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I am wondering what are the advantages/disadvantages of breaking down a logistic regression in multiple steps, when they are available.

Let me explain what I mean by multiple steps: Think of it like the customer journey: A cold lead (A) becomes a prospect (B) who then becomes a customer (C).

A -> B -> C

I'm interested in predicting the conversion from A to C, which can be done with a logistic regression.

I wonder if I could also do two logistic regressions, first from A to B, then from B to C, and multiply the predictions.

What are the differences between the two approaches?

Things to consider:

  • What if the conversion rate from A to B is small? (Then the sample size for the 2nd model is small as well)
  • Where does most of the signal come from? Maybe my explanatory variables explain most of A to B but nothing of B to C, or the other way around.
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That sounds like a sequential logit to me. You can compute a "total" effect of explanatory variables on the finale outcome and decompose that into a weighted sum of the effect of that explanatory variable on each step/transition. See: http://dx.doi.org/10.1177/0049124115591014

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  • $\begingroup$ Also take a look at state transition models. $\endgroup$ – Frank Harrell Jul 7 '17 at 12:02

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