
Y = a + bx + e
a = cw + d + e1
I could fit it all in one step by using MCMC for example (my model is more complicated than that, so I’ll have to …

Tiago Fragoso writes:

Suppose I fit a two stage regression model

Y = a + bx + e
a = cw + d + e1

I could fit it all in one step by using MCMC for example (my model is more complicated than that, so I’ll have to do it by MCMC). However, I could fit the first regression only using MCMC because those estimates are hard to obtain and perform the second regression using least squares or a separate MCMC.

So there’s an ‘one step’ inference based on doing it all at the same time and a ‘two step’ inference by fitting one and using the estimates on the further steps. What is gained or lost between both? Is anything done in this question?

My response…

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